Educational Perspectives - Lispl-Wicht/c-logo-s GitHub Wiki

cLogos intentionally distinguishes between the implementation of Logo and educational theories that help interpret its use.

Main Sections — elaborated so far

(The asterisk * references the current [sub]section under development.)

Introduction

Papert's constructionism is one of the most profound and influential interpretations of Logo. However, constructionism and Logo have distinct histories: Logo predates constructionism as a named educational theory, having originated within the work of the BBN team (1960s), while constructionism became a central theoretical framework for understanding Logo as a learning medium (1980s).

cLogos seeks to preserve the characteristics of Logo that have enabled such interpretations to emerge, without committing the language itself to a single pedagogical framework.

cLogos is not committed to one educational theory as the lens through which Logo must be understood. But educational theories are lenses through which Logo can be interpreted in complementary ways. Different lenses illuminate different aspects of the language. None of them exhausts it.

The same distinction applies here as elsewhere in cLogos: The relevant textbooks are specifications, not examples. In turn, learning theories are lenses, not implementations.

This page will gradually outline such lenses, starting from constructionism in Papert's own voice as the perspective most commonly associated with Logo.

Papert's Constructionism

From the abstract of Papert's 1986 proposal to the U.S. National Science Foundation "Constructionism: A New Opportunity For Elementary Science Education":

The word constructionism is a mnemonic for two aspects of the theory of science education underlying this proposal. From constructivist theories of psychology we take a view of learning as a reconstruction rather than as a transmission of knowledge. From a rich body of educational experience we take the view that learning is particularly effective when it is embedded in an activity the learner experiences as constructing a meaningful product (for example, a work of art, a functioning machine, a research report or a computer program.)

Papert's constructionism started as a theory of science education grounded in Piaget-inspired developmental constructivism and, in its practical orientation, informed by pragmatist ideas. From the proposal's Section 1.2.4:

Constructionism is a synthesis of the constructivist theory of developmental psychology [ See Bibliography, "Constructivism and Piaget, 1964, 1970, 1972, 1978 ] and the opportunities offered by technology to base education for science and mathematics on activities in which students work towards the construction of an intelligible entity rather than on the acquisition of knowledge and facts without a context in which they can be immediately used and understood.

A central feature of constructionism is that it goes beyond what is usually called "the cognitive" to include social and affective facets of mathematics and science education. This feature leads us to a new approach to understanding and penetrating educational barriers related to gender, to cultural factors prevalent in many American minority groups and to personality issues that are often classified as learning disabilities.

Our approach to affectivity is illustrated by a principle we call "appropriation", which places first priority on children making science their own. Much of our research is based on the working hypothesis that children (like anyone else) will learn science best if they use it. We do not mean by this that they can use it "when they grow up." We mean that they should be able to use it right now. And we do not mean that they use it only to perform activities imposed on them by teachers. We mean that they use it for purposes they experience as their own.

It is worth noting that the term constructionism has acquired different meanings in different disciplines. In educational theory, it is primarily associated with Papert's extension of Piagetian constructivism, emphasising learning through the construction of personally meaningful artefacts. In parts of psychology, sociology, and philosophy, however, constructionism (often discussed as social constructionism, and in some contexts related to social constructivism) refers to theories investigating how meaning, knowledge, and social reality are constituted through communication and social practices.

A further meaning appears in the foundations of mathematics. Mathematical constructivist traditions, such as Brouwer's intuitionism (1920s/30s), understand mathematical objects not as independently existing entities to be discovered, but as constructions generated through mathematical activity. This use of constructivism immediately concerns the epistemological foundations of mathematics rather than theories of learning or education. Nevertheless, it forms part of a broader historical background in which ideas of construction, activity, and the generation of knowledge have developed.

Although these traditions share an emphasis on construction rather than passive reception, they address different questions and should not be conflated. Therefore, throughout this page, Papert's constructionism is used as a precise attribution to distinguish this educational theory from other meanings associated with the term.

An oft-repeated anecdotal attribution to Piaget, apparently traceable to Thornburg (2013, p. 78), but without an identified primary source, portrays Papert as an exceptionally insightful interpreter and continuation of Piaget's work. However, Papert's own inspiring writing suggests a rather selective lens through which he considered the landscape of psychological and educational discourse of his time and before, as a mathematician at the MIT aiming to co-determine how the project of artificial intelligence would reshape the culture of learning and transform the institutions of education (Papert 1980, pp. 208-209). The following therefore intends to highlight certain regions of this landscape, providing additional perspectives that may enrich the set of analytic tools and make certain blind spots of observation visible.

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Cognitive Constructivism (Piaget)

Subsections:

Piaget developed his theory in close collaboration with colleagues and students, such as his later successor Inhelder, and Szemińska who conducted the experiment of the conservation of liquids Papert refers to in Mindstorms (Papert 1980, pp. 40-41).

Central to Piaget's theory from the 1930s is that learning involves the active construction of knowledge structures by the individual through interaction with the environment. Papert describes Piaget's position as recognising "children as builders of their own intellectual structures" which they acquire by "'Piagetian learning' or 'learning without being taught'" (p. 7). Papert posits that development of knowledge structures is dependant from the cultural material that surrounds the children (ibid.). He identifies them as "'objects-to-think-with', objects in which there is an intersection of cultural presence, embedded knowledge, and the possibility for personal identification", and asks how computational environments could provide new objects-to-think-with that reshape what kinds of reasoning become accessible (p. 11).

Piaget in turn investigated the development of cognitive structures and the conditions under which certain forms of reasoning emerge, and identified distinguishable developmental stages. Nonetheless, Piaget as well regarded development as "inter-individual relations" (Piaget 1995. Cited in: Lourenço 2012, p. 282).

The following table summarises Piaget's classical stage model; later research has questioned the strictness and universality of these boundaries.

Age Stage Thinking
0-2 Sensorimotor Object permanence
2-7 Preoperational Symbolic thought
7-11 Concrete Operational Logical thought
11+ Formal Operational Scientific reasoning

Also Papert assumed that the boundaries between these stages are less strict, particularly between the development of symbolic and logical thought, and scientific reasoning (Papert 1980, p. 21-22).

Typically, Piaget is summarised in a compatible way:

  1. Any child goes through the same stages at an individual rate.
  2. Later stages are not necessarily reached by every individual to the same extent.
  3. Biological maturation and environmental interaction determine child development.
  4. The child's thinking changes qualitatively in each stage.
  5. Each stage is characterised by a distinct type of intelligence.
  6. The children's cognitive development is an interplay of acquiring more information about the environment, and experiencing qualitative changes in thinking.

Piaget would have expected that mathematical reasoning could start to develop in the concrete operational stage. But it would be considered highly unusual if certain concepts would be acquired before the age of eleven.

For Papert, Logo provided new objects-to-think-with: computational objects that could make abstract ideas manipulable, inspectable, and personally meaningful (p. 22) and therefore become accessible at an earlier age enabling earlier transitions.

Piaget's theory is associated with four key factors:

  1. Biological maturation: the prerequisites of sensory and brain development influence the stage transitions.
  2. Interaction with the environment: engaging with the tangible surrounding world shapes the children's learning processes and understanding.
  3. Social experiences: interacting with the surrounding peers and adults provide further learning opportunities.
  4. Equilibration: the process of reaching a balance between new experiences and acquired knowledge that develops cognitive schemata.

The relative importance of individual construction and social mediation was seen as one of the central points of divergence between Piagetian and cultural-historical approaches.

But before these approaches are considered, Piagets influence beyond Papert should be contextualised a bit further.

Cognitive development (Bruner)

Another influential approach, developed from the 1960s onwards in dialogue with Piaget's work, is Jerome Bruner's theory of three modes of representation. Bruner proposed that human knowledge can be represented in complementary ways that become available successively during development while continuing to coexist throughout later learning.

Typical Age Mode Primary representation
0-1 Enactive Knowledge through physical action
1-4 Iconic Knowledge organised in sensory images
4-7 Symbolic Knowledge organised in symbol systems such as language

Unlike Piaget's developmental stages, Bruner's modes are not mutually exclusive. Once acquired, enactive, iconic, and symbolic representations remain available and may complement one another throughout life. Learning therefore need not rely on verbal explanation alone but may combine action, visual representation, and symbolic reasoning in ways that support discovery learning: learning through active exploration, problem-solving, and the learner's own construction of meaning.

Bruner's work already supports Papert's conviction that abstract thinking can become accessible earlier than Piaget's stage theory might suggest. For Papert, programming environments such as Logo provide opportunities to move continuously between acting, seeing, and symbolic description. In this sense, Logo becomes a medium in which enactive, iconic, and symbolic representations interact rather than remaining separate.

Papert appreciated Bruner's emphasis on multiple forms of representation, but argued that the distinction between these modes still remained too strongly centred on language. He suggested that knowledge always contains aspects that can be verbalised as well as aspects that resist verbal description while nevertheless remaining communicable through activity and shared practice (Papert 1980, p. 96). To illustrate this point, Papert contrasts two programming tasks whose development involves intertwined enactive, iconic, and symbolic processes rather than a simple progression from one representation to another (pp. 100–113).

Radical constructivism (von Glasersfeld)

The position that learning involves the active construction of knowledge structures by the individual inspired further interpretations with particular emphasis on the processes of "assimilation and accomodation" through which cognitive structures are continually reorganised in response to experience (von Glasersfeld 2014, p.96).

In critical engagement with Piaget and in combination with cybernetics views, von Glasersfeld published his conclusion in 1974 that learning is solely based on hypotheses about the world that we cannot experience immediately. Any individual constructs individual cognitive structures that are locally adjusted during equilibration when the schemata do not match concrete experiences.

Learning theories inspired by radical constructivism fundamentally question transmissive conceptions of teaching. If knowledge cannot simply be transferred from one mind to another, the educational task shifts from transmitting knowledge to creating situations in which learners can construct viable understandings for themselves. This raises important questions about how learning environments should be designed, how teachers can provide meaningful learning opportunities, and how shared understanding can emerge despite individually constructed knowledge.

"Moderate" Constructivism

Particularly in German mathematics education, since the 1980/90s a position often described as moderate constructivism emerged in response to the stronger epistemological conclusions of radical constructivism. Like Piagetian and radical constructivist approaches, it understands learning as an active process in which learners construct cognitive structures for themselves. Unlike radical constructivism, however, it assigns a more explicit role to teaching: didactic processes, carefully designed tasks, and instructional scaffolding are regarded as possible meaningful means of supporting this constructive development.

A compatible perspective, drawing on Luhmann's systems theory—which itself owes much to cybernetics—describes the relationship between learner, content, and teacher as an interactional field between the structure of appropriation, the structure of the subject matter, and the structure of mediation (another description of the didactic triangle). Within this view, communication breakdowns may contribute to learning difficulties. Conversely, productive co-constructive communication remains possible.

Related approaches in mathematics and science education

The concept of guided re-invention introduced by Freudenthal during the 1960s and 1970s in the Netherlands can be interpreted in terms of Bruner's discovery learning although it is closer to a tradition leading back to conceptions of Klein and Toeplitz from the 1920s and 1930s about the (historic) genetic method—a pedagogical approach that seeks to reconstruct the genesis of mathematical ideas within the learner rather than merely presenting their finished form.

A closely related concept of genetic learning introduced by Wagenschein in Germany during the 1950s onwards was developed in the same tradition but explicitly engaging with Piaget and with a focus on science education, also influenced by Banholzer's dissertation (1936) on children's questions in physics education in the light of Piaget's work.

During the 1970s, eventually the concept of basic notions ("Grundvorstellungen") became influential in German mathematics education as well in dialogue with Piaget's as with Bruner's work, utilising the learners' development of viable cognitive schemata (= basic notions) that support movement between enactive, iconic, and symbolic representations through processes of equilibration.—The engagement with Bruner is mirrored by the terminological blurring with Bruner's basic ideas, and fundamental ideas which refer to different concepts. (Also a topic's core idea, and a student's initial idea or preconception are distinct terms.)

These traditions developed largely independently of Papert's work and are rarely discussed alongside constructionism in the Logo literature. Whether or not these traditions directly influenced one another, they offer complementary perspectives on Logo as implemented in cLogos, connecting its central object of inquiry with broader traditions in mathematics and science education.

This section remains open to parallel approaches from different educational traditions.

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Experiential learning (Dewey)

Notice: Quotations in this section have occasionally been adapted by replacing singular masculine generics with equivalent plural constructions where this improves readability. Such editorial changes do not alter the meaning of the cited passages and are indicated where appropriate.

Papert ended his article in The Washington Post Education Review Sunday, October 27, 1996 with this reference to Dewey:

It is 100 years since John Dewey began arguing for the kind of change that would move schools away from authoritarian classrooms with abstract notions to environments in which learning is achieved through experimentation, practice and exposure to the real world. I, for one, believe the computer makes Dewey’s vision far more accessible epistemologically. It also makes it politically more likely to happen, for where Dewey had nothing but philosophical arguments, the present day movement for change has an army of agents. The ultimate pressure for the change will be child power.

In a footnote of Mindstorms he remarked:

People have lived with children for a long time. The fact that we had to wait for Piaget to tell us how children think and what we all forget about our thinking as children is so remarkable that it suggests a Freudian model of "cognitive repression." (Papert 1980, p. 41)

However, Dewey's work is such a close ally to Papert's work and his Constructionism framework that it is worthwhile to make the relation explicit which already the first part of Dewey's "How We Think" unveils—written as early as 1910.

Dewey (born in 1859) developed his educational philosophy influenced by Darwin's evolution theory, as Piaget (born in 1896) did develop his theory of psychologic development. Like Piaget's later work, Dewey's research crossed the boundaries of philosophy, psychology, and education. His philosophical reflections emerged not primarily from abstract speculation but from sustained engagement with educational practice, most notably through the The Laboratory School at the University of Chicago from 1894 to 1903. In this respect, Dewey already exemplifies the reflective integration of theory and practice that would later characterise much of educational constructivism.

There is another connection to the lineage that ultimately lead to Constructionism: Wiener—who termed the foundational discipline of self-regulatory systems as "Cybernetics" that also was an important starting point of later computer science—was deeply influenced by Dewey's philosophy.

These historical connections are only the visible traces of deeper conceptual intersections of compatible approaches that might most likely cross-fertilise, by asking slightly different questions to the same problem.

Dewey identifies the problem of education as how to discover

the forms of activity a) which are most congenial, best adapted to the immature stage of development; b) which have the most ulterior promise as preparation for the social responsibilities of adult life; and c) which, at the same time, have the maximum of influence in forming habits of acute observation and of consecutive inference. (Dewey 1910, p. 44)

This is highly compatible with Papert's notion of designing and cultivating objects-to-think-with. As he furthermore claims that "the educator must be an anthropologist" (Papert 1980, p. 32), Dewey already characterises the teachers' problem as the need of being

[students] of individual traits and habits; on the other side, [they need] to be [students] of the conditions that modify for better or worse the directions in which individual powers habitually express themselves. (Dewey 1910, p. 46)

Because:

... the [teachers need] an insight into existing habits and tendencies, the natural resources with which [they have] to ally [themselves]. (p. 30)

Dewey recognises a spectrum of naturalistically oriented educational theories, contrasting rationalistically oriented theories (pp. 58-59). At the extreme ends of this spectrum, training of thought becomes ineffective.

Both extreme positions reject the capability of logical thinking in children's minds. But they draw opposing conclusions:

  • While both agree that "the 'logical' is ... wholly artificial and extraneous", the one-eyed naturalists will reject any emphasis on logical thought, and solely "work towards the expression of existing aptitudes and tastes" (p. 61).
    The excessive rationalists, in turn, insist in material that covers "certain steps arranged in a certain order, which expresses preëminently an understanding of the subject, and the [pupils are] made to 'analyze' [their] procedure into these steps" (p. 60).
  • These naturalists tend to believe "in the almost magical educative efficacy of any kind of activity, granted it is an activity and not a passive absorption of academic and theoretical material" (pp. 43-44). Those rationalists "neglect activities almost entirely", if they don't admit to them as "a ... concession to the necessity of having occasional relief, or to the ... outside utilitarian demands upon the school" (p. 43).
  • The former understand discipline "as a painfully disagreeable forcing of mind from channels congenial to it into channels of constraint" and regard freedom as undirected self-expression (pp. 58-59), that should remain undisturbed from any obstacles (p. 65). The latter agree with the painful forcing yet consider it "as [necessary] preparation for a more or less remote future" and "then regard [discipline] as drill" (p. 64).

The naturalistic orientation may be identified approximately with what is often described as "learner-centred progressive" or "reform" pedagogy, while the rationalistic orientation approximates what may commonly be described as "teacher-centred conservative", often "authoritarian" pedagogy.[1] These expressions are used only as heuristic points of orientation and should not be understood as synonymous with the more fundamental distinction between naturalistic and rationalistic educational orientations.

Both orientations represent characteristic attempts to address enduring educational problems. Although Dewey is commonly regarded as a progressive educator, his educational philosophy can also be understood as an attempt to transcend this opposition. Rather than rejecting either orientation outright, his model of reflective thinking integrates concerns for the learners' activity with the careful guidance and organisation required for the development of thought.

Thus the problem of education can also be restated as

How to recognise and cultivate the logic already immanent in the learners' activity without either abandoning it to mere spontaneity, or replacing it by external organisation?

Because "drill" methods "in fact restrict and deaden intellectual activity" but also unreflected "direct immediate discharge or expression of an impulsive tendency is fatal to thinking" (pp. 63-64). Therefore Dewey concludes that "any teacher who is alive to the modes of thought naturally operative in the experience of the normal child will have no difficulty in avoiding" these extremes (p. 62).

Such a teacher will have no difficulty in seeing that the real problem of intellectual education is the transformation of natural powers into expert, tested powers: the transformation of more or less casual curiosity and sporadic suggestion into attitudes of alert, cautious, and thorough inquiry. He will see that the psychological and the logical, instead of being opposed to each other (or even independent of each other), are connected as the earlier and the later stages in one continuous process of normal growth. (ibid.)

Dewey's discussion suggests that Piaget entered an already ongoing conversation concerning the development of thought, one in which education and psychology had long been closely intertwined:

Only by making the most of the thought-factor, already active in the experiences of childhood, is there any promise or warrant for the emergence of superior reflective power at adolescence, or at any later period. (p. 66)

Thus:

Adolescence is not ... a synonym for magic. [... childhood is [not] almost entirely unreflective—a period of mere sensory, motor, and memory development while adolescence suddenly brings the manifestation of thought and reason.] Doubtless youth should bring with it an enlargement of the horizon of childhood, a susceptibility to larger concerns and issues, a more generous and a more general standpoint toward nature and social life (p. 65).

This development affords an opportunity for thinking of a more comprehensive and abstract type then previously obtained. [But] thinking itself remains just what it has been all the time: a matter of following up and testing conclusions suggested by the facts and events of life. Thinking begins as soon as the [babies] who lost [their] ball that [they are] playing with begin to foresee the possibility of something not yet existing—its recovery; and begin to forecast steps toward the realization of this possibility, and, by experimentation, to guide [their] acts by [their] ideas and thereby also test the ideas (p. 66).

This is remarkably close to the educational orientation later developed by Papert within his constructionist framework, and the foundation of an educational framework in its own right which can support the design of learning opportunities through Logo.

Seen in this light, Dewey's educational philosophy offers more than historical context. It also provides concrete design heuristics for educational technologies whose purpose is to support reflective inquiry. Several of Dewey's observations directly illuminate design decisions made in cLogos:

The difficulties that present themselves within the development of an experience, are, however, to be cherished by the educator, not minimized, for they are the natural stimuli to reflective inquiry. (pp. 64-65)

Likewise, the cLogos Charter states that "cLogos is not trying to make programming easier." Further Dewey's "transformation of natural powers into expert, tested powers" describes an educational movement that is mirrored in the Charter as the implementation "is trying to make structural thinking expressible at the level at which it is already being formed in the learner’s mind."

This also mirrors the so-called, Piaget-informed "Papert's principle":

Some of the most crucial steps in mental growth are based not simply on acquiring new skills, but on acquiring new administrative ways to use what one already knows. (Minsky 1988, p. 102)

Together with Dewey's remark about instruments

All forms of artificial apparatus are intentionally designed modifications of natural things in order that they may serve better than in their natural estate to indicate the hidden, the absent, and the remote. (p. 16)

a design heuristic can be derived in the light of today's challenges from applications of generative AI:

Educational technology should make thinking more accessible without making the learner's thinking disappear.

The question is therefore not what a tool can do instead of the learner, but what it enables the learner to notice, express, and discuss. Thus an equivalent formulation of the principle could also be:

A good educational technology does not replace thinking. It shifts thinking to places where it becomes more visible, discussable, and open to reflection.

This also explains the extension discipline made contractual in Section 7 of the cLogos Charter:

Logo is a medium for thinking, and cLogos must preserve the conditions under which that thinking remains valid.

Another aspect of Dewey's educational philosophy naturally leads towards the cultural-historical theories that follow. While How We Think primarily develops an account of reflective inquiry in the individual, Dewey's broader educational philosophy increasingly situates learning within social life and shared activity.

In Democracy and Education (1922), Dewey discusses the spectrum of educational ideas inherited from the eighteenth century, giving particular attention to Rousseau and his influential thought experiment Émile (Dewey 1922, pp. 106-108). Rousseau's educational ideal can be understood as a response to the political and social conditions of his time, envisioning an educational relationship in which a single mentor carefully arranges a single learner's experiences while shielding the child from the corrupting influences of society. Whether or not one accepts Dewey's historical interpretation in every detail, his central observation remains instructive: such a model necessarily assigns only a limited role to the social processes through which meaning itself is constituted.

Dewey, by contrast, gradually develops an educational philosophy in which communication, participation, and shared inquiry become constitutive of learning itself. His conception of education as a democratic form of associated living (p. 100) therefore provides a natural bridge towards cultural-historical theories, which investigates learning not merely as an individual cognitive process but as a socially mediated activity. The following section therefore examines how this social dimension became the central object of inquiry within the cultural-historical tradition.

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Cultural-historical (Activity) Theories (Vygotsky/Luria/Leontiev/Engeström)

Subsections:

Naturalistically oriented educators and rationalistically oriented educators agree in their extremes to the extent that the child's mind initially provides no capacity for logical thinking. Their disagreement lies in their assumptions how the learner acquires logical thinking. The one-eyed naturalists see it emerging instantly from years of spontaneous self-expression and unguided play in an environment with a variety of learning opportunities independently chosen by the learners. The excessive rationalists see logical thinking as something that can be cultivated primarily through highly structured external guidance. Despite their opposition, both positions may be understood as sharing a Cartesian inheritance. They can be interpreted as reifying what is fundamentally an analytic distinction: temporarily isolating one aspect of a complex system for purposes of investigation.

It is this movement which became prominent in European thinking since Descartes' philosophical work was giving one of the most influential formulations of the mind-body-problem as a dualism—that "I think, therefore I am" can be considered an analytic separation of body and mind: even if one may doubt the own senses, starting from the certainty of the own thought stands beyond, forming self-consciousness and identity of the mind (Descartes 1901, p. 11). Elevating this analytic means to a dominant mindset of Cartesianism in European philosophy and science is sometimes termed as "Western ways of knowing" (Gutiérrez et al. 2024, p. 759).

However, this -Ism is not undisputed also in European—and European-derived thinking, and the "West" is a brittle category on the terrestrial globe.[2] Considered in the light of the Cartesian coordinate system—another instrument that was advertised by Descartes as a mathematician—this separation can already be dissolved tangibly, with the body and the mind understood as its orthogonal axes: examining the body alone takes place on one axis, investigating the mind occurs on the other. The holistic consideraration of body and mind as synthesis expands as the graph of their correlation. Rejecting this correlation eventually yields the form of reductionism, that is evidenced in the extreme forms of naturalism and rationalism in education as described by Dewey.

Against this background, Vygotsky's project can be understood as addressing precisely this reduction in the discipline of psychology: "it is a mistake to study psychological functions individually, e.g., to study development of memory or development of perception" (Vasileva/Balyasnikova 2019, p. 5).

Within this current of developmental psychology, the social aspect of learning was in focus, shedding light on the interactional effects of learners instead of circling around the individual. In the following, Vygotsky's work is considered through informed sources, which contextualise his work, also in relation to Piaget. Subsequently, Engeström's expansion of Leontiev's[3] Activity Theory—in itself "a departure from Vygotsky's own ideas" (Vasileva/Balyasnikova 2019, p. 5)—is addressed, as well as the influence of the "cultural-historical approach" on German inclusive education. The discussion adds a further layer to the conversation with Papert's constructionism and to the design reasoning of cLogos.

Vygotsky's circle

Subsection:

Vygotsky was born in the same year as Piaget (1896), but died prematurely from tuberculosis in the Soviet Union in 1934. Two years later, Piaget published La naissance de l'intelligence chez l'enfant (The Origins of Intelligence in Children) in Switzerland, one of the landmark works in a research programme that he would continue to develop for several more decades.

During the last years of his life, from 1929 onwards, Vygotsky increasingly devoted himself to theoretical work, knowing that his illness severely limited the time available to him. Much of this work remained unfinished and was intended to be continued and empirically elaborated by his collaborators rather than prepared for publication by Vygotsky himself (Vasileva/Balyasnikova 2019, p. 3). Consequently, today's understanding of Vygotsky is mediated to a remarkable extent through later editors, collaborators, translators, and interpreters, each inevitably interpreting his manuscripts through the conceptual frameworks of their own research interests and scientific traditions (p. 2).

Therefore the "Troika," or the "Big Three" of Vygotsky's lifetime—himself, Luria (born 1903), and Leontiev (born 1902), and their "first generation student's" forming the "Big Five" as the "core of the so-called Vygotskian Circle" (p. 4), may be understood as the historical nucleus of a wider circle that continues through ongoing critical engagement with Vygotsky's legacy. The term "circle" therefore refers not only to the historical group surrounding Vygotsky, but also to the continuing dialogue through which his unfinished theoretical project has been interpreted, extended, criticised, and transformed.

Vygotsky's research programme developed within the political system of the Soviet Union established during the October Revolution of 1917. His particular interest in the development of the children's mind was shaped by the demands of the expanding educational system to form masses of undereducated children from precarious circumstances to productive members of the "new socialist society" (pp. 3-4).

His network of like-minded researchers opposed reductionist psychological views that attempted to explain complex psychological phenomena through isolated biological mechanisms, such as the localisation of specific functions in particular brain structures (p. 7). Today, nativism is seen as contrasting the Vygotskian view in psychology, "postulating that psychological abilities are largely innate or pre-formed" (p. 6).

Such approaches share with the extreme naturalist and rationalist educational positions a Cartesian inheritance insofar as they reify analytical distinctions between components of a complex developmental system. Perhaps they also support each other: when either logical thinking is assumed to emerge automatically after years of playful exploration, or to be installed through meticulously pre-structured material, both positions risk conceiving development as a quantitative accumulation that eventually enables already-existing cognitive capacities to unfold—the kind of maturation-oriented increase expected by nativist accounts. (ibid.).

By contrast, Vygotsky's "systemic approach to the development of mind" identifies the object of research as "psychological systems" instead of "individual functions," systems constituted by "interdependent elements" of which none "can be changed without affecting the whole system" (p. 5). A notion of quantitatively accumulated development is rejected, instead "the human mind becomes qualitatively different [from animal cognition] once it becomes semiotically mediated" (ibid.). In this framework, the animal cognition is distributed among "lower psychological functions (LPF) ... such as memory and concept formation," while the semiotically mediated processes constitute "higher psychological functions (HPF)", through which originally natural processes become reorganised into culturally mediated forms, including "decision-making, speech and language, and cultural transmission of knowledge" (p. 6). Vygotsky assumed that "initially isolated LPF merge with developmentally older HPF" during individual development, which yields new components in the mental system that modify both the system's state and "the properties of the component" (ibid.).

Again, "Papert's principle" finds another point of contact:

a mind cannot really grow very much merely by accumulating knowledge. It must also develop better ways to use what it already knows. (Minsky 1988, p. 102)

Vygotsky's conception suggests a gradual development of mind, but with a more flexible notion of developmental stages: stages of qualitatively different functional systems rather than fixed age-related states—enabling the investigation "which aspects of ability X change as they enter other functional systems, to what extend do they change, and under what environmental influences" (ibid.).

Here, the concept of the Zone of Proximal Development (ZPD) becomes relevant (originally: зона ближайшего развития, spoken: "zona blizhaysheva razvitiya" = zone of the nearest development), perhaps the most prominent term from Vygotsky's framework. The conventional formulation introduces two further levels: the Actual Level of Development (ALD) and the Potential Level of Development (PLD). The ALD designates the current state of matured problem-solving skills in a young learner's mind, assessed "with the help of independently solved tasks" (Lantolf 2020 cited in: Qin 2022, p. 139). The PLD, in turn, denotes the level of performance that becomes accessible through "tasks solved by the child under adult guidance" or collaboration "with more capable peers"; the ZPD is constituted by the distance between this potential level and the ALD (ibid.; Podolskiy 2012 in: Seel (Ed.), Encyclopedia of the Sciences of Learning , p. 3485).

It has therefore been argued that the ZPD is more convincingly interpreted as a relational concept, which concerns "the interaction between students, and between the students and their teacher" rather then an absolute state located within an individual learner's mind (Radford 2010, p. 3). This is in line with Vygotsky's thinking which "highlights the agency of various learners and the ... child's interaction with the environment" where the "role of the teacher ... is to sustain this interaction and not simply relay decontextualized knowledge" (Vasileva/Balyasnikova 2019, p. 10)—a position remarkably consistent with Dewey's view that the educator's task is to organise conditions under which reflective inquiry can emerge. However, another interpretation of the ZPD is being an individual learner's set of "functions that are not yet mature but are already in the process of maturation" (Qin 2022, p. 140)—an interpretation which overlaps with the concept of the PLD (see also Allal/Pelgrims Ducrey 2000).

Vygotsky's empirical research deliberately took place within the cultural-developmental context of the learners, their "socio-cultural semiotic environment" (p. 9)—which, in turn, "should be studied not in absolute terms as is, but in relation to a child" whose experiences differ according to individual circumstances such as age, family background etc. (p. 11). This aligns with Papert's conviction of the influence of the cultural material that surrounds the children.

In contrast to Papert—but in alignment with Bruner, who wrote the introduction to the English translation of Vygotsky's Thought and Language in the 1960s, published by MIT press—language was central to Vygotsky's developmental research from his position that language mediates human psychological processes semiotically (p. 9). As Vasileva and Balyasnikova point out, Bruner's decision to use "image" for Russian знак ("znak") instead of the more obvious "sign" might have influenced interpretations of Vygotsky's thinking outside its original context (p. 3). If "a linguistic sign (a word)" is understood as a cultural tool, closely related to the behaviour of a developing organism and comparable to the physical tools children employ in joint activity with others as they develop (p. 9), then the conceptual distance between Vygotsky and Papert becomes considerably smaller. Under this interpretation, Vygotsky's account aligns not only with Papert's emphasis on powerful cultural artefacts, but also with Dewey's understanding of inquiry as mediated by instruments. This understanding of signs as cultural tools leads directly to Luria's neuropsychological perspective, in which complex functional systems "do not mature by themselves but are formed in the process of communication and material activity of a child" (Luria 1969, p. 34; cited in Vasileva/Balyasnikova 2019, p. 7).

According to Vygotsky, language is established within the social dimension, where "speech develops first ... and later becomes internalized into mental processes" (p. 9). The crucial intertwining of "thought and speech" around the age of two constitutes the emergence of inner speech (p. 10). Within the ZPD, capacities represented by the PLD are transformed into independent abilities at the ALD through interpsychological activities between interacting individuals, which later become intrapsychological processes within the child's individual thinking (p. 9). Understanding learning as "a step ahead" of development, emerging while a child is "completing a challenging task with the help of a teacher or peers" (p. 10), allows connections to Bandura's Theory of Self-efficacy.

The environment of sign and language, in which these processes take place, is understood by Vygotsky as culture. Linguistic signs are "internalized human-specific cultural tools" (p. 11) through which humans coordinate socially constructed meanings and develop internal psychological processes (p. 9)—which reveals a conceptual affinity between Vygotsky's account and Blumer's Symbolic Interactionism. This perspective also offers another lens through which Cynthia Solomon's reflections on the distinctive "computer culture" at MIT may be understood, particularly her emphasis on its educational significance for learning programming with Logo (Solomon in: Solomon et al. 2020, pp. 10-13, 34-35).

As well Piaget's work can fruitfully be read in dialogue with Vygotsky, shown by numerous attempts to point out differences, similarities, and overlaps of both research programmes (Lourenço 2012, pp. 281-284). They share the developmental, non-reductionist, non-dualistic, procedural perspective, emphasise action as crucial for cognitive development and "focus ... the qualitative changes over quantitative ones" (p. 282). Both approaches are considered dialectic in their common emphasis on qualitative developmental changes, thus Piagets concept of assimilation/accomodation is seen as closely aligned with Vygotsky's successive "internalizations/externalizations" (p. 283). Also the priorly assumed difference of an "individualistic-collectivist" opposition of Piaget and Vygotsky could be refuted by Piaget's explicit emphasis on "inter-individual relations" in development (p. 282).

However, Lourenço interprets this difference as a contrast between Piaget's orientation toward "an autonomous subject when she confronts the physical ..., and the social world" whose responsibilty for "all his or her actions, operations, and social interactions" follows the subject's equilibration—and Vygotsky's emphasis on a subject whose higher psychological functions initially emerge through externally mediated activity (p. 284). This adds a layer of moral reasoning inherent to Piaget's framework, elaborated in his book Le jugement moral chez l’enfant from 1932 (The judgement of the child) (p. 284). However, questions about the initial development of moral distinctions are considered "meaningless in a systemic perspective"—instead the qualitative changes by taking account of the environmental influences become relevant (Vasileva/Balyasnikova 2019, p. 6). To what extent these orientations might be understandable by the ethical frameworks Piaget and Vygotsky committed (Lourenço 2012, pp. 284-285) may remain undecided. The claim shows at least the complementary quality of both approaches that might appear as a fruitful sustaining tension.

An application with Logo

A Vygotsky-informed position of the use of Logo in cooperative learning arrangements was contrasted with Papert's assumption, that already translating an intuition into a program increases the accessibility to reflection (Mevarech/Kramarski 1993, p. 99). Papert's full assumption from Mindstorms is as follows:

I see the computer as helping in two ways. First, the computer allows, or obliges, the child to externalize intuitive expectations. When the intuition is translated into a program it becomes more obtrusive and more accessible to reflection. Second, computational ideas can be taken up as materials for the work of remodeling intuitive knowledge. (Papert 1980, p. 145)

The assumption is illustrated in Mindstorms with a problem to solve with Logo in Turtle Talk. For their study on the effects of differently designed Logo learning arrangements regarding creativity and social relationships, Mevarech and Kramarski concluded, that Papert's assumption supports the view of

Logo, by its very nature, increases cognisance processes and creates a situation of shared expertise where the computer is the expert and the student is the novice. ... According to this approach, it is the computer, rather than a peer or adult, which constructs the zone of proximal development. (Mevarech/Kramarski 1993, p. 99)

This interpretation shifts the locus of guidance from the social relation between learners to the interaction between learner and computational environment. On the one hand, this might be contrary to what Papert had in mind:

In many schools today, the phrase "computer-aided instruction" means making the computer teach the child. One might say the computer is being used to program the child. In my vision, the child programs the computer and, in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building. (Papert 1980, p. 5)

Still, within a Vygotskyan framework, Papert's assumption may have the consequence concluded by Mevarech and Kremarski. Yet it is also possible, that their interpretation of the ZPD differs slightly from the interpretation suggested by Radford, which focuses the co-constructive relation between the child and the computer, as well as between child, adult or more competent peer, and other peers, rather than understanding the expert as the ZPD's sole constructor. Furthermore, within this interpretation, the computer remains part of the socio-cultural environment as tool, not as participant. From this perspective, the computer may transform the conditions under which the ZPD emerges without itself becoming one of the interacting subjects constituting it. Papert's vision is not necessarily incompatible with this relational notion of the ZPD.

These theoretical nuances do not diminish the methodological value of the study. Rather, the study provides an exemplary design for comparing cooperative and individual Logo-based computer-aided learning (CAL) environments with non-CAL control conditions within the ordinary context of schooling—90 minutes per week over the course of an academic year. Here, CAL denotes open learning environments that support exploration and problem solving, in contrast to computer-aided instruction (CAI), where the computer primarily presents predefined tasks together with evaluative feedback (Clements/Nastasi 1985, p. 17).[4]

Together with a parallel study designed to examine possible effects on participants' creativity and interpersonal relationships in a problem-solving-oriented Logo learning environment, an instructive Logo programming class termed "Guided-Logo environment," and a non-computer-aided mathematics class (Mevarech/Kramarski 1992), Mevarech and Kramarski presented results—despite methodological constraints (p. 107; Mevarech/Kramarski 1993, p. 273)—suggesting significant differences between the cooperative, problem-oriented learning environments, the individualised instructive environments, and the control groups. Overall, the cooperative, problem-oriented groups showed the most favourable outcomes among the compared arrangements.

(Further research on Logo-based learning environments, including studies addressing their social dimensions from 1985 onwards, is reviewed by Clements and Sarama (1997, p. 25--28).)

Engeström's activity theory

Subsections:

Engeström's activity theory is situated within what he describes as the third generation of Cultural-Historical Activity Theory (CHAT), succeeding Leontiev's second generation, which itself developed from the first generation originating in Vygotsky's work (Burner/Svendsen 2025, pp. 315-319; Engeström, 2001, pp. 134-135).

Here, another advanced definition of the ZPD is applied, also understood as a "Third Space" constituted by "discursive spaces" (Gutierrez et al. 1999, pp. 286-287). Engeström reinterprets the concept of the ZPD from individual development towards collective transformation of activity systems:

It is the distance between the present everyday actions of the individuals and the historically new form of the societal activity that can be collectively generated as a solution to the double bind potentially embedded in the everyday actions. (Engeström 1987, p. 174; cited in: Engeström 2001, p. 137).

This definition already contains two terms of Leontiev's Activity Theory: action and activity. His third distinction was that of the operation (Burner/Svendsen 2025, p. 317). These analytic distinctions extend Vygotsky's account of mediated action (p. 316) by differentiating the structure of purposeful human practice, while retaining semiotic mediation as the central explanatory principle.

Focusing "the object and motive", as Leontiev suggested (p. 317), clarifies that the term "object" does not primarily denote the opposite of "subject" in this framework. Instead, the "object is the goal of the activity" (p. 318), which is the "response" in Vygotsky's "basic triangle" on which the subject cannot act directly (p. 316). In this sense, "object-oriented theory" (p. 314) refers to the shared object toward which an activity is directed, rather than to the philosophical subject-object distinction or the programming paradigm of object-oriented programming.[5] Engeström characterises this shift in the understanding of objects between Piagetian and cultural-historical perspectives as follows:

This meant that objects ceased to be just raw material for the formation of logical operations in the subject as they were for Piaget. Objects became cultural entities and the object-orientedness of action became the key to understanding human psyche. (Engeström 2001, p. 134)

Papert's constructivist framing shares important affinities with cultural-historical perspectives, although he articulated these primarily through Piagetian concepts.

The relation between subject, object, mediating tool, action, operation, and activity may be illustrated through a simple Logo programming activity (following the structure of the example of shifting gears, Burner/Svendsen 2025 p. 317), where the Logo environment functions as the mediating tool.

When a learner enters a complete Logo instruction at the Logo prompt ?, such as:

? show 2 + 3

or equivalently

? show sum 2 3

the composition of the procedure sum with the procedure show is the action of asking Logo to display the value which sum outputs to show by using its inputs 2 and 3. As the learner becomes fluent in composing complete Logo instructions, consciously combining procedures gradually ceases to require deliberate planning. Under stable conditions, what initially demanded conscious action becomes routinised operation. Thus the activity of programming in Logo—whose object is to learn by teaching the computer to carry out tasks—"is realized through actions" (ibid.).

Terminological caveat. Activity Theory and Logo both employ the terms 'action' and 'operation', but assign them different meanings. Within Logo, an operation is a procedure that outputs a value, whereas an action (or command) produces an observable effect (see here). In Activity Theory, by contrast, action and operation denote different analytical levels of human activity. Consequently, analyses of Logo programming informed by Activity Theory require careful separation between the conceptual vocabulary used to describe the learners' activity and the technical vocabulary of the programming language itself.

The third generation of activity theory emerged in response to tensions that highlighted the need for cross-cultural research, which had remained comparatively underdeveloped in earlier generations of the cultural-historical approach (Burner/Svendsen 2025, p. 318; Vasileva/Balyasnikove 2019 pp. 8-9; Engeström 2001, pp. 135-136).

Engeström started with "graphically" expanding Vygotsky's "basic triangle" as the "tip of the iceberg"—in "its common reformulation" (Engeström 2001, pp. 134):

Vygotsky's "basic triangle"

The first theoretical shift was already accomplished before Engeström, by turning Vygotsky's triangle "upside down" (Burner/Svendsen 2025, p. 318), and replacing the edges of the undirected graph with bidirectional arrows, each drawn through. Whereas Vygotsky's original diagram emphasises that subject S and response R are connected only through mediation by X, the common reinterpretation therefore visually suggests direct relations between all nodes.

This triangle represents individual actions interrelated with underlying group actions, together "embedded in a collective activity system", hence applying Leontiev's framework (p. 134-135):

Engeström's activity system

The placement of "Mediating artifacts" in the expanded activity system diagram appears somewhat ambiguous, as artefacts function not as an independent element comparable to object, rules, or community, but as mediational means through which subjects orient themselves toward objects.[6] Yet apart from that, this extended graph enables several observations. The oval depicting the object is supposed to indicate, that "object-oriented actions are always, explicitly or implicitly, characterized by ambiguity, surprise, interpretation, sense making, and potential for change" (p. 134). Beyond that, the subject, the community, and the object are mutually related with all nodes of the system. Therefore, each represents a point of intersection among five relations within the whole system, whereas mediating artefacts (or tools and signs), rules, and division of labour appear as structural conditions of the activity system, connecting three edges. So this advanced triangle communicates: the activity system is not merely a collection of external constraints around an individual; subject, object, and community are mutually constituted within a shared activity.

This regular triangular visualisation enables certain forms of modelling interacting activity systems. However, an alternative visualisation—created with Graphviz from this source—that recalls Vygotsky's emphasis on mediation may instead highlight the activity system as a network of relations, or even as a relational space, thereby opening different analytical perspectives.

Activity system graph

Such a heuristic attempt to capture the relations may at first foster a topological view, as another conceptual instrument for creatively exploring the changing foci on the space. Such experimentation—changing directions, adjusting emphasis, or adding further activity systems whose objects intersect—may reveal additional interpretive layers.

Canonically, the interaction of at least two interacting activity systems is represented in triangular form (p. 136).

Engeström's minimal model of interacting activity systems

Here, in a context of applying the activity theory in an intervention study in the field of medical child care

the object moves from an initial state of unreflected, situationally given 'raw material' (object 1; e.g., a specific patient entering a physician's office) to a collectively meaningful object constructed by the activity system (object 2, e.g., the patient constructed as a specimen of a biomedical disease category and thus an instantiation of the general object of illness/health), and to potentially shared or jointly constructed object (object 3, e.g., a collaboratively constructed understanding of the patient's life situation and care plan). (ibid.)

This clear representation emphasises the points of contact in an elegantly structured diagrammatic way. A Graphviz representation may dynamically yield surprising visual cues by rearranging the connected graphs with each added node and edge. This alternative perspective does not replace the canonical representation. Rather, it may support different analytical conjectures by foregrounding relational structure instead of triangular decomposition.

Engeström summarises the third generation of Activity Theory in five interrelated principles: (p. 136-137):

  1. The prime unit of analysis is "a collective, artifact-mediated and object-oriented activity system, seen in its network relations to other activity systems." Notice: As the graph representation suggests, internally an activity system is also a network of relations, which is made explicit through the second principle.

  2. Activity systems are multi-voiced. They are always communities "of multiple point of views, traditions and interests. The division of labor in an activity creates different positions for the participants, the participants carry their own histories, and the activity system itself carries multiple layers and strands of history engraved in its artifacts, rules and conventions." This implies tension that supports conflicts and also innovations.

  3. Activity systems have a vivid history—as consequence of the second principle. "Activity systems take shape and get transformed over lengthy periods of time. Their problems and potentials can only be understood against their own history."

  4. For activity systems, contradictions serve "as sources of change and development"—following from both the third and the second principle. "Contradictions are not the same as problems or conflicts. Contradictions are historically accumulating structural tensions within and between activity systems."

  5. Activity systems have the potential of "expansive transformations. [...] An expansive transformation is accomplished when the object and motive of the activity are reconceptualized" by participants to dissolve contradictions and therefore "to embrace a radically wider horizon of possibilities than in the previous mode of the activity. A full cycle of expansive transformation may be understood as a collective journey through the zone of proximal development of the activity.

In the light of these principles, Engeström's expanded definition of the ZPD can be revisited:

It is the distance between the present everyday actions of the individuals and the historically new form of the societal activity that can be collectively generated as a solution to the double bind potentially embedded in the everyday actions.

As a collective journey through the ZPD of the activity, the activity system's expansive transformation constitutes a mutual learning process of the participants and the activity system itself. Informed by Bateson's theory of learning (1972) of whom he adopts the double bind concept that Bateson applied in his (deliberately provocative) distinction of "three levels of learning" (pp. 138-139):

  • Learning I "refers to conditioning, acquisition of responses deemed correct in the given context," such as learning environments restricted to the transmission and reproduction of predefined responses.
  • Learning II denotes the result of such a setting which manifests in adapting to "the deep seated rules and patterns of behavior characteristics to the context itself." Here, the potential for a double bind becomes relevant, if "the context bombards participants with contradictory demands" which leaves them unsettled and incapable of acting.
  • Learning III is seen as "essentially a collective endeavor," when the pressure of the continuous double bind moves "a person or a group ... to radically question the sense and meaning of the context and to construct a wider alternative context."

In a positive interpretation of the potential of changing a system that is partly dysfunctional, the cycle of expansive transformation of an activity-system as collective journey through the system's ZPD, the zone's definition entails Learning III "as learning activity" that becomes the "object of expansive learning activity [of] the entire activity system in which the learners are engaged." Or:

Expansive learning is understood as a circular process in which strategic actions based on contradictions drive new strategic actions and contradictions in a cyclic process. (Burner/Svendsen 2025, p. 319)

This makes the ZPD of activity systems the distance between the systems' levels of actual development, in which contradictions manifest as unresolved tensions and breakdowns, and that level of potential development, in which these contradictions in and between the systems may be dissolved.

The reformulation allows for a narrower assessment: While Engeström's CHAT framework was developed primarily for analysing expansive learning in organisations and workplaces, its conceptual vocabulary provides valuable tools for examining educational settings. At the same time, classroom learning introduces additional concerns—notably the simultaneous development of disciplinary understanding and individual learners within heterogeneous communities—which call for complementary perspectives.

Third Space

Gutiérrez and colleagues developed an analytic framework in dialogue with CHAT for school contexts. They described a "hybrid activity system" in a Californian bilingual elementary school (Gutiérrez et al. 1999, p. 288), which they visualised through Engeström's diagram (p. 289), identifying potential contradictions, or "points of disruption" (p. 286) on the edge of mediating artefacts and the system's object, as well as between that object and the division of labour (see also Engeström 2001, p. 144-145).

Activity system

Consequently, the researchers define an activity system as the "social practice(s)" constituted by the components corresponding with the diagram nodes, including "norms, values, division of labor, the goals of the community, and its participants' enduring disposition toward the social practice" (Gutierrez et al. 1999, p. 287).

Furthermore, they understand "learning contexts" as "immanently hybrid, that is polycontextual, multivoiced, and multiscripted" (ibid.). Hybridity within such a context is described particularly as the collision of diverse "cultural and linguistic practices, histories and epistemologies," which require negotiation of "what is known" (p. 288). The polycontextuality of a learning context is described as being "constitutive of multiple and connected activity systems" (ibid.). Multivoicedness in Engeström's definition reflects the description of hybrid contexts as communities of different points of views, traditions, and interests of participants connected through one or more activity systems. Ultimately, "learning communities construct scripts [as] normative patterns of talk and interaction over time" (p. 287). Therefore a hybrid learning context is conceived as constituted by various such scripts, formal and informal. Together, those contexts are characterised by diversity aspects including "racial, ethnic, socioeconomic, and linguistic diversity" as well as "diversity in the mediational tools, roles, and the activity systems themselves" (p. 287).

This conception is exemplified by "urban classroom settings" with their complex "networks of relations and activity systems"; it suggests that the deliberate expansion of learning—that is taking advantage of tensions within and between activity systems—may be utilised within learning contexts through "diverse, and, even conflicting mediational tools" (pp. 287-288).

An educational approach in a multiaged class of second and third graders, that was theoretically informed by "cultural-historical and Freirian theories" (p. 290), was observed and analysed within the outlined framework which enabled findings about a productive expansive learning process for literacy learning through allowing the tensions in the system to transform the participation and discourses within, and thereby transforming the activity itself (p. 286). Hence, the activity created opportunities for Learning III: participants could question aspects of the existing context while simultaneously developing new patterns of participation and interaction. In this sense, Learning III did not simply replace Learning I or Learning II, but transformed the conditions under which both could take place.

This proceeded through a classroom activity that started from a tension—a conflict between pupils that brought one pupil to call another "a 'homo'" and therefore challenged the classroom community's rule of "the expectation of mutual respect"—and gradually transformed the activity across six weeks with parental consent by generating a specific Third Space, characterised by providing corresponding expansive learning as ZPD bridging "the official and unofficial spaces of home and school" (pp. 291-293).

Third Space as bridge

This conceptualisation of the Third Space as an expanded, hybrid activity within the ZPD suggested the arrangement of the classroom transcript to distinguish communication that took place in the Official Space, the Unofficial Space, and the mediating Third Space (pp. 294-298). This separation enabled the systematic analysis of the hybrid language practices within the ZPD (p. 301). Thus, these spaces constitute through communication within the classroom reflecting the different aspects of the participant's lifeworlds[7]. Within the ZPD as Third Space, the use of register shifts between formal and colloquial language serves the bridging function. The Official Space targets Learning I, and the Unofficial Space gives room for productively challenging "the normative scripts, practices, and participation frameworks of the" Official Space (p. 293). Thus, action from the Unofficial Space may be reframed as valuable contribution in such a classroom culture, instead being "considered counterscript" (p. 295).

Such a conception of the educator's participation in the activity system equally also suggests connections to Dewey's framework and, at a more abstract level, to Luhmann's notion of structural coupling of communication systems as well as psychic systems in the sense of Luhmann's systems theory. Yet essentially, the analysis illustrates how expansive learning as a collective process may take place in school: Learning III creates opportunities to question and transform the normative patterns of Learning II through hybrid language practices, thereby reshaping the conditions of individual Learning I.

As ongoing development of CHAT, a "fourth generation" is targeted since around 2010 that aims at widening the theory's horizon once more to "objects of a great scale seeking to solve societal problems, such as poverty or the lack of education at a global level, which requires the creation of expansive learning alliances that provide answers to the complexity of these world's problems" (Burner/Svendsen 2025, p. 321). Thus while the second generation enriched the first by contextualising the relation of subject, mediating artefact, and object within its activity system, the third generation opened the analytical horizon by focusing on sense-making processes through which interrelated activity systems connected by shared objects are transformed. On this level, the fourth generation adds depth by globalising these relations.

Even this theoretical attempt—that bears a resemblance to Klafki's conception of key problem's to be addressed in education—informs further approaches in educational research. Burner and Svendsen reference examples of identifying concerns of fourth generation objects to design learning opportunities in an "Inquiry Based Science Teaching (IBST)" framework to "transform data and information into valuable knowledge" (p. 322). The outlined approach, however, must ultimately be realised locally in schools, where concrete educational work connects the global concerns of fourth-generation CHAT with the interrelated activity systems described by the third generation, as illustrated by Gutiérrez et al.

Focused on CHAT as research methodology, Grimalt-Álvaro and Ametller propose a modification of the activity system diagram as plane, rendering a pyramid when considering "the interaction between activity systems working on a negotiated object within the third generation of CHAT" (Grimalt-Álvaro/Ametller 2021, p. 5). Considered as a practical heuristic, this interpretation may also become a valuable contribution to educators' reflection on shared objects' relation and the own positioning within ongoing classroom action.

Activity system's as layered planes

In general, educational practice theoretically informed by CHAT may develop an awareness of the situatedness of educational action within activity systems: the individual learner may be considered through the lens of the first-generation model of Vygotsky's basic triangle; the classroom community, including educators, through the second-generation activity system; and interrelated activity systems through a third-generation perspective. The fourth generation's perspective may then help integrate curricular subject-matter demands with relevant shared objects understood as aspects of wider societal problems. A further approach to special education, developed within the CHAT tradition in the 1980s, will be introduced shortly; it may enrich this discussion particularly with regard to the latter perspective. Before turning to that approach, however, the consequences of CHAT for Logo environments will be considered in the following subsection.

Logo environments

Research on Logo practices in school contexts between 1985 and 1995 consistently suggested that potentially "Logo environments facilitate social interaction and positively focus that interaction on learning" (Clements/Sarama 1997, pp. 25–26). Moreover, fostering social interaction through Logo activities showed particularly positive effects on social problem solving, together with an increased disposition to engage in productive conflicts. Observed conflicts within Logo-based learning contexts were rather characterised as "disagreements about ideas"—which pupils working together with Logo were more likely to resolve than control groups working with CAI software (p. 26). By contrast, pupils working in "paper-and-pencil environments" showed less conflict potential (ibid.) together with a lower disposition to engage with their peers (p. 25).

This overall assessment is further nuanced by the study of Mevarech and Kramarski, which suggests observable differences between group work within a Logo-based learning environment targeting problem solving, Logo learning in an instructive setting, individualised Logo learning environments, and non-Logo environments. A problem-solving-oriented environment showed more noticeable effects than less autonomous or solitary Logo activities. Thus, the reported social effects cannot simply be attributed to the presence of Logo itself. Rather, they appear to depend on the way in which Logo activities are embedded within the organisation of learning.

The first iteration of the Lisp workshop's own design-based research—in another setting and not involving a Logo environment—likewise suggested that a balance between group autonomy and guidance may characterise a productive learning atmosphere for integrating computer-based programming experiences as an educational tool (Heller 2026a, pp. 71–80; Heller 2026b, pp. 35–38). This suggests that a viable classroom culture and appropriate professional guidance are not merely contextual additions to such activities, but conditions through which their educational potential can become effective.

Taken together, these findings suggest design principles for the integration of Logo activities, rather than properties that can be attributed to the Logo programming environment in isolation. At the same time, Logo is not a neutral mediational artefact. Its syntax and interactive structure shape how learners formulate, externalise, inspect, and revise actions in relation to the computer. Commands and operations make different forms of action and their consequences explicit, while the immediate interaction with the Logo environment provides opportunities to observe, discuss, and modify the effects of these actions. The Logo environment can thus itself be understood as a deliberately structured mediational setting: its syntax and interaction model particular relations between learner, instruction, action, and observable outcome. These characteristics may make Logo particularly suitable for activity systems in which programming itself becomes an object of shared attention and negotiation. Whether such possibilities become educationally productive, however, depends on the surrounding activity system and its organisation of participation.

In this respect, the concept of the Third Space as a bridge between Official and Unofficial Spaces appears promising for reflecting on and developing the conditions under which Logo-based learning environments may become productive mediating artefact. Mwanza's proposed CHAT-based framework for designing viable Human-Computer Interaction may provide a further point of reference for such an approach (Mwanza 2001). Rather than assuming that Logo itself drives positive social-emotional development, such a perspective places the emphasis on the interaction between the artefact, the participants, the teacher's mediation, and the evolving norms of the learning community.

Shared object of inquiry ("Gemeinsamer Gegenstand" of Feuser/Jantzen/Holzkamp)

Subsection:

Sasse and Schulzeck trace the formation of Feuser's concept of the shared object of inquiry (gemeinsamer Gegenstand) to the beginning of the 1980s, emerging from a lively discourse that had developed within German critical and materialist inclusive education[8] since the 1970s, particularly around Jantzen's work, in dialogue with Klafki's critical-constructive didactics and in critical engagement with German Critical Psychology as represented by Holzkamp (Sasse/Schulzeck 2023b. In: Sasse/Schulzeck (ed.), p. 59)[9].

Both critical and materialist inclusive education and Critical Psychology were theoretically informed by the cultural-historical approaches developed by Vygotsky's circle. Holzkamp engaged primarily with Leontiev's work, whereas Jantzen and Feuser also drew on Vygotsky, Luria, and other representatives of the circle (p. 59). After several years of intellectual convergence, however, Jantzen and Feuser rejected further affiliation with Critical Psychology in 1985, considering its subsequent development no longer helpful for their own theoretical work (p. 60). Sasse and Schulzeck nevertheless identify Critical Psychology as fundamental to understanding Feuser's concept of the shared object of inquiry as a category of inclusive education, introduced in 1982 (pp. 60–61). Thus, although Feuser's theoretical engagement reached directly into the first-generation cultural-historical tradition—in CHAT terms—the influence of Holzkamp's Critical Psychology provides an important connection to the second-generation development, particularly through Holzkamp's engagement with Leontiev.

Feuser defined inclusion[10] as the shared activity (Play/Learning/Work) around the shared object of inquiry/product in cooperation of persons with and without disabilities. (p. 61)[11] The shared object is thus not merely a common topic of activity, but a mediating structure through which different participants can engage in a common activity without requiring identical forms of participation.

Following Holzkamp's characterisation of how people sustain their existence through their development within the circumstances into which they are born as "development-logical", Feuser further defined disability as a "development-logical" result of a person's attempts to sustain their own existence by adapting most appropriately to those conditions which isolate the individual, rather than a pathological consequence (ibid.). Also the concepts of cooperation, activity, and object are used in Holzkamp's preceding work, supporting Feuser's later conception (p. 61). Holzkamp's formulations further reveal the cultural-historical inspiration of his conceptual reconstruction, alongside the critique of dualism and the Marxian tradition underlying it:

Regarding "the human-world-context that has become historical" and the terminology of the traditional psychological discourse within the 1970s, "the interaction concept of the bourgeoisie is suspended within the concept of cooperation"—so is "the behaviour concept of the bourgoisie suspended within the concept of activity," and "the concept of stimulus conditions is suspended within the concept of object meanings."[12] (p. 62)

Another distinctive feature of Feuser's concept as an educational theory informed by cultural-historical approaches is its adoption of the ZPD concept (p. 64). The way Sasse and Schulzeck subsequently introduce and operationalise it, however, suggests a formulation that differs from the co-constructive space considered in the sense of Radford, Engeström, and Gutiérrez et al. Zone der nächsten Entwicklung, as their translation of зона ближайшего развития, is rendered here as the "zone of the next development" rather than the "zone of the nearest" or "closest development." More importantly, Sasse and Schulzeck introduce the "zone of actual development" as its complementary term, referring to the possibility that the ability to accomplish tasks learned through the support of others may subsequently move into that zone (p. 65). The potential level of development, however, is not mentioned at this point. This formulation may therefore blur the distinction between the ZPD as a relation between the actual level of development and the potential level of development itself, and adds another individualised interpretation. Maintaining this distinction avoids conceiving developmental possibilities as spaces located within the learner that exchange structures or abilities, rather than as a relational field constituted through activity and assistance. Nonetheless, Kracke refers to a notion of the ZPD in this context which may be in line with the relational interpretation (Kracke 2023. In: Sasse/Schulzeck (ed.), pp. 43-44).

This possible terminological or conceptual conflation does not, however, impede the three authors' development of a promising co-constructive planning tool for designing learning environments (Sasse/Schulzeck 2023a. In: Sasse/Schulzeck (ed.), p. 59), pp. 11-40). Their differentiation matrix (Differenzierungsmatrix) incorporates Feuser's concept of the shared object read in combination with Holzkamp's conception (pp. 69, 72) as one axis of the shared object's increasing thematic complexity; the other axis concerns increasing it's cognitive complexity (Kracke 2023, pp. 41-56). The matrix provides a framework through which educators can jointly consider the specific developmental and learning conditions of a group and plan differentiated learning opportunities. In this sense, the matrix itself may be understood as supporting a ZPD among educators: the shared object becomes the focus of a collective process in which participants bring their different perspectives and knowledge into a common activity of designing inclusive learning environments—again established in the classroom through the matrix as well. The enacted structure therefore appears compatible with a CHAT-informed understanding of the ZPD even where its terminology remains somewhat different.

Feuser insisted that the shared object should not be conceived as something perceptible to the senses that can be used among several learners; and he rejected attempts to define it with the terminology of "classic pedagogy" or of general didactics (Sasse/Schulzeck 2023b, pp. 57-58). Consequently, he outlined a general inclusive pedagogy and development-logical didactics where the educators are challenged to individualise the shared object in accordance with the subject's developmental logic. (p. 65). Following Holzkamp, the developmental logic of becoming a human individual is the absence of a species-specific natural environment, thus being forced to attain the ability to establish the order of developmental stages corresponding with the idiosyncrasies of the respective societal requirements (p. 66). Sasse and Schulzeck conclude that Feuser, by contrast, focused on a development-logical individualisation of pedagogical offerings alongside the specific learning conditions of all pupils—inclusive general pedagogy took shape as subject-scientifically informed pedagogy aiming at forming the need of the human for the human, and structuring human activity for the most mature control of reality (ibid.).

However, Sasse and Schulzeck highlight that subject-scientifical, cooperation, and control of reality are terms already utilised in the theory of Holzkamp and his colleagues which, in turn, builds on Leontiev. It relates to an anthropological epistemology in which learning is considered an activity characterised by individual motivations and emotions of the subject, that aims at agency, which is defined by participating in societal control of reality for deliberate control over the own circumstances (p. 67). The subject learns when she reaches the limit of her agency—her learning challenge to overcome. Following Holzkamp, cooperation eventually takes shape as a process of co-construction wherein learning challenges and objects are negotiated as relevant for the participants in individual variations (p. 73). This is rather a joint interest in the same object for different reasons than a distribution of labour, but also a chance to organise the process of unlocking the shared object together (p. 71). The process of individualisation and appropriation is understood as differentiating possible learning objects from the shared object, which is ultimately not a physical object but may emerge through engaging with such an object in thought.[13]

The second-generation CHAT model, as visualised in Engeström's activity-system triangle, may also serve as an analytical tool for examining this conception of Holzkamp and Feuser, grounded in Leontiev and Vygotsky. The shared object might therefore be regarded in the light of CHAT's conception of the object as mediated through artefacts within an activity system, whose other relations connect subject and community and whose structural conditions shape the activity. The shared object of learning in this conception could therefore be understood in terms of Papert's object-to-think-with (Papert 1980, pp. 11, 23, 182): a mediating artefact through which the shared activity of unlocking meaning becomes possible, while the object itself is constructed differently through that activity by the community of learners and by each individual subject. The developers of the differentiation matrix call this shared object the learning object to be jointly defined (Gemeinsam zu definierender Lerngegenstand), or shared learning object (Gemeinsamer Lerngegenstand; Sasse/Schulzeck 2023b, pp. 69, 71; Kracke 2023, p. 47). The characterisation of these interdependent processes within the activity system, however, suggests shared object of inquiry as a useful complementary term: while shared learning object foregrounds what may potentially be learned, shared object of inquiry foregrounds the collective activity through which its meaning is jointly opened up.

This shared object of inquiry is conceptualised along two dimensions, its cognitive complexity and its thematic complexity, whose combination forms the differentiation matrix (Sasse 2023. In: Sasse/Schulzeck (ed.), p. 59), pp. 21-22).

Sasse, Basic Structure of the Differentiation Matrix

This relation serves as a generalisation of Kutzer's learning structure grid (Lernstrukturgitter) from inclusive mathematics education (1979), that maps Piaget/Bruner informed cognitive levels of mathematical thinking onto the complexity of mathematical structures to be applied for learners in primary education from first to sixth grade (pp. 20-21; diagram taken from University of Innsbruck).

Kutzer, Learning Structure Grid

The differentiation matrix, in turn, serves as a means of organising the didactical decisions for preparing the differentiation of the shared object of inquiry—represented by the learning opportunities (p. 21), offered in a learning unit spanning several weeks, and arranged within the matrix according to the heuristic assessment of the educators participating during the planning for a specific group of learners. Here, a Piaget- and Aebli-informed perspective on the shared object's cognitive complexity is combined with a Vygotsky/Leontiev-informed perspective on its thematic complexity (Kracke 2023, p. 47-53), within Vygotsky's basic triangle—the tip of the CHAT diagram.
abstract level (meta-cognition)
symbolic level / representation
completely imagined action
partly imagined action
ostensive-practical action
complexity 1 complexity 2 complexity 3 complexity 4 complexity 5

This matrix serves both as planning tool, and as presentation of the learning environment whose fields contain the short descriptions of the respective learning tasks that enable distinct ways of dealing with the shared object of inquiry on different cognitive levels and from thematic perspectives of different complexity, e.g., "complexity 1" = Electricity in everyday life; "complexity 2" = Electricity production; "complexity 3" = Circuits; "complexity 4" = What is electrictiy?; "complexity 5" = renewable energies (Rieche 2023. In: Sasse/Schulzeck (ed.), p. 346). This presentation guides the use of the learning material associated with the tasks. The differentiation matrix's third function is that of documenting the learning process. The pupils participate by choosing their own trajectory through the learning environment, documented on their individual copy of the matrix, and with intersections in mandatory fields (= tasks). (Held 2023. In: Sasse/Schulzeck (ed.), p. 59), p. 106).

Conceptually, the differentiation matrix can therefore be understood as the intersection of two complementary perspectives on the shared object of inquiry: a Vygotskyan-, Piagetian-, and Aebli-informed perspective on the cognitive demands and modes of individual learners' engagement with it, and a Vygotskyan- and Leontiev-informed perspective on its thematic complexity within the activity system and its community (see Aebli and Klafki brought into dialogue for the connection to Klafki).

Notice:
This differentiation model is distinct from the Tomlinson model, which differentiates instructional elements—content, process, products, and affect/environment—in relation to the learners’ readiness, interest, and learning profile, using a variety of instructional strategies (Tomlinson 1999/2008, cited in Chen/Chen 2018). These dimensions are also represented as a matrix relating the three learner factors to the four instructional elements in materials such as those presented by the NCoC (2018). While the two models organise differentiation along different primary dimensions, both address the challenge of providing differentiated learning opportunities in response to learners’ varying needs.

Logo Microworlds as shared objects of inquiry

Papert introduced the term microworld in Mindstorms for self-contained models or environments in a Logo setting, such as the Turtle environment, that constitute "self-contained worlds, in which certain questions are relevant and others are not ... 'microworlds', each with its own assumptions and constraints" (Papert 1980, p. 117). Papert saw the potential of exploring these constrained worlds through self-directed, systematic inquiry, thereby connecting learners' lifeworlds with "their personal life to the formal domain of scientific theory construction" and providing "the opportunity to carry out [learning] projects of greater complexity than is usually possible in the physical world" (pp. 117–118). Counterintuitively at first glance, even an example in which a learner creates an own microworld by imposing stricter constraints within a less restricted microworld ultimately enables increasing complexity in the longer term (pp. 118–119)—possibly because it provides an experience of self-directed scaffolding: the learner discovers that the complexity of the given world can be deliberately constrained without making it disappear.

Thus, within the Turtle microworld, which Papert describes as "an intuitive analog of the differential equation" (p. 66), "the Turtle [itself] instead of the point is taken as the building block" (pp. 121–122). Rather than beginning with the symbolic Euclidean conception of geometry, learners can therefore explore geometrical forms through the gradual emergence of figures from (even restricted) Turtle movements, potentially making geometric concepts more accessible. Likewise, the Turtle microworld can be extended into a Newtonian microworld that simulates ideal conditions for observing the first of Newton's axioms: A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. Papert outlines such a learning environment for implementation in TURTLE TALK, enabling further observations and applications beyond the exploration of idealised physics—for instance, in a programmed game that makes use of this distinct microworld (p. 122).

Papert's conception of the microworld therefore provides a particularly promising point of contact with the shared object of inquiry. A microworld does not merely mediate an encounter with an externally defined subject matter; its assumptions and constraints constitute a domain within which learners can jointly investigate, modify, and construct meanings. Once such a microworld is itself made explicit and shareable, the artefact through which learning is mediated can simultaneously become an object of collective inquiry.

cLogos will utilise this idea also as a technical specification, where it will become both a means of making explorations explicit as microworlds with particular assumptions and constraints, and a means of distributing them for joint development. The declaration and use of microworlds as learning environments may then also be integrated into the elaboration of differentiation matrices: tasks may build on existing microworlds, or lead to the discovery and exploration of emerging microworlds as products of reflection during the learning process. Eventually a microworld may constitute the shared object of inquiry itself or proves to be a productive representation of the overarching object, that suggests diverse activities across disciplines, within various Logo-based learning environments as well as in analogue settings.

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General didactics (Aebli/Fröbel/Klafki)

Subsections:

In 1962, Gilbert introduced the term "mathetics" as a novel English word for a technology of "the systematic application of reinforcement theory to the analysis and reconstruction of those complex behavior repertories usually known as 'subject-matter mastery,' 'knowledge,' and 'skill.'" (Gilbert 1962, p. 8). The word was derived from ancient Greek μαθεῖν (mathein) for to learn (p. 7). In turn, the nouns μάθημα (mathema), something learned, and τέχνη (téchnē)—art, craft, or skill—are associated with the formation of the term mathematics, the art of knowledge.

Papert later seized this proposal in Mindstorms, where he defined mathetics as "the set of principles that govern learning" (p. 52), and identified "a fundamental mathetic principle: Make sense of what you want to learn"—the principle that guided the introduction of Turtle Geometry in Logo teaching (p. 63). Papert understood mathetic principles as "ideas that illuminate and facilitate the process of learning" (p. 102). Another mathetic principle applied in doing Turtle Geometry is "[make] components to favor modularity" (p. 60). More general principles are "relate what is new and to be learned to something you already know"—again a formulation of what Minsky called "Papert's principle"—and "take what is new and make it your own: Make something new with it, play with it, build with it" (p. 129).

The term mathetics, however, is rather old. It is introduced as mathetica, the art of learning (ars discendi) in a collection of Comenius's notes on teaching, that was published posthumously (Comenius 1680, p. 1). The term is introduced before the corresponding art or craft of teaching (ars docendi), didactica (p. 39). The ordering is suggestive: the art of learning precedes the craft of teaching. It therefore resonates strikingly with Papert's expectation that educators become anthropologists and with Dewey's conception of educators as students of the conditions of learning within and surrounding learners. Yet the distinction between the art of learning and the craft of teaching is not absent from the Great Didactic (Didactica Magna). Its didactic principles already repeatedly attend to the conditions under which learners can learn effectively (Comenius 1907, pp. 111ff.).

The work of Comenius himself can be considered as a bridge from Renaissance thinking to the upcoming Age of Enlightenment (Jergus 2018. In: Peters (ed.), p. 198). Within this emerging modern discourse, three perspectives on education can be distinguished, each concerned both with the social function of teaching and with the possibilities of individual development through learning. The first two can be characterised as rationalistic and naturalistic orientations as seen above in the discussion of Dewey and Vygotsky. The former orientation aims at the emancipation of the individual mind from custom and preconceived oppinions through transmissive training of logic reasoning. The latter targets the freedom of natural development—in Rousseau's conception within carefully designed learning environments, that train the freedom of reasoning through the affordances of the environments.

The third perspective is concerned with the freedom to participate. In Gutierrez et al.'s study about the Third Space in the classroom, the involved teacher represented an ambitious objective (Gutierrez et al. 1999, p. 290):

... My teaching is informed by my beliefs about learning, and I believe that learning is a social process. Therefore, I try to set up everything that happens in the classroom to occur socially. ... One of my goals is to give voice to the children, but not only voice, but to break the power structures of society, not to reproduce them; but to create a brand new structure in which they have the power so that not only does it create independence and self-esteem, but that they feel that they have what it takes to succeed in life, not only academically but in every area of their life. (A. Rivera, personal communication, February 1995)

This belief informing the teaching is not merely an inspiration; it is a promise that demands verification, as Nyerere pointed out thirty years before, in the context of the then young state of Tanzania, overcoming colonial suppression and heteronomy:

The content of education is ... to prepare young people to live in and to serve the society, and to transmit the knowledge, skills, and values and attitudes of the society. Wherever education fails in one of these fields, then the society falters in its progress, or there is social unrest as people find that their education has prepared them for a future which is not open to them. (Nyerere 1967, p. 2)

Such considerations already informed the so-called philanthropist perspective during the Enlightenment era: freedom of reason and freedom of development needed to be situated in a society within the tension field of reproducing society and innovating it—with an emphasis on acknowledging the estates-based society at the time (Basedow 1785, p. 62ff.). The craft of teaching became part of a pedagogy, or discipline of education, which is concerned with preparing the environment in which learning may take place to become a member of a society which provides a place for the skilled individual within the own societal subdivision.

Philanthropists aimed at reforming the school system and lesson planning. With a different direction but similar approaches, subsequently Pestalozzi developed and promoted a learner-oriented pedagogical method for people living in poverty, which became influential during the 19th century and beyond (Schmitt 1996, p. 56-59). Among others also Herbart was directly inspired by him (Rein 1927, p. 3) and added a general pedagogy to the tradition of a methodologically developed craft of teaching which includes general didactics as education through classroom work (Erziehung durch Unterricht; Herbart 1806, p. 25).

Another attempt was a rather drill-oriented method, represented in Monitorial systems, which organised the instruction of even larger groups of learners within a setting of adult teachers meticulously instructing more advanced students to teach their less advanced schoolmates autonomously. This system of mentorship was independently developed by Lancaster, Bell, and Raikes—the latter himself identified as a philanthropist. The system's purpose was efficient mass teaching despite teacher shortage, granting practical education to the poor. A more scaffolded version with greater emphasis on professional supervision of the mentors and more responsibility of the professional teachers was developed as the Elementary School Institution of Eckernförde (Baumfelder 1838).

Together, such approaches contributed to the formation of didactics as an academic discipline concerned with enabling educators to attend systematically to pupils' learning processes within learning groups as part of general pedagogy which entails "mathetics" as the object of lesson planning.

Didactics addresses a persistent tension: education must be organised for groups of learners with limited institutional resources, while at the same time attending to the differing needs and developmental conditions of individual pupils and preparing them for participation in society. In this sense, didactics is the professional discipline of educators: specialised didactics addresses viable methods and strategies within particular subjects, broadly corresponding to pedagogical content knowledge, whereas general didactics concerns principles of teaching and learning that transcend individual subjects and thus corresponds more broadly to pedagogical knowledge. This distinction between general and specialised didactics is characteristic of several continental European traditions, although the disciplinary boundaries and theoretical relations between the two vary considerably across countries. Ultimately, even an exclusive focus on the art of learning leads towards didactics as soon as mathetic insights are used to foster the learning processes of others.

Basic forms of teaching (Aebli)

Subsection:

Piaget's developmental-psychological insights were first applied to general didactics by Aebli (1951), a former primary- and secondary-school teacher who studied psychology at Piaget's institute under Piaget's mentorship. Aebli also completed his doctoral work under Piaget's supervision who commended Aebli's extraordinary achievements in both education and empirical psychology, suggesting that he was particularly well placed to initiate an integration of Piaget's work with the professional knowledge of a school educator (Piaget 1951. In: Aebli 1976, pp. 8-9). In the foreword to the 1963 German translation of his original work, Aebli himself acknowledged that his subsequent research had led him to depart from some essential aspects of Piaget's conceptions. Nevertheless, he continued to regard the aspects of his mentor's theory that had informed his original study as among the most viable and well-founded elements of Piaget's work (p. 12).

As a starting point, Aebli outlines the roots of what Papert later called the "dissociated model [of rote learning]" (Papert 1980, p. 47). He traces this didactic model to the tradition of visual instruction, or object-lesson, whose roots reach from Comenius through Rousseau and the philanthropists to Pestalozzi, but which was subsequently reconceptualised from the perspective of a sensualist-empirical psychology and epistemology (Aebli 1976, p. 17). This perspective reflects the positivistic orientation that became characteristic of much nineteenth-century academic discourse beyond educational theory. Aebli traces the philosophical lineage of the sensualist-empirical orientation further to Taine, Mill, and ultimately Hume (p. 19)—himself a prominent modern exponent of the Aristotelian psychological principle of the association of ideas. In the terminology developed above, this orientation can also be understood as privileging the rationalistic perspective over the naturalistic one. Probably, that perspective was also justifiable in terms of nineteenth-century pragmatic societal needs, such as the "necessity that many people be 'programmed' to perform such operations as long divisions quickly and accurately" (Papert 1980, p. 51). Yet such a consideration does not by itself clarify the educational rationale underlying the counter-concepts that emerged in response to it.

The core assumptions of this positivistic foundation, reflected in the "didactics of visual instruction," or "didactics of coloured chalk," are those of children as tabula rasa, differing primarily in their degrees of sensory receptivity: they record sensory impressions in the mind, from which particularities are gradually "stripped away" through abstraction. The resulting didactic model, with effects that have persisted into twentieth-century and partly contemporary schooling, privileges the presentation of shapes, diagrams, and illustrations, often with regions differentiated by colour, by a teacher addressing the class as an audience (Aebli 1976, pp. 18–23).

Aebli acknowledges that this didactic position, represented among others by Diesterweg (p. 17), identifies a necessary condition for the development of concepts and operations. At the same time, he argues that visual instruction requires a transition towards meaningful activity if learners are to develop a notion of the respective learning object: coloured-chalk illustrations cannot simply be received passively; their meaningful context must be actively reconstructed by the learner (pp. 21–23). Whereas Papert speaks of dissociated learning and "a balkanized image of human knowledge" (Papert 1980, p. 39), Aebli had already argued, on the basis of his own teaching experience and research, that the common way of teaching ... isolates artificially what should be related to each other, therefore prevents the child from understanding and forces her to seek refuge in rote learning and formulas (Aebli 1976, p. 25).

A movement towards such a holistic approach can be seen in the didactics of the activity school (école active), a broad designation for the several progressive and reform-oriented pedagogical movements of the late nineteenth and early twentieth centuries, including the German work-school tradition (Arbeitsschule). Drawing on the works of four educational theorists and practitioners associated with activity school frameworks, Aebli illustrates how such attempts moved beyond sensualist-empirical and associationist approaches, yet remained unsatisfying from his Piaget-informed perspective (pp. 26-27).

While Lay utilised the psychological concepts of reflex arc and kinaesthetic sensation in material-based learning arrangements, he ultimately cleaved to the sensualist-empirical mindset (pp. 27-34). Dewey in turn—and similarly Claparède—develops an instrumentalist interpretation of thinking that opposes the didactics of visual instruction: the subject uses its own mental functions as tools meant to support its actions (pp. 35-39). On this account, Deweyan teaching is characterised by influencing the child's learning trajectory through mediating activities and materials within an environment which provides the necessary tools and tasks for gradually systematising and advancing the individual and social learning processes (pp. 39-40). However, Aebli posits that both Dewey and Claparède retained associatist elements in their concepts. Despite initially characterising psychological development as an active process of adaptation to the environment, the process of thought is essentially defined as inferences associating observational data with their meanings as well as interrelating the contents of mind, risking a static conception of the intrinsic nature of thought. Dewey's later philosophical work thus marked a turn towards an operational understanding of thought, yet remained underdeveloped on the psychological side (pp. 42-43). Kerschensteiner in turn, an important and Dewey-influenced proponent of the work-school tradition, emphasised the operational aspect of concept formation in such a way that activity is thereby reduced to an external means for intensive mental operations in his system. Although the pupils' own activities are crucial for their learning processes—such as observing and studying exemplary cases instead of a comprehensive collection of facts, to develop concepts and operations as constructive acts—the emphasis is on self-control over one's own results within a Kantian duty-based ethical framework fostering a dispassionate mindset. Aebli opposes this underlying moral claim from his psychological-didactical position grounded in Piaget's work (pp. 44-52).

The purpose of such foundations is to develop viable concepts of processes that enable distinctions between the psychologically intended process of learning from unintended processes of acquisition (p. 47)—to direct and maintain educators' skillful didactic strategies. This pertains to any such attempt, whether in the still observable didactics predominant in the nineteenth and twentieth centuries or in contemporary action-oriented approaches tracing back to the activity-school tradition and its precursors. Also, Papert's later constructionism can be understood as a member of this tradition—although probably developed without awareness of Aebli's 1951 study,[14] it remains closely related to the latter's general didactics, rooted in a dialogue between the activity-school approaches and the psychodevelopmental findings of their common mentor, Piaget.

Aebli dissolves the tension between associativist and operationalist thinking by pointing out Piaget's findings on mental image, action, and operation and giving examples of his empirical method. An image is characterised as a snapshot of reversible operational transformations. Such an image can only recall facts already experienced through the child's own activity rather than transmit experiences originating outside her. This conclusion was indicated in experimental settings such as the following: children were asked to put down the same amount of small plates below a row of six. Within a certain age range they had no difficulties to multiply the original row once and to be convinced of the equal amount of plates. However, if one row was transformed into a heap, their certainty decreased. By exploring the plates and restoring the rows, the experience could be gained to develop their own concept of cardinality (pp. 55-56). Papert describes his personal anecdote of such processes as the gears of his childhood, becoming his first personal object-to-think-with (Papert 1980, pp. vi-vii). This insight suggests the didactic potential of Logo's Turtle environment, as well as of interactive mechanical and computer-aided geometric environments that similarly make operations externally manipulable.

The observation of children ranging across several ages revealed that actions need to be conducted explicitly as long as their result cannot be imagined in a concrete case: the concrete action is not yet transformed into the idea of the action (Aebli 1976, p. 57). At a very early age, Piaget could study a sixteen month old infant's behaviour while dealing with the problem that a watch chain in a box which was opened only a gap could not be reached. After fingering, the child attentively looked at the box and started shutting and opening her mouth, gradually opening it wider. This was interpreted as an engagement with the problem of a hollow space, externalising the thought process for problem solving in the analogue movement of the mouth as the desired action to take place, still without an idea of how to reproduce the corresponding action on the box. First indications of imagined operations were then observed starting around the age of two (pp. 57-58).

The images emerging in the mind during these processes are then considered as active reproductions which are newly created in the mind each time. Thus images are imitations of the object no "photographies of the mind." It could empirically be shown that an image is an intrinsic rendition of the movements during the perceiving exploration of an object. This characterises mental images and operations as serving two different tasks of thinking but sharing their origin in the same sensomotorical activity (pp. 58-60). This again may provide connections to Papert's suggested concept of "syntonic learning," as "body syntonic" where the activity is "firmly related to children's sense and knowledge about their own bodies" (Papert 1980, p. 63). Internalisation requires action, and the reproduction of demonstrated actions in turn requires the learner's own prior experience; thus, ready-made diagrams as well as merely staged activities are likely to fail as mediative artefacts (Aebli 1976, p. 62)—particularly where children are expected to remain still and silently attentive while the action is demonstrated to them.

This engagement with objects by the subject develops activity schemata such as grasping, sucking, cutting, exploring, ordering, counting, and adding, which are in turn applied to objects in concrete or internalised form, enabling experiences to be assimilated through further processes of internalisation. The absence of such schemata renders the subject mentally blind to the corresponding properties of the things (pp. 85-86).

In the contemporary context of CAI software, gamification, and "artificially intelligent" machine-learning applications, these findings already reveal critical questions about their potential effects on cognitive development:

  • What can the children actually do here that they could not do before?

  • Which activity belongs to the child, which activity has been delegated to the system, and which activity schemata can emerge from the relationship between the two?

  • Which operations are made available for manipulation?

  • How much control do the children have over the operations underlying the applications through which they produce something?

  • Essentially: Does the activity allow the learner to develop and apply activity schemata, or does the software perform the relevant activity on the learner’s behalf?

If the answer points to the children as mainly passive users of the software, the application risks restaging the associativist "coloured chalk" didactics in a digital form, with its emphasis on the reception of representations rather than on the productive assimilation of experience.

Aebli dedicated his professional life to educational psychology and teacher training, developing his general didactics from the psychological didactics presented in his 1951 thesis. In his mature conception, Aebli eventually organises twelve basic forms of teaching within a three-dimensional didactic configuration space, or body. The first dimension concerns five media of didactic communication (M), the second three structural forms (S), and the third four functions of learning processes (L). Their combination yields 60 possible cells, corresponding to different configurations of media, structures, and learning-process functions; Aebli does not attempt to describe all of these combinations individually (Aebli 2019, pp. 24–26).

  • Media of didactic communication
    • M1: Storytelling and lecturing,
    • M2: Demonstrating,
    • M3: Viewing and observing,
    • M4: Reading with pupils,
    • M5: Writing and text composition.
  • Structure
    • S1: Developing an action sequence,
    • S2: Building an operation,
    • S3: Concept formation.
  • Learning processes
    • L1: Problem-solving construction,
    • L2: Working through,
    • L3: Practising and repeating,
    • L4: Applying.

Considering these twelve forms individually provides a basis for reflecting on their possible combinations when planning and analysing teaching interventions. They enable analytical questions such as:

  • What is the medium through which the content is encountered?
  • What kind of structure is being developed—an action schema, an operation, or a concept?
  • What learning-process function is currently foregrounded—construction, working-through, practising, or application?

A teaching intervention may thus be located analytically within a cell of the body, identifiable as a specific (Mx,Sy,Lz). Over the course of an intervention, or across a series of interventions, different cells may be foregrounded, allowing the teacher to analyse and reflect on how the didactic configuration changes over time.

Aebli's body of basic forms

As Aebli puts it:

A socio-scientific theory reveals a weakness if it cannot be formulated in terms that are close to everyday thinking, at least emerge from it and feed back into it. Of course, every theory—even didactic theory—aims to formulate its concepts and knowledge systematically and to link them in a transparent way; this requires abstraction and a purified, economical vocabulary. However, this vocabulary must be constituted in such a way that it constantly reminds learners of their non-scientific prior experience, while enabling them to work through this prior experience in the light of new insights and to organise it more appropriately (p. 20).

In this spirit, he presents the basic forms of teaching in three parts and twelve chapters, each subdivided into a psychological and a didactic section. Aebli gives particular attention to reading and writing within this framework, acknowledging that these cultural techniques had long remained neglected: Piaget's psychology, from which I come, struggled for a long time to gain access to [reading and writing]. Hence, it took me so long to address [the subject] myself (p. 12).

With Bruner, Aebli states that knowledge is stored in three psychological media—the symbolic, enactive, and iconic. At the beginning of teacher training, three basic forms of teaching—storytelling (M1), demonstrating (M2), and jointly viewing (M3)—are practised which correspond with these three media. In turn, those three basic forms are closely associated with three media of communication: verbal presentation, practical demonstration through action, and verbal commentary. Yet these media are already intertwined in perception, as can be observed when pupils (re-)enact elements of a story while listening to it—their movements indicate aspects of the protagonist’s actions. Thus, not only the symbolic medium of language but also visually ostensive elements and experienced actions concurrently resonate within the pupils’ minds. These three basic forms constitute the basis of teaching through spoken language, action, and image. They are complemented by the two further basic forms of reading with pupils (M4), and writing and text composition (M5). Despite the emphasis on written language, the distinct mental processes involved in perceiving and producing spoken and written language—and the differences between reading and writing—must be taken closely into account when fostering these skills. (pp. 31-32)

Aebli further posits that didactic expertise is characterised by structured content knowledge that continues to expand throughout professional life and forms the basis of media competence: no literacy without something to say, no practical skill without technical knowledge, and no cognitive ability without subject knowledge related to the objects under consideration. Educators also need pedagogical knowledge that enables them to speak about how people act; but they must likewise be able to act themselves and demonstrate what they are teaching. They cannot be suspended from content knowledge without being degraded to merely presenting "instructive media." By contrast, the term media competence refers to the psychological media that serve as media of experience formation. This formation begins with the development of action schemata, which are gradually systematised through abstraction into operational knowledge and ultimately into conceptual knowledge. This process of knowledge development requires an awareness of the structures inherent in the objects of learning addressed through the three structural forms, S1 to S3. This constitutes the closest link to specialised didactics, which focuses general didactic principles on the subject matter of particular disciplines. Finally, the third dimension mirrors the learning process itself as the psychologically and didactically informed fostering of construction (L1), working through (L2), practising (L3), and applying (L4) knowledge. (pp. 26-27)

Aebli's general didactics and Papert's constructionism

Aebli’s trajectory illustrates that working within a Piaget-informed framework need not mean preserving Piagetian psychology as a completed body of knowledge and applying it to new educational contexts. His work demonstrates another possibility: developmental psychology can serve as a starting point for further empirical, theoretical, and didactic development from within the disciplines concerned. This makes Aebli particularly relevant here, since he worked directly at the intersection of developmental psychology, general didactics, and teacher education.

Papert’s constructionism can be understood as another development from within a Piaget-informed framework, though one that places greater emphasis on technologically mediated activity and the construction of meaningful public objects. The difference need not be understood as a conflict between incompatible theories. Rather, Aebli and Papert may illuminate different aspects of the same educational object.

Deborah’s engagement with the Turtle microworld, already considered as a shared object of inquiry within a framework informed by Feuser/Holzkamp et al., provides an opportunity to consider this distinction at the level of activity. Her initial appropriation of the microworld involved constraining its possibilities before gradually widening the field of action (Papert 1980, pp. 118-119). From a constructionist perspective, this need not be interpreted primarily in terms of openness, freedom, or unlimited possibility; rather, it can be understood as the learner’s active construction of a sufficiently bounded, personally meaningful microworld within the larger environment. Read through Aebli’s framework, the same process invites questions about the action schemata, operations, and conceptual structures that become available through this progressive engagement. These questions, in turn, can help the educator accompany and support the learner’s engagement with the chosen medium.

Approaches to (Self-)Formation (Bildung) (Fröbel/Klafki)

Subsections:

Usually, Bildung (/ˈbɪldʊŋ/) is translated as education, or it is deemed not easily translatable into English. Understanding Bildung as education may foreground the direct or indirect processes of fostering and guidance associated with the Latin ēdūcō and the ancient Greek παιδαγωγία (paidagōgía). The latter evokes the image of leading a child, while the former is commonly associated with bringing forth or guiding development, including the growth of a plant, the bearing of an animal, or the demeanour of a child (Matthes 2024. In: Götz et al. (eds.), p. 274)—with possible connotations of externally imposed form.

However, the term Bildung developed during the late Enlightenment and German Idealism through idealising reinterpretations of παιδεία (paideía) together with φιλανθρωπία (philanthrōpía), or hūmānitas (Klafki 1986, pp. 456–457). It is mainly associated with W. von Humboldt (Sjöström/Eilks 2020, p. 55), owing to his influence on educational policy in Prussia (Klafki 1986, pp. 460-461). Yet the concept reflects an ongoing discourse that developed alongside the constitution of civil society in German-speaking countries at the beginning of the nineteenth century. Various thinkers contributed to its formation, including Lessing and Wieland, Herder and Fichte, Schiller, Goethe, Hegel, as well as Kant, Pestalozzi, Herbart, Schleiermacher, Fröbel, and Diesterweg (p. 455), also Scandinavian contributors such as Grundtvig, and Agardh (Sjöström/Eilks 2020, p. 56).

This discourse was not concerned exclusively with the design of an educational system. More fundamentally, it addressed the development of a coherent personal and social identity amid dramatic societal change: the dissolution of the aristocratic order, the ascendancy of bourgeois society, and the emergence of the proletarian workforce during early industrialisation. Bildung thus became associated not merely with the transmission of knowledge or the organisation of instruction, but with the formation of persons capable of understanding and participating in a changing society. (pp. 457-458)

In this context, Humboldt proposed a comparatively democratic conception of Bildung as a project intended for everyone, grounded in self-determination, self-direction, and self-activity across societal classes (p. 460). This idea also informed his conception of a comprehensive school as a societal institution intended to foster such processes of self-guided learning (pp. 458–460). This commitment to self-determination is characterised by the relation between individuality and generality in the works of Pestalozzi, Herder, Humboldt, and Schleiermacher (pp. 463–464).

However, Bildung was also reinterpreted as a marker of class distinction (pp. 465-466): those who could afford primarily self-directed learning for the cultivation of their own character—members of the educated classes (Bildungsbürger)—were contrasted with those who had to acquire a profession for their livelihood. This distinction continues to inform a hierarchical understanding of Bildung as a superior form of knowledge acquisition and Ausbildung as a subordinate form of vocational training—one associated with extrinsic motivation and externally directed learning. It is also reinforced by Humboldt's conception of a general foundational Bildung that should be temporally and institutionally separated from subsequent specialised vocational Ausbildung, thereby contributing to their hierarchical rather than reciprocal relationship (pp. 471-472). The term’s history as a politically contested concept, repeatedly reinterpreted across generations, may itself have contributed to the perception of its untranslatability.

Buckingham suggests literacy in its broader sense of a "means of cultural understanding" as a term that at least overlaps with Bildung (Buckingham 2010. In: Bachmair (ed.), pp. 59-60). Nevertheless, here the literal translation formation, or more precisely self-formation, is considered appropriate for capturing the essence of the term
(see Dietrich et al. 2013, pp. 22-25; also Sjöström/Eilks 2020, p. 56). This should be distinguished from Dewey’s understanding of "education as formation." In his criticism of the Herbartian tradition, which was shaped in part by his experience of its successors, Dewey associates this approach with the external shaping of learners according to prescribed didactic principles (Dewey 1922, pp. 81-84).[15] The emphasis on self-determination certainly brings the concept closer to approaches associated with the activity school, insofar as formation is pursued by fostering independent learning processes that inspire self-formation within society (Matthes 2024, pp. 276, 279–280; Dietrich et al. 2013, pp. 22–23).

Fröbel

Subsection:

Coming from modest circumstances, Fröbel developed his vocation as an educator beginning in 1805, at the age of 23, through a lifelong process of self-formation, continually extending his knowledge and abilities through experience, study, and work (Seidel 1883. In: Fröbel, pp. VII–XII). This included working with Pestalozzi for two years and critically engaging with the pedagogical conception he encountered there; subsequently Fröbel studied natural sciences, with a particular emphasis on crystallography as a foundation for his own pedagogical vision, which he continued to develop through his practice as an educator (pp. X–XII). He understood the educator's work as a human garden (Menschengarten), "reaching out" for a nurturer's careful eye (Fröbel 1827. In: Heiland/BBF (ed.), p. 32R). The garden metaphor subsequently reappeared in his conception of a children's garden (Kindergarten) as a paradise of development to return to the children (Fröbel 1848. In: Heiland/BBF (ed.), p. 50).[16]

Fröbel presented the conception he developed with colleagues as the Common German Educational Institution in Keilhau near Rudolstadt (Fröbel 1822). There he states:

All phenomena and events of human life, together with their effects, as they affect the individual or a community, have their basis in the course and stage of development of the disposition and mind of that individual and community; thus, even contradictory and, more generally, defective manifestations of life have their sole source in a contradictory and defective development and formation of that disposition and mind.[17]

He observes a common uneasiness with the circumstances of his time, which are experienced as contradictions to healthy human development, from which the demand for necessary change emerges. Fröbel and his allies are concerned with the concrete development of disposition and mind within an educational environment that responds to the individual's course of development while remaining connected to the family and the larger community. This development, however, is not to be shaped according to arbitrary external principles, but according to the necessary and enduring laws inherent in human disposition and mind, which Fröbel regards as underlying and conditioning other phenomena of human life. This conception of development consequently becomes a principle for the organisation of educational practice.

In his didactics laid out in Human Education (Menschenerziehung, first published in 1826; Seidel 1883, p. I), Fröbel argues for fostering development through processes of self-formation starting in the earliest childhood within the family to be continued in school—two interconnected contexts of development in his model (Fröbel 1883, p. 161). He opposes pedagogical approaches centred on the transmission of knowledge, instead insisting on supporting the developmental potential inherent in children (pp. 162-164). For this purpose, he suggests various common means of supporting self-formation (gemeinsame Bildungsmittel) intended for those involved in family and (pre-)school life to nurture children's learning (pp.164-245). These practices provide the foundation for school education, which is continued through what he calls more school-based means of supporting self-formation (mehr schulische Bildungsmittel) pp. 245-281.

Fröbel distinguishes three phases of child development, the suckling, the infant, and the pupil.[18] The first phase is characterised by the baby's non-verbal encountering of the world through the senses and activities such as sucking and grasping—crucially requiring frequent opportunities to get in contact with the world through tools (pp. 27-30). The second phase is characterised by increasingly developed bodily control and the emergence of speech—fostered within the family through play as the characteristic activity of childhood, alongside careful language education as the educating persons' primary concern (pp. 31-56). Across these phases, development is therefore not conceived as a process occurring independently of activity and education, but as one that unfolds through the child's progressively changing ways of engaging with the world.

In contrast with Rousseau—who imagined a single male tutor selected for the male child "of rank" before birth and responsible for the education of that individual throughout his life to remain unaffected by wealthy people's socialisation (Rousseau 1918, pp. 19-21)—Fröbel explicitly identified women as the more suitable educators for children generally with his Draft of a Plan for the Establishment and Implementation of a Children’s Garden (Kindergarten), a General Institution for Promoting Comprehensive Attention to Children’s Lives, Particularly through the Cultivation of their Impulse to Act[19]; he attributed women's particular educative competence to their traditional social position (Fröbel 1840, pp. 5-7). These educators were intended to professionally support the families in developmentally appropriate childcare during the infant phase, prior to schooling; Fröbel calls the children entrusted to the Kindergarten Bildlinge—a neologism that might be rendered as formationlings, designating them not merely as children under care but as persons in the process Bildung, including their own activity and development beyond this phase (p. 9).

Ultimately, the recognition of language as distinct from the things it denotes—as a thing in itself—marks the transition to the third phase of childhood: the former infants develop into pupils, and their educational environment is extended through schooling (Fröbel 1883, pp. 58–59). Fröbel defines school as the pursuit of bringing the nature and life inherent in things and in the individual's self to the pupil's mind, and identifies school lessons as the means and path towards the purpose of schooling: fostering insights into the unity of things and utilising this unity for everyday life's activity (pp. 80–81).

Across these phases and adapted to them, Fröbel proposes the common means of supporting self-formation. These include physical exercises; observation and exploration of the surrounding natural environment, providing opportunities for language development through exercises and lyrics; the development of spatial perception through meaningful handicraft work and geometrical drawing exercises; engagement with colours through painting; self-directed learning through free play;[20] as well as storytelling and excursions (pp. 164–166]). A Bildungsmittel therefore is not necessarily a single activity. It is an organised means through which a plurality of formative activities can become possible. For Fröbel, the unifying principle of these activities is a religious conception of the world, through which the various forms of learning are understood as connected to one another.

The more school-based means supporting self-formation build upon these common means established within the early working bond of family and educators. They include arithmetic and geometry, as well as focused practices for refining spoken language and fostering writing and reading skills.

Within these Bildungsmittel, Fröbel's gifts (Gaben) occupy a particularly systematic place as material means of their enactment. Drawing on observations of children's play and of the objects and tools with which they engaged, he developed a coherent series of materials and explored the formative possibilities afforded by their use (see Fröbel 1839, In: Heilandt/BBF (ed.), pp. 249-250, 254-255, 257). The gifts were arranged in a progression of increasing complexity and offered to children in ways adapted to their development. Their purpose was therefore not simply to provide objects for play, but to furnish an environment in which children's activity could become increasingly differentiated and through which relations, forms and patterns could be experienced and explored. The gifts therefore provide a particularly tangible example of Fröbel's broader conception of education: rather than supplying knowledge for passive acquisition, educational means are to support the child's own activity and thereby mediate processes of self-formation.

Logo as another Bildungsmittel

Papert's claim that "we had to wait for Piaget to tell us how children think" finds another counterexample in Fröbel, whose systematic pedagogical and didactic work—like Dewey's—was deeply concerned with children's thinking processes and the ways in which they engage with and make sense of the world surrounding them. Moreover, Fröbel's development of tools for learning through play—based on observations of children's activities and considerations of the learning possibilities afforded by such tools in relation to particular learning contents, and situated within a progressively extending social context—may provide fruitful connections to Logo. From a Fröbelian perspective, the educational programming environment itself might therefore be regarded as an organised mediating environment—a further Bildungsmittel supporting processes of self-formation through facilities for interacting with the environment, such as Logo's programming facilities and through microworlds, whose constraints are deliberately established by the learner or educator to structure the space of possible problems and actions.

Klafki

Subsections:

Klafki introduced the distinction of Bildungsinhalt and Bildungsgehalt into the discourse of general didactics. A possible translation of the former is educational content or content to be taught, while the latter may be understood as educational substance or content with educational substance (Meyer/Rakhkochkine 2017, p. 21-22). As alternatives, the terms formative content and self-formational substance are used here, emphasising the distinction between the content selected for education and the formative substance it can make accessible to the learner.

This distinction opens the selection of formative content within the established educational system to critical examination. It thereby raises a further question: what should education mean when self-formation is conceived as a possibility addressed to everyone—as general education or general formation, Allgemeinbildung? Klafki takes up from Hegel's dialectics the reciprocal mediation of subject and world through which the subject comes to itself, while critically appropriating this relation without Hegel's metaphysical conception of an absolute Spirit as the ultimate ground of the historical process. For Klafki, the self-formation of the individual towards the capacity for self-determination is possible only through the medium of a universal (Allgemeines): engagement with historical objectivations of humanity and the conditions underlying them, not in retrospective historicisation but in orientation towards possibilities and tasks of further human development. (Klafki 1986, pp. 462-463).

This renders individuality and sociality central concepts within the classical conception of Bildung. Human formation is understood as necessarily developing a substantial individuality, which is always constituted in relation to the social context rather than directed towards isolated individuality. The constitution of the individual does not restrict or diminish the validity of the universal; rather, individualisation is understood as a condition for unfolding the potential richness of the universal. (p. 463)

Klafki resists drawing directly on the concrete answers of German Classicism. Instead, he asks how the universal through which human self-determination acquires substance must be understood under late twentieth-century conditions. For him, what can provide a pedagogically binding orientation for Bildung must be what centrally concerns us and, foreseeably, succeeding generations: the key problems of our societal and individual existence. (p. 466)

Ultimately, Klafki identifies a third fundamental determination of Allgemeinbildung in the classical conception: alongside self-formation (1) for everyone and (2) in relation to a universal, Bildung is also conceived as (3) comprehensive human formation. This entails the development of multidimensional possibilities for human beings to relate to nature and to human-historical reality, at least across moral, epistemic, aesthetic—including play—and vocational dimensions, while remaining bound to the unity of the responsible person (pp. 466-472). The resulting conception is therefore not one of accumulating competencies or perspectives, but of developing the capacity to relate to reality in its different dimensions while retaining responsibility for their integration within one's own person.

Thus, the individual's self-formation aims at becoming and remaining capable of a reflective, meaning-seeking reason within an increasingly complex world, in which human beings participate in ever more differentiated forms of labour that may become opaque and beyond their individual influence. Klafki therefore expects pedagogically responsible education to foster a critical understanding of science and technology and of their effects on nature, society, and the individual. (pp. 467-468)

Klafki therefore concludes that, for the present, Allgemeinbildung means self-formation for everyone towards the capacities for self-determination, co-determination, and solidarity. It entails a critical engagement with a continually reconsidered structure of the universal, beginning from what concerns us all, as well as the formation of all human dimensions of ability recognisable in the present. Since the task of democratisation can never be regarded as finally accomplished, Klafki argues that Allgemeinbildung must also oppose emerging tendencies towards depoliticisation and be understood as political formation towards the active participation in an ongoing process of democratisation (pp. 474–475).

He acknowledges the different conditions of childhood and adulthood in the late 20th century, characterising them as strongly influenced by traffic, mass media, consumption incentives, and a simultaneous shortage of spaces suitable for children's free play and experience. These conditions shape, without determining, the socialisation of pupils and educators both outside and within school, and shape the lifeworld from which meaningful learning processes must take their bearings. For Klafki, the classical reform-pedagogical image of the primary-school child no longer corresponds to these circumstances. He instead observes a growing tension between different dimensions of the child's personality, reflecting contradictions and inconsistencies experienced within society. As an example, he notes that contemporary primary-school children may be capable of discussing aggression at a remarkably differentiated level without yet being equally capable of practically regulating their own aggression. He interprets this discrepancy as indicating two things: contemporary children may be capable of being challenged cognitively to a greater extent than was previously assumed, while their experiences of contradiction can provide opportunities for critical reflection when processed through appropriate concrete examples and forms of expression; at the same time, it has become more difficult to support children in bringing the possibilities and needs associated with their different dimensions of ability into a balance that is satisfying to themselves. (Klafki 1992. In: Lauterbach et al. (ed.), p. 17)

However, it is the duty of school, particularly primary school, to provide a child-appropriate space of experience in which children can process experiences they bring with them, gain and reflect on new experiences, and progressively develop their comprehensive self-formation (p. 18). Within this space, Klafki proposes curriculum-theoretical considerations of Bildungsinhalt and Bildungsgehalt, particularly for General Studies, oriented towards interconnected key problems characteristic of the present epoch (epochaltypische Schlüsselprobleme). These include the question of war and peace; the ecological question; the growth of the world population and the associated problem of limited resources; socially produced inequalities; the need for a critical engagement with contemporary technological, information, and communication media, including their possibilities and risks, their effects on the division of labour, employment, and interpersonal communication; and the relationship between individual claims to happiness, interpersonal responsibility, and recognition of others (pp. 19–21).

Klafki introduced a critical-constructive didactical framework for analysing the self-formational substance of curricula and larger lesson series in the light of epochal-typical key problems and the continuing development of Allgemeinbildung. He presents this framework as a critical transformation of humanistic didactics (Geisteswissenschaftliche Didaktik), the dominant approach in German educational thought during the Weimar Republic until 1933 and in West Germany between 1945 and around 1960 (Klafki 2007, pp. 84–86). The critical aspect of this transformed approach lies in analysing the conditions and impediments that prevent teaching and learning from contributing to the development of self-determination, co-determination, and solidarity; its constructive aspect lies in the practical orientation of this analysis towards developing, designing, and testing possible ways of overcoming such impediments (pp. 89–90).

This critical-constructive perspective also revises the didactic analysis that Klafki first introduced in his doctoral dissertation (Klafki 1957). The analysis is guided by seven interdependent fundamental questions, addressed to educators as prompts for critically and self-reflexively examining their lesson planning, including potential difficulties arising for and within a particular group of learners (Klafki 1997. In: Gudjons/Winkel (ed.), pp. 17-31):

  1. What significance does the selected thematic context and intended learning objective have for the concrete learners' and educators' present?
    This includes both general conditions of socialisation and more specific conditions, such as living in a particular region or belonging to a particular social or cultural group. It also requires educators to reflect on their own preconceptions, prejudices, and interests as constitutive perspectives that may themselves become subject to questioning during the learning process. These considerations may prepare educators for the different perspectives of the pupils and for their discussion. (p. 19-21)

  2. What significance does it have for the learners' and educators' future?
    This question complements the first and involves the same reflective movements. (ibid.)

  3. What is the selected thematic context's exemplary significance?
    The potential topic needs to provide opportunities to explore more general relationships, regularities, structures, contradictions, and possibilities for action. (pp. 21-25)

The first three questions constitute what Klafki calls the Begründungszusammenhang (context of justification), concerning the pedagogical grounds for selecting the content. Each of these questions is interrelated with the fourth question, while the fifth question is to be answered in relation to the results of this analysis:

  1. What is the topic's structure, and what are the educational objectives? Here, various subquestions guide the analysis of this aspect (pp. 25-27):
    a) From which perspectives is the topic to be addressed?
    b) What is the topic's inherent methodological structure when considered from the respective perspectives identified?
    c) What are the moments that constitute the topic from the respective perspectives?
    d) How are the identified moments (structural factors) related to one another?
    e) Does the topic have a layered structure, such as surface and deep structures?
    f) What are the larger contexts in which the topic is situated, depending on the perspectives taken?
    g) What are the necessary conceptual and kategorial prerequisites for engaging with the topic, and which methods and procedures do the pupils need to bring with them or acquire in the course of working through the topic?

    Kategorial prerequisites refers to Klafki's concept of kategorial formation (kategoriale Bildung) which describes a reciprocal opening-up (doppelseitiges Erschließen) of learner and world through the disclosure and appropriation of general structures—category-mediated formation. Such a formation has a material and a formal side. On the material side, formative paradigmatic content becomes accessible to the learner; on the formal side, its appropriation constitutes a self-formational movement towards generalisable insights (Klafki 1970 cited in: Hauck-von den Driesch 2003, p. 110).

  2. In what ways can the successful process of appropriation or engagement be demonstrated or assessed?
    This question addresses both the teacher and the pupils. The latter are to become increasingly able to evaluate their own learning processes in relation to understood or jointly determined and justified objectives, within their group and through the ability to discuss disagreements critically and constructively. (Klafki 1997, pp. 27-28)

These two questions concern the thematic structuring and Erweisbarkeit (demonstrability) during the overarching analysis of lesson series planning. The sixth question is to be answered in relation to them:

  1. How may the topic become accessible and representable (in the broader sense of the term)?
    Access may be provided, among other things, through concrete actions, games, explorations, reconstructions or constructions, through presentation or defamiliarisation through media such as pictures, models, mashups, movies etc. Again, the analysis of the conditions provides indications of approaches suitable for the concrete group of learners, as well as of possible interfering factors. Klafki poses an example of a learning series about the topic of holidays, where different groups reacted differently to the same intervention intended as an introductory impulse: the use of travel brochures to initiate reflection on their own holiday experiences left many children uninterested for whom foreign travel was socially and experientially distant. Consequently, Klafki emphasises that answering the sixth question also involves considerations of the institutional conditions of schooling, including the question of how given conditions can be altered for the purpose of conducting the planned lessons. (pp. 29–30)

This question hence outlines the problem of accessibility and representability. It connects to the seventh question in this framework to be answered in its regard, facing the problem of structuring the teaching and learning process:

  1. How can the process of teaching and learning be structured methodically?
    Here, Klafki connects to "older and more recent approaches of teaching and learning research and classroom interaction analysis." Teaching and learning methods need to be considered both as ways of learning and learning aids serving the respective topic, and as motivations, mediations as well as possible limitations of social learning processes; these considerations inform the deliberate planning of applying particular methods taken into account. (p. 30)

Klafki characterises this general didactical concept of lesson planing as an instrument to name and raise the educators' awareness of dimensions and general criteria of lesson planning that inform concrete, reasoned decisions within the respective concrete pedagogical situations. It needs to be specified by the specialised didactics of the disciplines involved in the planned lessons. However, these specifications are grounded in the answers established through the analysis informed by the general didactical foundational questions. Klafki's framework explicitly aims at joint planning of thematically determined sequences of lessons which are treated as planning units. Such planning is intended to become open in the sense of enabling the educators to flexible classroom actions: the criterion for the didactical quality of a concrete scheme is the extent to which the planning enabled both the educators to didactically reasonable, flexible actions within the classroom, and the pupils to productive learning processes that contributed to their developing capacities for self-determination and solidarity. The complexity of the instrument recommends its occasional, exemplary full application as a reflexive tool in educators' ongoing professionalisation. (pp. 31-32)

Aebli and Klafki brought into dialogue

Aebli formulates his critique of Klafki's first version of the didactical analysis—based on five foundational questions—from his developmental psychological perspective as more multifaceted and complex than necessary, being potentially overextended and speculative, while essentially requiring a conceptual analysis of the respective topic (Aebli 2019, pp. 262-264). However, Klafki's revised version outlined here reveals that Aebli's and Klafki's general didactical approaches address different aspects of the didactical problem: while Aebli aims at making the cognitive structure of learning analysable and making teaching operationally tractable—his didactics therefore naturally connect with Klafki's seventh question, but also with subquestion g of the fourth question—Klafki aims at a reflexive planning of thematically connected lesson sequences that goes beyond questions of knowledge acquisition and also includes questions of the (self-)formation of the person in relation to the world.

The differentiation matrix can be seen as a possible way of bringing both systems into fruitful dialogue in the light of the shared learning object, where Aebli's approach underlies the vertical cognitive axis, and Klafki's critical-constructive considerations may guide the planning of the thematic complexity on the horizontal axis. In this relation, the concrete cognitive progression within each column of the matrix may be considered in the light of Klafki's questions 4g and 7, while Aebli's account of cognitive demands may help translate Klafki's thematic intentions into teachable arrangements that inform the design of each row. See also Kracke 2023, pp. 47-49; Sasse/Schulzeck 2023, pp. 74-75.

Microworlds as Potential Paradigmatic Operational Fields, and Topics Significant for Learners' Present and Future

The term microworld is not exclusive to Logo as conceptualised by Papert in Mindstorms, nor does it refer to a single, uniform type of learning environment.[21] It has also been used in psychological research on complex problem-solving since the 1970s, which has subsequently influenced educational research (Dörner/Funke 2017, p. 2; Funke 2010). In this context, microworlds are computer-based simulations of complex systems, such as a city, in which participants may assume roles such as that of a municipal administrator and explore the consequences of their decisions. These environments typically provide a predefined set of actions through a user interface, such as control buttons or limited textual input, rather than requiring users to formulate and execute programs as a means of interacting with the simulated system.

This distinction helps to clarify the particular potential of Logo-based microworlds. Rather than merely selecting from predefined actions, learners can formulate, modify, and execute procedures that shape their interaction with the environment. However, the educational potential of a microworld does not follow from its designation as such, but from the relations between its structure, the learner's activity, and the possible objects of learning. The question, therefore, is under what conditions a Logo microworld might provide a potential paradigmatic operational field in which learners can engage in activities that make topics significant both for their present experience and for their future learning, from a CHAT-informed perspective.

Assessing this potential therefore requires considering not only the learning opportunities a microworld affords, but also the formational, educational significance of the topics with which learners engage. In Klafki’s terms, this includes examining their significance for learners’ present and future lives. This significance encompasses both learners’ immediate experiences and learning processes and the broader biographical, historical, and societal horizons within which these take place. While the former can be related more directly to learners’ existing knowledge and experiences, the latter necessarily involves a degree of anticipatory and speculative reflection on possible future life situations and forms of social participation.

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Representation, mediation, and meaning

Subsections:

The purpose of this section is to bring together selected perspectives on how meaning is constructed and negotiated in classroom activity, and on the roles that representations, artefacts, language, and social interaction play in this process. Rather than seeking to integrate these perspectives into a unified theoretical account, the section presents them as distinct but potentially complementary lenses for understanding mathematical and computational activity, informing the design of learning environments, and analysing classroom interactions.

Symbolic Interactionism (Blumer)

Although this research orientation has taken many forms and has been developed by numerous contributors since the late nineteenth century (Denzin 1992, p. 2-3; Faberman 1985, p. 13). Blumer's formulation of Symbolic Interactionism (SI) is of particular interest here. He coined the term "in an offhand way" (Blumer 1969, p. 1), which subsequently came to label a tradition rooted in the work of James, Mead, Cooley, and also Dewey. Blumer himself identifies Mead as the main influence on his approach, which nevertheless developed into a distinct methodological perspective (Blumer 1969, p. 1-2; McPhail/Rexroat 1979, p. 449).

Here, three premises guide the analysis (Blumer 1969, p. 2):

  1. Human beings act toward things on the basis of the meanings that the things have for them.
  2. The meaning of such things is derived from, or arises out of, the social interaction that one has with one's fellows.
  3. These meanings are handled in, and modified through, an interpretive process used by the person in dealing with the things [that person] encounters.

Blumer emphasises that the meanings that things have for human beings cannot simply be disregarded, but must be treated as objects of inquiry in their own right; he therefore criticises the behaviourist paradigm in psychology and sociology of his time, where factors such as stimuli, attitudes, motives, status demands, and social roles were alleged to produce behaviour, while meaning was either deemed irrelevant or treated merely as a link between such factors and the behaviour they were assumed to produce (pp. 2-3). Moreover, Blumer sees meaning as arising out of the process of interaction between people. In doing so, he opposes what he describes as a "traditional position of 'realism' in philosophy", according to which meaning is inherent in things and no process of meaning formation is involved: meaning is simply disengaged by observing the thing that is deemed to "have" it (pp. 3-4). Ultimately, Blumer conceptualises interpretation as a two-step process (p. 5). First, it is an internalised social process in which the actor interacts with themselves: through inner communication, the person forms, selects, and directs the meanings of the things that become targets of their action. Second, this inner communication makes interpretation a matter of handling meanings in relation to the situation in which the action is to take place.

Heuristic inquiry (Pólya)

Semiotics and Programming Languages (Zemanek)

Theory of Semiotic Mediation (Bartolini Bussi/Mariotti)

Register shifts as transformations (Duval)

Dual conceptions and mathematical discourse (Sfard)

Artefact-centred activity and instrumental genesis (Rabardel)

Semiotic activity in social practice (Radford)

Bootstrap (Schanzer et al.)

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Environment

Scaffolding (Wood/Bruner/Ross)

Cognitive Load Theory (Sweller/Chandler)

Staged learning aids (Gestufte Lernhilfen)

"Help me to help myself" (Montessori)

Creating socially meaningful artefacts supported by teachers (Freinet)

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Agency

Dialogue, agency, and critical literacy (Freire)

Education for Self-Reliance (Nyerere)

Education in a language that is not one's own (Ngũgĩ wa Thiong'o)

Annotations

[1] Dewey introduced "Education as Conservative and Progressive" through his sixth chapter of "Democracy and Education." The conservative model of education discussed by Dewey is largely directed at the Herbartian tradition that had become influential by the late nineteenth century, which he opposed. Dewey contrasts these orientations by characterising conservative education as "accommodating the future to the past," whereas progressive education uses "the past as a resource in a developing future" (Dewey 1922, pp. 92-93).

[2] The terminology of Western thought is nevertheless also used by Papert, who refers to "the history of Western thought" (Papert 1980, p. 119), as well as by Holma et al., who speak of "current Western ways of thinking" and "modern Western thinking" (Holma et al. 2023, p. 269). Such usage reflects a persistent geographical and ideological dichotomy whose modern political form was strongly shaped by the Cold War division between the capitalist "West" and the communist "East" after 1945, a distinction that acquires its apparent absoluteness only when the globe is represented as a two-dimensional map centred on a particular standpoint. This opposition itself has deeper historical antecedents in the shifting distinction between "Occident" and "Orient", although these categories have never denoted stable or homogeneous cultural entities. The subsequent globalisation of intellectual, economic, and political exchange has made Western thought increasingly difficult to sustain as a coherent category. Yet the categorisation was already problematic during the Cold War: communist societies remained deeply entangled with scientific and philosophical traditions that had developed in Europe since the seventeenth century, while those traditions themselves crossed political and cultural boundaries.

[3] Лео́нтьев is the Cyrillic form of the researcher's name, often transliterated as Leont'ev in literature on cultural-historical activity theory. The apostrophe represents the Cyrillic soft sign ь and serves the purposes of transliteration, particularly bibliographic identification. In some sans-serif fonts, it may visually suggest an "i", while in some serif typefaces it may instead resemble a "j", suggesting a y-like sound to readers familiar with languages using that value for j. Leontiev, however, is preferred here as one possible approximation of the Russian pronunciation that remains independent of the typeface.

[4] A contemporary example (2026) of a predominantly CAI-oriented environment is the Anton app, which is widely used in primary schools in Berlin and other German educational contexts.

[5] Miettinen (1999, p. 175) uses "object-oriented" for German "gegenständliche" in Marx's Theses on Feuerbach (1845), who in his first thesis states: "aber er [i.e. Feuerbach] faßt die menschliche Tätigkeit selbst nicht als gegenständliche Tätigkeit" (= "but Feuerbach does not conceive the human activity in itself as 'object-oriented' activity"). Miettinen's translation is particularly relevant here because it connects Marx's gegenständliche Tätigkeit to the later activity-theoretical notion of object-oriented activity. The proposition forms part of Marx's critique of the philosophical tradition of "materialism" in his time, which he characterises as "der anschauende Materialismus" ("contemplative materialism") in the ninth thesis. This materialism is described in the first thesis as merely conceiving the object, the reality, the sensuality as objects of contemplation ("nur unter der Form des Objekts oder der Anschauung gefaßt"). Marx opposes this contemplative materialism with a conception of reality grounded in practical, social human activity, developed more fully in his later historical-materialist work.

[6] The present analysis follows the spatial logic of the diagram as published by Engeström (1987), although the placement differs from the clearer mediation relation represented in Vygotsky's original triangle.

[7] "Lifeworld" is used here as a useful, intuitively intelligible general term, although it does not belong directly to the CHAT framework. The term has its philosophical origin in Husserl's phenomenology, particularly his later critique of the objectivist abstraction of the sciences from the pre-scientific world of lived experience. In sociology, Schütz appropriated phenomenological concepts in The Phenomenology of the Social World, thereby contributing to the development of sociological approaches concerned with the constitution of everyday social reality and influencing later constructivist and communication-theoretical traditions.

[8] The term in use at the time was literally “education for the disabled” (Behindertenpädagogik). However, the work of Jantzen and Feuser was directed towards developing a theoretical foundation for what is today understood as inclusive education.

[9] Page references refer to the second edition published in 2023; the revised third edition is scheduled for publication in 2026.

[10] Originally "Integration", the synonym of inclusion in Germany at that time.

[11] Original quote: Integration = die gemeinsame Tätigkeit (Spielen/Lernen/Arbeit) am gemeinsamen Gegenstand/Produkt in Kooperation von behinderten und nicht-behinderten Menschen.

[12] Original quotes: "... 'in Kritik an traditionell-psychologischer Begrifflichkeit' mit Blick auf den 'historisch gewordenenen Mensch-Welt-Zusammenhang' [ersetzte Holzkamp] unter anderem folgende Begriffe: 'im Konzept der "Kooperation"' ist das 'bürgerliche Interaktionskonzept aufgehoben', "im Konzept der "Tätigkeit" das bürgerliche "Verhaltens"-Konzept, im Konzept der "Gegenstandsbedeutungen" das bürgerliche Konzept der "Reizgegebenheiten."'"

[13] This resembles Hegel's notion phrased in his quote: By thinking a physical object, I transform it into a thought and thereby remove its sensual quality; I make it something essentially and immediately my own: for only in thought am I with myself; only comprehension— conceptual grasping—pierces through the object, which no longer opposes me, and from which I have taken the particularity that it held against me for itself. ("Indem ich einen Gegenstand denke, mache ich ihn zum Gedanken und nehme ihm das Sinnliche; ich mache ihn zu etwas, das wesentlich und unmittelbar das Meinige ist: denn erst im Denken bin ich bei mir, erst das Begreifen ist das Durchbohren des Gegenstandes, der nicht mehr mir gegenübersteht und dem ich das Eigene genommen habe, das er für sich gegen mich hatte." Hegel 1986, p. 47) — Here, Begreifen carries the double sense of intellectual comprehension and literal grasping (greifen), which is difficult to preserve in English. And although I am with myself in my thought echoes Descartes, the dialectical movement does not reduce the relation to a split between subject and object, but relates the thinking subject to perceivable objects.

[14] Aebli completed his doctoral degree at Piaget's institute in 1951. Papert worked there from 1958 to 1963.

[15] This criticism should not, however, be taken as an exhaustive assessment of Herbart’s own work or of its possible contribution to a more systematic understanding of teaching and learning.

[16] Coincidentally, the garden metaphor reappears in the cLogos project, emerging from the description of forking a GitHub tree and leading to a Taxonomy of care and stewardship, complementing a prior Taxonomy of bugs. Thus, this garden, too, requires the gardeners' careful eyes. These gardeners are stewards who do not manufacture the garden's growth but cultivate and nurture it through caring for responsible growth.

[17] Original quote: "Alle Erscheinungen und Begegnisse des menschlichen Lebens mit ihren Wirkungen, so wie sie den Einzelnen oder eine Gesammtheit treffen, haben ihren Grund in dem Entwickelungsgange und der Entwickelungsstufe des Gemüthes und Geistes dieses Einzelnen, dieser Gesammtheit; so daß also auch die widersprechenden, überhaupt fehlerhaften Erscheinungen des Lebens in widersprechender, fehlerhafter Entwickelung und Ausbildung des Gemüthes und Geistes derselben ihre einzige Quelle haben."

[18] Fröbel's original distinction is Säugling (= suckling/baby), Kind (= child), Knabe (= boy child). However, as a Kind he describes a child already able to walk during language development, which in contemporary German would be called a Kleinkind (= infant). The use of Knabe also reflects the gendered educational vocabulary of his time; here it is therefore interpreted functionally as Schulkind (= pupil).

[19] Original quote: "Entwurf eines Planes zur Begründung und Ausführung eines Kinder–Gartens, einer allgemeinen Anstalt zur Verbreitung allseitiger Beachtung des Lebens der Kinder, besonders durch Pflege ihres Thätigkeitstriebes"

[20] What later appears as "self-directed learning through free play" can thus be recognised as only one element within Fröbel's considerably broader conception of Bildungsmittel. Possible selective receptions that elevated free play into a general pedagogical principle, framed here as "one-eyed naturalistic orientations" arguably detached it from the wider system of activities through which Fröbel conceived development.

[21] In German science education and political education, the terms microworld and macroworld may also be used to distinguish between phenomena and processes considered at the micro and macro levels, respectively. See, for instance, Gehlert 2020, pp. 291, 544; Grammes 1995.

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