Mathematics Assessment and Intervention - KeynesYouDigIt/Knowledge GitHub Wiki

Four critical questions:

  • What do we want all students to know?
  • How will we know if students learn it?
  • How will we respond when some students do not learn?
  • How will we extend the learning for students who are already proficient?

These questions need to be standardized across all teachers to create equity.

The learning process:

  • Reflect- Work the task and ask, "Is this the best solution strategy?
  • Refine- receive FAST feedback and ask "Do I embrace my errors?"
  • Act- Persevere and ask, "Do I seek to undertand my own learning?"

Developing Assessments

Asessments are an instrument, how you administer them and what you do with the results is a process.

High quality assessment criteria:

  • Identification and emphasis on essential learning standards (with student-friendly language)
    • On the assessment, and directly tied to the tasks
    • "I can" statements
    • Only 3-6 per unit, 1-2 per mid-unit
      • Break down/unwrap into learning objectives for lessons, daily skills students should demonstrate
      • Learning objectives should reuse language from the standard, explain methods and tasks
    • These are the "big ideas" you expect students to learn
    • One proficiency level for the standard (not for LOs or questions)
  • Balance of higher- and lower- cognitive demand tasks
    • Shoot for a 70/30 rigor balance
    • Low-level tasks are memorization and rote procedures (do this, what is this)
    • High-level tasks do not have a set of predetermined procedures to follow, or ask students to justify the procedure (explain why, show your work)
    • Balance procedural fluency with conceptual fluency
  • Variety of assement-task formats and use of technology
    • Multiple question formats and modeling tasks. Use of technology is clear.
  • Appropriate and clear scoring rubric
    • What's the value of the task, then what evidence is required to receive full credit?
    • Blind double-score to validate rubric
  • Clarity of directions
    • Which tasks do you have to justify your choice or explain your solution?
    • Which tasks can you use technology for?
  • Academic language
    • Language in tasks is fair and understood by students
    • Matches language expected of students
  • Visual presentation
    • Easy to read with space for student work and feedback
  • Time allotment is fair
    • Do the assessment yourself, then have students do it. Find "your number" as a multiplier for estimating in the future.

Guaranteed Curriculum: What every student will be able to do regardless of their teacher Viable Curriculum: Adequate time to learn the guaranteed curriculum

Assessment formats:

Selected Response

  • Multiple choice
    • Question is a stem, wrong answer is a distractor
    • Every distractor should result from a common misconception
    • Each incorrect answer should provide as much data about student learning as a correct response
    • If you don't know what the common misconceptions are, do an open-ended question to gather data
    • Allowing for more than one right answer raises the rigor
    • The answers should be similar in length. If one stands out, students tend to pick that one.
    • Allow partial credit for shown work
  • Fill in the blank
  • Matching
    • The "from" list needs to be shorter than the "to" list. Otherwise, students will use process of elimination at the end, and one misunderstanding may be double-scored
    • Allow something to be matched more than one time
  • True/false
  • Questions with immediate right/wrong answer

Constructed Response

  • Short answer, shows reasoning
    • Precisely explain what kind of work you require
    • Keep the task's wording simple
    • Keep the contexts familiar to the students

Cognitive Demand Guide

Low

Memorization

  • Reproducing facts, rules, formulae, and definitions
  • Cannot be solved with procedures
  • Not ambiguous- exact reproduction needed
  • No connection to concepts

Procedures without connections

  • Algorithmic and specifically asked for
  • No ambiguity about what to do or how to do it
  • No connection to underlying concepts
  • Focus is on correct answers rather than understanding
  • No explanations required

High

Procedures with connections

  • Focus on use of procedures for understanding
  • Suggest broad pathways to follow that are connected to the underlying ideas
  • Represented multiple ways (diagrams, manipulatives, symbols)
  • Cannot be followed mindlessly

Doing Mathematics

  • Complex, non-algorithmic thinking
  • Explore and understand the nature of concepts, processes, and relationships
  • Demands self-monitoring and regulation of one's own cognitive processes
  • Access relevant knowledge and experience
  • Actively examine task constraints
  • May involve some level of anxiety due to the ambiguity

FAST Feedback

If our feedback doesn't change the students in some way, it has probably been a waste of time.

  • Fair
    • Only on the quality of the demonstrated work, not on other student characteristics
  • Accurate
    • Why an answer is right or wrong in terms that a student can understand
  • Specific
    • Specific enough that the student can identify the error in their logic, not so specific that you solve the problem for them
  • Timely
    • Within 48 hours, before too much new material has taken hold

Formative Assessment Process

  • Agreed upon standards for the unit
    • Clear, commonly worded, referenced throughout the unit
  • Common unit tests
  • Calibration of scoring agreements and student feedback
    • Regularly double-score assessments. If there is more than a point of variance, a third grader also grades and everyone has a discussion about what was unclear. Calculate your "inter-grader reliability."
    • Would it be scary if someone else graded your students? Why?
    • Use anchor papers
    • What we say in our feedback and how we say it has a big impact on how students self-identify
    • "What related facts do you know that might help you?"
    • "How could you use a graphing strategy?"
  • Student self-assessment and action after the end-of-unit assessment
    • Create a system for students to self-assess
    • Students should be able to articulate what they can and can't do
    • "As soon as a student gets a grade on a test, the learning stops."
    • You need to teach students how to reflect
    • Use proficiency graphs
    • "Reason I got this wrong" -> "Correct Answer" -> "Reason my new answer is correct"
    • Purpose is to help students take ownership of their learning
    • Peer feedback
  • Student self-assessment and action after the mid-unit assessments
    • Create a system for students to self-assess
  • Team response to student using tier-2 intervention criteria
    • Just in time

Tier-2 Interventions

Response to Intervention system:

  • Tier-1 interventions: Reteach the whole class
  • Tier-2 interventions: Reteach a small identified group
  • Tier-3 interventions: 1:1

WIN- "What I Need" time, designated spot for interventions

Criteria

  • Systematic and Required
    • Set aside time during the day
    • Set aside time in the next unit for remediation
    • Students can't opt out
    • Ideas:
      • Mandatory study hall
      • Homework help sessions
      • Peer-tutor program
      • Parent or community-led support teams
      • Lunchtime learning
      • Additional classes
      • Topic-specific learning center
      • "Assembly bell" schedule twice a week- assembly time is used for interventions
  • Targeted by standard
    • Interventions should target specific standards
    • Which specific skills do they need help with?
  • Fluid and flexible
    • Students should move in and out of interventions as needed, not fixed groups
  • Just in time
    • Real-time feedback
  • Proven to show evidence of student learning
    • Monitor progress during the intervention
    • Requires your strongest teachers
    • Requires new methods and deeper conceptual understanding

Student Trackers

  • Increase student ownership of learning
  • Highlight the things they are (or are not doing) to receive the help they need
  • Should reference student-friendly standard language
  • Students should also be able to indicate their confidence with their work (+ / check / ?)
    • Can also indicate if they were able to just do it, do them by substituting answers in, making an educated guess, or a pure guess)