Planning Adaptive Instruction

Computational Core

Use scripts/kst_utils.py analytics for all class-wide computations. Do not compute mastery rates, target scores, or clusters manually.

# Run class-wide analytics:
python3 scripts/kst_utils.py analytics <graph-path>

# Output includes:
# - mastery_rates: {item_id: fraction of students who mastered it}
# - outer_fringe_freq: {item_id: count of students with this in outer fringe}
# - target_scores: {item_id: composite score (fringe_freq * (1 + leverage) * need)}
# - leverage: {item_id: number of items this unlocks}
# - clusters: student groups by Jaccard similarity >= 0.6
# - n_students: total student count

# Supplementary checks:
python3 scripts/kst_utils.py stats <graph-path>
python3 scripts/kst_utils.py validate <graph-path>

Methodology

1. Class-Wide State Analysis

Item-level statistics (from kst_utils analytics):

• Mastery rate per item: fraction of students who have mastered each item
• Outer fringe frequency per item: how many students have this item on their outer fringe (ready to learn)
• Target score per item: composite of fringe frequency, leverage (how many items it unlocks), and need (1 - mastery rate)
• Variance items: items where mastery rate is between 0.3 and 0.7 (high disagreement -- these differentiate the class)

CbKST competence-level analysis:

• Fraction of students possessing each competence (from competence_state)
• Commonly missing competences: competences absent from > 50% of students
• Fringe competences: competences that, if taught, would move the most students' outer fringes

Identifying teaching targets:

Select items with highest target scores, constrained by:

1. Competence need: Items requiring commonly missing competences are higher priority (teaching one competence enables multiple items)
2. Prerequisite feasibility: The item's prerequisites must be mastered by a sufficient fraction of the class (typically > 60%) for whole-class instruction
3. Session scope: Limit targets to what can realistically be covered in the session duration

2. Student Clustering

The analytics command clusters students by Jaccard similarity (threshold >= 0.6). For each cluster, analyze:

• Shared foundation: Items mastered by all members of the cluster
• Competence profile: Competences possessed by all/most members
• Cluster targets: Items on the outer fringe of most/all cluster members
• Missing competences: Competences needed for cluster targets but not yet possessed
• Distinguishing features: What separates this cluster from others (items/competences that differ)

3. Learning/Forgetting Considerations

• Forgetting risk assessment: For each student, identify inner fringe items mastered > 2 weeks ago. Aggregate to find items with class-wide forgetting risk.
• Class-wide forgetting risk: Items where many students mastered them long ago and may need reinforcement.
• Spacing decisions: If review items overlap with teaching targets' prerequisites, integrate review into the session opening rather than as a separate activity.

For the full bivariate Markov model and forgetting-aware session planning detail, see references/differentiation-strategies.md.

4. Peer Tutoring Opportunities

Identify peer tutoring pairings where one student's knowledge directly supports another's learning:

• Tutor's inner fringe overlaps learner's outer fringe: The tutor has recently mastered the item the learner is ready to learn. This means the tutor can explain with fresh understanding.
• Bidirectional pairings: The ideal pairing is where Student A can tutor Student B on item X, and Student B can tutor Student A on item Y (each has knowledge the other needs).
• Competence-based matching: Pair students who share most competences but differ on 1-2, so the tutor can teach the specific missing competence.

5. UDL 3.0 Session Design

Apply UDL principles to the session structure:

• Engagement: Offer choice in differentiated activities; connect content to student goals; build in collaborative and individual work
• Representation: Present key concepts in multiple formats during the core instruction; provide visual summaries and worked examples; activate prerequisite knowledge explicitly
• Action & Expression: Allow varied demonstration of learning during the checkpoint; provide planning support for differentiated work; offer formative feedback throughout

For extended UDL 3.0 session design guidance with examples for each principle, see references/differentiation-strategies.md.

6. Optimal Session Sequencing

Structure the session in four phases:

7. Prerequisite Ordering

Within the session, respect the surmise relation and competence_relations:

• Teach prerequisite items/competences before the items that depend on them
• If a session targets multiple items, order them by the prerequisite chain
• If items are independent (no prerequisite relationship), order by target score (highest first)

Output

1. Class State Overview

Students assessed: <n>
Domain items: <total>

Mastery distribution:
  0-25% mastered:  <n> students
  25-50% mastered: <n> students
  50-75% mastered: <n> students
  75-100% mastered: <n> students

Competence distribution:
  <comp-id>: <n>/<total> students possess (<percentage>)
  ...

Class-wide outer fringe (top targets by composite score):
  <item-id>: target_score=<value>, fringe_freq=<n>, mastery=<rate>, leverage=<n>
  ...

Forgetting risk items (mastered >2wk ago by >30% of class):
  <item-id>: <n> students at risk
  ...

2. Student Clusters

For each cluster:

### Cluster <n>: <descriptive name> (<n> students)

Students: [<student-ids>]
Shared foundation: [<item-ids mastered by all>]
Competence profile: [<comp-ids possessed by all>]
Targets (shared outer fringe): [<item-ids>]
Missing competences: [<comp-ids needed for targets>]
Distinguishing features: <what separates this cluster from others>

3. Instruction Plan

## Session Plan: <title>
Duration: <n> minutes | Format: <format>
UDL Notes: <brief UDL 3.0 design highlights>

### Opening (<n> min)
- Review: <forgetting-risk items to revisit>
- Activate: <prerequisite items/competences to recall>
- Goals: "By the end of this session, you will be able to..."

### Core Instruction (<n> min)
- Target items: [<item-ids>] (competences: [<comp-ids>])
- Sequence: <item-a> (prerequisite) -> <item-b> (depends on a) -> <item-c>
- Representation: <text explanation> + <visual diagram> + <worked example>
- Key vocabulary: <terms to define>
- Engagement: <real-world connection or motivating question>

### Differentiated Work (<n> min)

**Group 1: <cluster-name>** (<n> students)
  Activity: <description targeting their specific outer fringe>
  Choice options: <option A> or <option B>

**Group 2: <cluster-name>** (<n> students)
  Activity: <description targeting their specific outer fringe>
  Choice options: <option A> or <option B>

[Additional groups as needed]

### Peer Tutoring Pairings
  <Student A> <-> <Student B>: A tutors B on <item-x>, B tutors A on <item-y>
  ...

### Assessment Checkpoint (<n> min)
  Questions:
  1. <question targeting session item 1>
  2. <question targeting session item 2>
  ...
  Update states based on responses.

### Wrap-Up (<n> min)
  - Summary of key concepts
  - Preview of next session targets
  - Self-reflection prompt

4. Session Impact Projection

Items/competences targeted this session: <n>
Students expected to advance (have targets in outer fringe): <n>/<total>
New items unlocked if targets mastered: [<item-ids>]
Forgetting risk addressed: <n> items reviewed for <n> students
Estimated class mastery rate change: <current>% -> <projected>%

5. Recommendations

• Items that could not be addressed this session (for future sessions)
• Students who may need individual attention or /generating-learning-materials
• Whether class-wide re-assessment is recommended before the next session
• Suggestions for session format adjustments based on observed clustering patterns
• Peer tutoring effectiveness indicators to watch during the session

References

• CAST (2024). Universal Design for Learning Guidelines version 3.0. See references/bibliography.md.
• Cosyn, E. et al. (2021). ALEKS practical perspective. See references/bibliography.md.
• de Chiusole, D. et al. (2022). Learning, forgetting, and the correlation of knowledge. See references/bibliography.md.
• Heller, J. & Stefanutti, L. (2024). Knowledge Structures. See references/bibliography.md.
• Tomlinson, C. A. (2001). How to Differentiate Instruction. See references/bibliography.md.
• Vygotsky, L. S. (1978). Mind in Society. See references/bibliography.md.

See references/bibliography.md for the complete bibliography.