Adaptive Math Diagnostics & Gap Identification
Diagnose math gaps through Socratic questioning and response analysis
What You Can Do
You can move beyond surface-level "the student doesn't understand algebra" to pinpoint exactly where understanding breaks down. By asking strategic Socratic questions and analyzing student responses, you'll distinguish between missing prerequisites, misconceptions about core principles, execution errors, and lack of strategic knowledge—enabling truly personalized instruction across math and science domains.
Features
guides you to ask layered questions that reveal thinking patterns without telling the answer
sorts difficulties into foundational, conceptual, procedural, or strategic categories for targeted intervention
identifies and documents specific false beliefs or misunderstandings that block progress
adjusts questioning depth and direction based on student responses in real time
works for arithmetic, algebra, geometry, calculus, statistics, physics, chemistry, and biology
produces clear records of identified gaps for learning plans and parent/institution communication
uses conversational dialogue instead of formal testing to reduce anxiety and reveal authentic understanding
pinpoints why students perform strongly on some problems but struggle with similar ones
Example Output
Example 1: Algebra student
You ask: "Walk me through how you'd solve 2x + 5 = 13."
Student: "I'd subtract 5 from both sides to get 2x = 8, then divide by 2 to get x = 4."
You ask: "Great. Now, without solving it, tell me: does 2x + 5 = 13 mean the same thing as x = 4?"
Student: "Uh... I guess not really. One has x and the other is just a number."
Gap identified: Conceptual — Student can execute the procedure but doesn't understand that equations express equality relationships.
Example 2: Geometry student
You ask: "Why is the sum of angles in a triangle always 180°?"
Student: "Because... that's just what triangles are?"
You ask: "Have you seen a proof of that? Or learned where it comes from?"
Student: "No, we just memorized it."
Gap identified: Foundational — Student lacks prerequisite understanding of angle relationships and parallel line properties needed to justify the rule.
Example 3: Statistics student
You ask: "If you roll a die 6 times, will you definitely get each number 1–6 once?"
Student: "Yeah, because there are 6 numbers and 6 rolls."
Gap identified: Conceptual — Student confuses expected value with guaranteed outcome; doesn't understand probability distribution and variance.
What's Included
- SKILL.md instruction file with core diagnostic workflow and phase-by-phase guidance:
- Socratic Question Bank: categorized prompts for foundational, conceptual, procedural, and strategic gap detection across math/science domains
- Gap Classification Checklist: decision tree for sorting identified issues into the four gap categories
- Diagnostic Interview Template: structured conversation flow with entry-point problems, follow-up sequences, and documentation fields
- Misconception Library: common false beliefs in algebra, geometry, calculus, and science with targeted clarification questions
Who It's For
- Math tutors working with K–12 or adult learners who need diagnostic assessment before intervention
- High school and college instructors preparing to reteach or remediate students with learning gaps
- Special education teachers conducting individualized education plan (IEP) assessments in mathematics
- Homeschool educators baseline-testing students or troubleshooting inconsistent performance
- Curriculum coordinators documenting student misconceptions to inform program redesign
Best For
- Baseline diagnostics for new students or at the start of a unit to identify starting points
- Stuck-point troubleshooting when a student hits a wall and you need to find the root cause
- Inconsistency investigation when a student solves similar problems with wildly different results
- Transition validation confirming that gaps are actually closed before moving to more advanced topics
- Progress documentation creating evidence of learning for parents, institutions, or intervention programs
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