12.3 Analyzing Assessment Data to Guide Instruction & Differentiate
Key Takeaways
- Diagnostic assessment precedes instruction, formative assessment occurs during it to adjust teaching, and summative assessment evaluates learning after it.
- Formative assessment is defined by its use, not its format: a quiz is formative only if its results change subsequent instruction.
- Item-level analysis reveals what a total score conceals, because two students with the same score may have entirely different gaps.
- A wrong answer chosen by most of a class usually indicates a specific shared misconception rather than random error.
- Differentiation adjusts the path to a shared mathematical goal through content, process, or product, rather than lowering the goal.
12.3 Analyzing Assessment Data to Guide Instruction & Differentiate
Skill 7 of Competency 5 is about the loop from data to decision: analyze and interpret individual student assessment data ... to guide instructional decisions and differentiate instruction. Items give you results and ask what to do next.
Assessment types by purpose
| Type | When | Purpose | Examples |
|---|---|---|---|
| Diagnostic | Before instruction | Identify prior knowledge and gaps | Pre-test, entry ticket, prerequisite check |
| Formative | During instruction | Adjust teaching in progress | Exit ticket, whiteboard response, observation, questioning |
| Summative | After instruction | Evaluate what was learned | Unit test, final project, state assessment |
[!IMPORTANT] Formative versus summative is determined by how the results are used, not by the format. A quiz whose results cause a teacher to reteach a concept is functioning formatively. The same quiz recorded in a gradebook and never revisited is summative. Items describe a use and ask for the classification, so read for what happens to the data.
Formative assessment is characterized by being frequent, low-stakes, and quickly actionable. An exit ticket that a teacher reads that evening and uses to regroup students the next morning is the paradigm case.
Assessment formats to recognize: selected-response items, constructed-response and short-answer items, performance tasks, projects, portfolios accumulated over time, observation with a checklist, and student self-assessment. Each surfaces different evidence. Selected-response items cover many topics efficiently but conceal reasoning; constructed responses reveal reasoning but cover less ground per minute.
Item-level analysis
A total score is a summary that hides the information you need.
Two students each score 12 out of 20. Student A missed six items all involving negative coefficients. Student B missed six items scattered across every topic. Same score, different diagnosis: A has one specific gap and needs targeted work on signed numbers; B's errors suggest a broader issue, possibly with reading the problems, with pacing, or with attention.
Working item by item, ask three questions:
- Which items did this student miss?
- What do the missed items have in common?
- Which wrong answer did the student choose, and what would produce it?
Distractor analysis
Well-constructed multiple-choice items build each wrong option from a specific error, which makes the chosen distractor diagnostic.
Item: A jacket costs $80 and is marked down 25%. What is the sale price? A. $60 — correct B. $20 — computed the discount amount, not the sale price C. $100 — added 25% instead of subtracting D. $55 — subtracted $25 rather than 25%
A student choosing B understands percent computation but did not finish the problem. A student choosing D confused a percent with a dollar amount. These call for different responses, and the total score would show only "incorrect" for both.
Class-level patterns matter as much as individual ones. If 70% of a class selects the same wrong answer, that is not random error — it is a shared misconception, and the appropriate response is whole-class reteaching, not individual remediation. If errors are scattered across different distractors, individual or small-group follow-up fits better.
From data to instructional decision
+---------------------------------------------------------------------------+
| MOST of the class missed it -> reteach to the whole class, |
| using a different approach |
| A SMALL GROUP missed it -> small-group targeted instruction |
| ONE student missed it -> individual conferencing |
| Errors are all the SAME -> address that specific |
| misconception directly |
| Errors are SCATTERED -> investigate broader causes |
| Most students MASTERED it -> move on; extend for those ready |
+---------------------------------------------------------------------------+
The recurring wrong answer in these items is "reteach the lesson the same way." If an approach did not work the first time, repeating it is unlikely to work the second. Effective reteaching changes the representation — moving back a stage on the CRA continuum from section 12.2, or introducing a model the first lesson did not use.
Differentiation
Differentiation adjusts instruction to student needs while holding the mathematical goal constant. Three dimensions:
- Content — what students work with. Different numbers in the same problem structure, or a scaffolded version of the same task.
- Process — how they engage. Manipulatives for some, symbolic work for others; individual, paired, or small-group formats.
- Product — how they demonstrate learning. A written explanation, a diagram, a verbal explanation, or a constructed model.
Flexible grouping is the standard implementation: groups formed from current assessment data and reformed as needs change, rather than fixed ability tracks. A student may need support with fraction operations and extension in geometry, which fixed grouping cannot accommodate.
A common item: after an exit ticket, four students cannot find the area of a composite figure while the rest can. The best response is a small-group session with those four using a decomposition model, while the others work an extension task — not reteaching the whole class, and not assigning the four an unrelated easier worksheet.
What data cannot tell you
Two cautions the exam tests:
- A single data point is weak evidence. One low quiz score may reflect illness, distraction, or an unfamiliar item format rather than a knowledge gap. Multiple measures over time give a more reliable picture.
- Assessment must match the objective. A test of computational fluency provides no evidence about problem-solving ability, and a multiple-choice test cannot show whether a student can construct a valid argument. If the objective was justification, the assessment must ask students to justify.
A teacher gives an exit ticket, reviews the responses that evening, and reorganizes the next day's lesson around the two concepts most students missed. What type of assessment is this, and why?
On a percent item, 68% of a class selects the distractor that gives the discount amount rather than the sale price. What is the best instructional response?
Two students each score 14 out of 20 on a unit test. Student A missed items only on solving inequalities; Student B missed items spread across every topic. What does this comparison illustrate?