Mathematics case study

From Diagnostic Evidence to Targeted Teaching

Year 6 Mathematics · Formative assessment

A Te Mātaiaho-aligned Year 6 sequence combining explicit place-value teaching, visual representations, diagnostic evidence, needs-based grouping, and planned extension.

THE TEACHING QUESTION

How can I identify which parts of decimal place value need another representation, explanation, or extension?

EVIDENCE I USED

I used a six-item diagnostic, place-value representations, a hinge question, verbal and written strategy explanations, practice responses, exit tickets, and short application tasks.

TEACHING DECISION

The evidence informed needs-based grouping, visual place-value models, targeted prompts, independent practice, and extension. I planned the next lesson around the specific criterion that was not yet secure rather than giving everyone more of the same practice.

CONCEPT-LEVEL RESPONSE

The status flow was class-wide. The teaching response was concept-specific.

Each check was read through a mathematical lens so that support and extension could target the idea beneath the answer.

Diagnostic evidence, teaching response, and follow-up evidence by mathematical concept
ConceptDiagnostic lensTeaching responseFollow-up evidence
Decimal representationMatch models, fractions, and decimals; explain the value represented.Reconnect grids, fraction language, decimal notation, and place-value charts in guided matching tasks.A matched representation and an explanation of what remains equal.
Tenths, hundredths, and zeroDistinguish 0.4 from 0.04 and explain zero as a placeholder.Rebuild the values on a 10 × 10 grid, name the unit aloud, and locate every digit on the chart.An exit response comparing 0.3 and 0.03, including the role of zero.
Scaling by 10 and 100Separate the answer, estimate, model, and explanation; use 1.2 ÷ 100 as a hinge question.Use fixed decimal-point place-value charts and digit cards, then target chart practice where fewer than four checks are secure.Accurate ×/÷ calculations supported by a reasonable estimate and place-value explanation.
Inverse reasoning and applicationCheck operation choice, inverse reasoning, units, and whether an answer is reasonable.Use work-backwards problems and measurement contexts; reteach, practise, or extend from the five-criterion profile.A short context solved, labelled, explained, and checked with the inverse operation.

Evidence boundary The concept-level criteria and teaching responses come from the lesson sequence. The retained public data supports the daily class-status flow, but it does not contain a numeric before-and-after tally for each concept.

RECORDED PROGRESS

Assessment changed the next teaching move.

Aggregated status changes across three daily checks, shown alongside the targeted teaching response recorded in the sequence.

Mathematics status flow from Monday to WednesdayThree columns show aggregated Emerging, Developing, Proficient, and Extending classifications on Monday, Tuesday, and Wednesday. Lines show how many classifications moved or stayed in each status.Mon 17 Aug27 assessedTue 18 Aug27 assessedWed 19 Aug27 assessed8 Emerging to Emerging, Mon 17 Aug to Tue 18 Aug5 Emerging to Proficient, Mon 17 Aug to Tue 18 Aug2 Developing to Proficient, Mon 17 Aug to Tue 18 Aug8 Proficient to Proficient, Mon 17 Aug to Tue 18 Aug3 Extending to Extending, Mon 17 Aug to Tue 18 Aug1 Extending to Proficient, Mon 17 Aug to Tue 18 Aug3 Emerging to Emerging, Tue 18 Aug to Wed 19 Aug5 Emerging to Proficient, Tue 18 Aug to Wed 19 Aug15 Proficient to Proficient, Tue 18 Aug to Wed 19 Aug1 Proficient to Extending, Tue 18 Aug to Wed 19 Aug3 Extending to Extending, Tue 18 Aug to Wed 19 AugEmerging · 13Developing · 2Proficient · 8Extending · 4Emerging · 8Developing · 0Proficient · 16Extending · 3Emerging · 3Developing · 0Proficient · 20Extending · 4
Line weight represents the number of learners in each aggregated status pathway. Highlighted lines show classifications moving into Proficient.
Daily status totals and recorded teaching responses
Assessment pointStatus totalsTeaching response
Mon 17 Aug27 assessedEmerging: 13 · Developing: 2 · Proficient: 8 · Extending: 4Six-item diagnostic; represent tenths and hundredths; use a place-value chart; identify support and extension needs.
Tue 18 Aug27 assessedEmerging: 8 · Developing: 0 · Proficient: 16 · Extending: 3Retrieve from the previous check; use place-value charts and digit cards for ×/÷10 and 100; provide targeted practice or extension.
Wed 19 Aug27 assessedEmerging: 3 · Developing: 0 · Proficient: 20 · Extending: 4Use the 1.2 ÷ 100 = 0.012 hinge question, inverse operations, and application; use the next check to plan reteaching or enrichment.

Evidence boundary The flow shows aggregated status changes across daily checks. The current public dataset does not publish individual answers or map each question-level error to one learner’s pathway.

WHAT HAPPENED NEXT

Across the three recorded checks, status classifications changed alongside these targeted teaching responses: 5 Emerging and 2 Developing classifications moved to Proficient between Monday and Tuesday, and a further 5 Emerging classifications moved to Proficient between Tuesday and Wednesday. These are aggregated status changes, not individual answer records or a causal claim.

REFLECTION & NEXT STEP

The flow makes the progress visible while keeping the claim bounded: the next step is to connect future item-level evidence to the same responsive grouping process without publishing identifiable records.

RELEVANT PROFESSIONAL PRACTICE

Standard 2Know the content and how to teach itStandard 4Plan for and implement effective teaching and learningStandard 6Assess, provide feedback, and report on learning