Entry diagnosis: find the first missing support

Where we are on the map

Diagnosis is the gateway to the course. It evaluates the learning chain, rather than the person, and finds its first weak link.

Begin with a familiar image

A doctor checks symptoms before choosing a treatment. Here you mark every answer with +, ?, or −, so we observe confidence and reasoning as well as the final number.

Precise meaning

A + means you can explain the method; ? means you have an answer but doubt the reason; − means you do not know how to begin. The first ? or − identifies the starting point.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

problem → my method → answer → explanation → confidence mark

Worked example

Dividing 12 objects into four equal groups gives 3 in each group. 12 ÷ 4 = 3; the explanation names what the division means.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

Calling the 8 in 3/8 “eight shaded pieces” is wrong. Eight says how many equal parts make the whole; three says how many of them are selected.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Answer all ten problems and mark each one with +, ?, or −. Explain your first uncertain answer in two sentences.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

Your result sends you to the earliest support you need: number meaning, fractions, ratio, percent, or equations.

Course contents