How it works

One method. Every Path.

Every SubjectPath diagnostic works the same way, whatever the subject: map the standards, ask the right questions, find where understanding breaks down, and build the path forward.

1. Map the standards

Each Path starts with a published standards framework, mapped as a graph of which skills build on which.

2. Ask adaptively

Each next question is chosen based on the answers so far, so students spend time only where it tells us something.

3. Find the break point

Answers are traced back through the graph to the skill where prerequisites hold but understanding stops. Each wrong answer is tagged to a misconception.

4. Build the path

Results feed a skill path of lessons and skill checks that starts at the break point.

An example

Following one wrong answer back

Question · standard 4.NF.B.3b

Which shows one way to decompose $\frac{5}{6}$ into a sum of fractions with denominator 6?

A. $\frac{2}{6} + \frac{3}{6}$
B. $\frac{2}{3} + \frac{3}{3}$
C. $\frac{5}{3} + \frac{5}{3}$
D. $\frac{1}{6} + \frac{1}{6}$ Student's answer

Misconception tagged on answer D

“Reports the unit fraction regardless of count”: building the sum only from unit fractions, which gives 2/6, not 5/6.

Tracing back through prerequisites

4.NF.B.3b
Decompose a fraction into a sum of fractions with the same denominator.
Missed
4.NF.B.3a
Understand adding and subtracting fractions as joining and separating parts of the same whole.
Missed: the break point
3.NF.A.1
Understand a unit fraction 1/b as one of b equal parts of a whole.
Holds

The unit-fraction idea holds, but joining parts of the same whole doesn't yet. That's where this student's path starts.

Illustrative example. The question, its standard, its prerequisites and the misconception are real content from the Algebra Readiness Path. The student's answers are invented to show the method.

See it with your students' answers

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