Mapping what a student knows
· 2 min read
What does it mean to know where a student is? One answer comes from knowledge space theory.
What the research describes
Doignon and Falmagne’s knowledge space theory describes what a learner knows as the set of problems they can solve, and frames assessment as efficiently finding that set among the possible ones.
This work is about assessment in general, not about SubjectPath.
Why structure helps
Skills aren’t independent. A student who can solve a problem that builds on several earlier skills very likely has those earlier skills too. That structure means an assessment doesn’t have to test everything: each answer narrows down which combinations of skills are possible.
How SubjectPath applies this idea
Each Path maps its standards framework as a graph of prerequisites: which skills build on which. In Algebra Readiness, the diagnostic uses that map to trace a student’s answers back to the skill where prerequisites hold but understanding stops. The same map becomes the student’s skill tree afterwards, so practice moves forward through it one skill at a time.
A small example
Imagine three skills, where the third builds on the second and the second builds on the first. A student who solves problems using the third skill very likely has the first two as well. A student who misses problems on the second skill but solves problems on the first has shown where the chain breaks. Knowledge space theory frames this as efficient assessment: knowing the structure means not every skill has to be tested separately.
From map to practice
The same structure that guides the diagnostic guides what comes after it. Once the break point is found, the map shows which skills sit just above it and which depend on those, so practice can move up the map one skill at a time.
Source
- Doignon, J.-P., & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23(2), 175–196.