This framework is a helpful tool for interventionists. It can help interventionists know what kind of work to do with a student, based on whether they understand the concept but lack the ability to skillfully perform the operations, or if they don't understand the concept, or if they're having trouble generalizing the concept in novel situations (e.g. solving problems they haven't encountered before).

An example for multiplication is:

Concept Understanding: Understanding what multiplication means (skip counting; scaling up); understanding the area model.

Procedure Acquisition: Developing the procedure through C-R-A and knowing why the procedure works.

Fluency: Skillful performance of multi-digit multiplication (not making errors).

Generalization of concepts and skills to advanced problem solving, including using mental math to check the reasonableness of solutions.

Diagnostic assessments should tell interventionists where each student is on this continuum. A diagnostic assessment is used when a screener shows that a student is having difficulty with multi-digit multiplication. For example, if a screener shows that a student is repeatedly not shifting the partial product to the left when multiplying by the tens or hundreds place, a diagnostic assessment would be needed to determine whether the student understands how to multiply by 10 or 100. Instruction would include using base ten blocks, number lines marked in tens, and the partial product method to establish the basis for the algorithm.

An example for multiplication is:Diagnostic assessments should tell interventionists where each student is on this continuum. A diagnostic assessment is used when a screener shows that a student is having difficulty with multi-digit multiplication. For example, if a screener shows that a student is repeatedly not shifting the partial product to the left when multiplying by the tens or hundreds place, a diagnostic assessment would be needed to determine whether the student understands how to multiply by 10 or 100. Instruction would include using base ten blocks, number lines marked in tens, and the partial product method to establish the basis for the algorithm.