1. Treat screening as a prompt for instruction

A universal mathematics screen is a way to flag possible risk, not a diagnosis or a permanent placement. When a student has difficulty, inspect the work for the idea or procedure behind the error: counting all instead of composing a number, for example, calls for a different lesson than a transcription slip. Confirm the signal with classroom work and a brief follow-up before changing the intensity of support.

2. Make number relationships visible

The IES guide recommends explicit, systematic instruction and visual representations. If a child solves 8 + 5 by counting every object, model moving two counters to complete a group of ten, then show the same move on a number line and in an equation. Ask the learner to describe why the split works. Fade prompts only after the student can select and explain a representation independently; a picture used without connecting it to the quantities may become decoration rather than a reasoning tool.

3. Match intervention to the mathematical obstacle

In a small group, name one teachable target, model a worked example, guide practice, and return to previously taught material so it remains available. For a word problem, have pupils mark the known quantities, the relationship, and the unknown, then sketch or tabulate that relationship before choosing an operation. Ask them to explain why the answer fits the question. This addresses the structure of the problem instead of training students to hunt for operation keywords.

4. WWC expert-panel perspective: What the WWC panel recommends about response and implementation

The What Works Clearinghouse (WWC) practice guide for elementary and middle school mathematics recommends screening, explicit and systematic intervention instruction, visual representations, and progress monitoring. It covers grades 1–8, and evidence strength differs by recommendation: screening is rated moderate, explicit and systematic instruction strong, and progress monitoring minimal. The review routine below translates those institutional recommendations into classroom questions; it is not a quotation from an unnamed specialist or a promise of an individual student’s outcome.

5. What the National Academies report does—and does not—show

The National Research Council’s 2001 consensus report Adding It Up examines mathematics learning from pre-K through grade 8 and describes proficiency as five interwoven strands. It is a synthesis and educational framework, not an experiment estimating the effect of one classroom intervention. Read alongside the WWC guide for grades 1–8, it can help teachers look for connections among representations, procedures, and reasoning; it cannot predict an individual student’s response.

Sources: WWC | Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools · Adding It Up: Helping Children Learn Mathematics