Addressing Accessibility in Mathematics
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Math Accessibility

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Diagnostic Probes

A probe is a short, highly focused, quick-to-administer diagnostic assessment designed to pinpoint key foundational ideas that students do understand, as well as any specific misconceptions they may have, regarding a particular mathematics concept. A probe is composed of 3–6 items designed for completion by students in about 10–15 minutes. Each item requires a two-part response from the student: a selected response and a written explanation using words and/or pictures. Together, these two pieces of data provide important evidence of a student’s understanding and thinking about a mathematics topic to inform instruction. Probes are intended to be used to gather information about student understanding that can be used to plan instruction. As such, they are not assigned a score or letter grade. Below is a link to some probes and supporting implementation information.

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Sample Probes

Administering Probes

Suggestions and Considerations for Using a Probe discusses the what, why, when and how of paper/pencil administration of a probe to students.

Suggestions for Student Interviews offers instructions for administering a probe as a student interview. This method is a great alternative for capturing a more complete picture of student thinking from students who struggle with written explanations. Explain Everything and Show Me are apps for recording student work using a tablet. Below are examples of pre- and post- interviews conducted and recorded using the Explain Everything app on an iPad.

Probe Interview prior to instruction


Probe Interview after to instruction


A PDF of a PowerPoint presentation made from screenshots of the Fraction Representation probe provides an example of a probe formatted for tablet administration. This file can be uploaded to the tablet so students can write and record their approach.

More Information on Probes

Our series of books of probes spanning grades K-12 is available from Corwin Publishers:

UST Gr K-2 UST Gr 3-5 UST Gr 6-8 UST Gr 9-12

Our article “Targeting Instruction with Formative Assessment Probes” in the October 2016 issue of Teaching Children Mathematics discusses how to use probes to gather and interpret evidence of students' mathematics understandings and misconceptions and then target instruction to address identified needs.