# 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.

## Sample Probes

• Fraction Representation
This probe assesses understanding of the relationship between numeric and visual representations of fractions between 0 and 1.
• Comparing Fractions
This probe assesses what understanding students have of comparing fractions represented numerically and what reasoning they use to compare fractions.
• Locating Fractions on the Number Line
This probe assesses foundational understandings and common misconceptions related to locating and interpreting fractions on the number line.
• Find the Fraction or Mixed Number
This is another number line probe that assesses understanding of how to determine the fraction or mixed number that names a point.
• Word Problems for Fraction Addition and Subtraction
This probe assesses ability to interpret fraction addition and subtraction word problems and represent the situation as an expression.
This probe assesses understanding of the relationship between numeric and visual representations of decimals between 0 and 1.
• Number Equivalence
This probe assesses understanding of the relationship between fractions, decimals and percentages.

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.