A probe is a short, highly focused, quick-to-administer formative assessment tool. Each probe focuses on a specific mathematics concept and is carefully designed to elicit evidence of students' understandings, misconceptions, and difficulties. 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 that can be used to plan and teach targeted instruction that is responsive to students' strengths and needs. As such, probes are not assigned a score or letter grade. To support teachers in analyzing their students' work, the Probe Guides provide information and examples of successful approaches, common misconceptions, and difficulties. We have provided sample probes with accompanying guides below as well as implementation suggestions.

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- Locating Fractions on the Number Line Probe and Guide

*Assesses foundational understandings and common misconceptions related to locating and interpreting fractions on the number line.* - Label the Missing Points on a Number Line Probe and Guide

*Assesses understanding of how to determine the fraction or mixed number that names a point.* - Comparing Fractions Probe and Guide

*Assesses ability to compare fractions represented numerically and the approaches/reasoning used to make comparisons.* - Ordering Fractions Probe and Guide

*Assesses ability to put fractions in order from least to greatest.* *Resource for Targeting Instruction:*Strategic Sequence of Fraction Card Sets

This sequence of card sets is designed to support students in building their abilities to compare and order fractions. It increases in level of challenge: 1) groups of fractions with the same denominator; 2) groups of fractions with the same numerator; and 3) groups of fractions with different denominators and numerators. Use the findings from the Ordering Fractions Probe to select fraction sets for your students' strengths and needs.- Does the Expression Match the Word Problem? Probe and Guide

*Assesses ability to interpret fraction addition and subtraction word problems and select numeric expression(s) to represent the situation.* - Choosing Expressions to Represent Situations Probe and Guide

*Assesses ability to interpret word problems (fraction subtraction, multiplication, and division) and represent the situations with numeric expression(s).*

Probes can be used in paper-and-pencil format or as interviews.

Suggestions and Considerations for Using Probes discusses the what, why, when, and how of administering a paper-and-pencil probe to students.

**Interviews:** Using probes to conduct interviews is a powerful way to gather a fuller picture of student thinking, particularly from students who have difficulty explaining their ideas in writing. During the interview, the student is asked to 'think aloud' as they work on the probe items. The teacher's role is to listen and ask questions to find out more about the student's thinking, but not to provide instruction. After the interview, the teacher uses the findings to plan targeted instruction that builds on students' strengths and addresses areas of challenge.

__Our Articles about Probes__:

- "The Power of Interviewing Students" (2021,
*Mathematics Teacher*) describes the use of probes in a middle grades intervention class and provides suggestions for teachers. - "Targeting Instruction with Formative Assessment Probes" (2016,
*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.

**Example Interviews:** We have provided two examples of a teacher interviewing a 6th grade student by using the *Probe: Label the Missing Points on the Number Line*. The teacher conducted an initial interview to find out about the student's abilities to identify missing fractions on a number line. By using the interview findings, the teacher planned instruction to address the strengths and challenges of this student and others with similar learning needs. After teaching a sequence of targeted instruction, she did a second interview with the same probe to check in on his progress.

Initial Probe Interview

Probe Interview after instruction

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

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This project is supported by the National Science Foundation Grant No. 1621294. Opinions expressed are those of the authors and not necessarily those of the Foundation.