Assessing Mathematical Understanding

March 2012

Assessing Mathematical Understanding is a set of mathematics assessments for kindergarten and first-grade students that provides both cumulative data about students’ progress over time and in-depth diagnostic information. Aligned with the Common Core State Standards for Mathematics, it is intended as a tool to help teachers track student progress, identify particular difficulties, and generally inform instructional planning.

Goals of Assessing Mathematical Understanding

  • To enhance teachers’ ability to meet individual student needs
  • To facilitate teacher collaboration around student learning
  • To promote student learning in mathematics


  • Individual assessment interviews are conducted by the teacher or another qualified staff member two to three times during the school year. The student record provides a cumulative report of mathematical progress during that period.
  • The one-on-one interview structure allows the teacher to collect rich data about student knowledge that is not limited to the answer the student gives, but also includes observations of the strategies and explanations the student uses.
  • The diagnostic assessment allows the teacher to ascertain an individual student’s strengths, weaknesses, knowledge, and skills in a particular concept area.
  • The content of each grade-level assessment is aligned with the Common Core State Standards for Mathematics.

An Overview of Assessing Mathematical Understanding

A Guide for Assessing Mathematical Understanding

The guide contains all the information needed to use the Assessing Mathematical Understanding materials. Sections in the guide include a review of the research on the importance of early learning experiences, a rationale for assessing student understanding, potential misuses of assessments, and recommended instructional practices. The mathematical concepts and student learning goals and how they are aligned with the Common Core State Standards for Mathematics are described. Directions explain how to administer the assessments and keep track of student data using the reproducible records.

Kindergarten and First-Grade

The primary goal of Assessing Mathematical Understanding is to enhance teachers’ ability to meet individual student needs. By using this assessment and understanding the organizational framework on which it is based, teachers can enhance their understanding of how students learn. Using students’ responses to the assessment items as a guide, teachers can differentiate instruction and create learning environments that better support their students’ mathematical development.

The kindergarten and first-grade assessments are designed to be administered to each student by the teacher several times during the year to document progress. Each student record is designed to provide cumulative documentation of the student’s growth in mathematical proficiency during the course of the school year. Before using the kindergarten and first-grade assessments, teachers should be sure to review the directions in the guide.

View the Kindergarten and First-Grade Videos.

Diagnostic Assessment

The diagnostic assessment provides in-depth data for particular students. The teacher may choose to use the diagnostic assessment with students whom she believes would benefit from additional mathematical challenges or students who may be struggling with mathematical concepts. For each of these students, the teacher can identify a particular concept area and administer the bank of items in that section of the diagnostic assessment. The diagnostic interview and student record provide detailed information about the student’s mathematical knowledge and help the teacher decide how to adjust curriculum and instruction to meet the needs of that child. Before using the diagnostic assessment, teachers should be sure to review the directions in the guide.

View the Diagnostic Assessment Video.

Download Our Assessing Mathematical Understanding

For Best Results We Recommend the Following When Printing These Files

  • Duplex print the entire document to ensure that student and teacher pages are oriented correctly
  • Print in color as some assessment items are better interpreted in color
  • Print at full size to ensure correct responses to measurement items are consistent with measuring tools

Attention dual-language classroom teachers: Assessments for Russian- and Spanish-speaking kindergarteners and first-graders are also available.



View the K-1 and Diagnostic Assessment Videos.