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AMC - Assessing for Student Understanding

AMC Assessments have been carefully designed so each question elicits several levels of student thinking. This gives teachers the most information possible about each individual student in the shortest amount of time.

Kathy Richardson’s ground-breaking work presents teachers with a continuum of assessments that follows the stages of children’s development of math concepts so teachers can identify where children are in their development and provide appropriate instruction. AMC assessments focus on the concepts of Counting, Comparing, Number Composition and Decomposition, Place Value, Addition and Subtraction, and beginning Multiplication and Division.

Overview of AMC:

  • Formative, Summative and Diagnostic
  • Uncover the child’s edge of understanding
  • Short Personal Interviews
  • Focus on Number
  • Designed to give teachers the most information possible in the shortest amount of time
  • Aligned with Common Core State Standards - Math
  • Inform Classroom Instruction
  • Identify Students Who Need Intervention
  • Available in two formats - Web Based Version or Paper Student Interview Form

AMC is based on the premise that teachers will be able to provide more effective instruction and ensure maximum learning for all students when they (teachers) are aware of the steps children progress through as they are developing an understanding of foundational mathematical ideas.

The heart and foundation of mathematics for young children is the development of number concepts. A child’s understanding of number and number relationships impacts every other area of mathematical study. AMC assessments are formative, summative, and diagnostic.

Formative: provides teachers the information necessary to differentiate instruction for core grade level concepts.

Summative: provides information on students’ progress toward benchmark goals.

Diagnostic: identifies students’ knowledge of core mathematical ideas and provides evidence of misconceptions.

With the AMC assessments teachers and administrators can monitor student progress throughout the school year, providing critical information about what the student understands. With this data, classroom teachers can target instruction and both teachers and administrators gain a complete picture of each student’s progress.


The Nine Assessments

  • Counting Objects
  • Changing Numbers
  • More/Less Trains
  • Number Arrangements
  • Combination Trains
  • Hiding Assessment
  • Ten Frames
  • Grouping Tens
  • Two Digit Addition and Subtraction

Short Personal Interviews

The assessments are conducted in short one-on-one student/teacher interviews. This format is critical since “we learn most about how our students think and what they can do when we sit beside them and observe their mathematical work”. Because of the ages and capabilities of young students, mathematics assessment should rely more on observation and conversations and less on writing. “What students write on paper offers only a glimpse of what they know and think” (Richardson, Assessing Math Concepts). Each assessment can take as little as five minutes and no more than fifteen minutes.

Student responses can be captured using paper Student Interview forms or the web-based program. Teachers using the web-based version can use any desktop computer, iPad, or laptop with internet access.

AMC Instructional Levels

The Assessing Math Concepts Instructional Levels identify the particular level of insight and facility a student has reached with a given mathematical concept. Click here to read about each of these levels for each of nine assessments.

Below are clips from three AMC student interviews

Guidelines for Using AMC

Because number concepts develop in relatively predictable ways, there are particular concepts and Critical Learning Phases that the majority of children at specific grade levels need to work with. Teachers can use the AMC assessments to determine the instructional needs of their students along a continuum as they develop competence with the particular concepts. This document provides guidance for teachers who are using AMC to plan appropriate instruction for the whole class as they focus on various concepts throughout the year.
Download PDF Document | 340 KB

The AMC Books

Each book provides the teacher background information for giving and using the assessment tasks, instructions for doing classroom observations, tips for organizing information and suggestions for instruction. Black line masters are included and can be reproduced for classroom assessment activities.
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Assessing at Work – Monitoring Student Progress

Assessing Math Concepts gives teachers “Assessing at Work” activities for each of the assessments to give teachers a focused way to keep track of student’s ongoing progress.. Everything teachers need to monitor student progress is provided - instructions, blackline masters and “Assessing At Work” forms are in the AMC books.

Watch an example of Kathy Richardson demonstrating an AMC “Assessing at Work” activity using the Number Combination Cards. This activity is from the AMC Combination Trains assessment:

Reporting and Data

Powerful web-based reporting is available that summarizes results for teachers and administrations.
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Please call Math Perspectives with Questions 1-360-715-2782