Getting Into Math: How Assessments Contribute to Effective Instruction

Many parents and educators today express concerns that there is too much assessment in school. As a result, in some parts of the country, there has been a grassroots effort to decrease the amount testing. 

There is little doubt that in some cases there has been excessive testing. More concerning is that all too often, assessment systems are not closely aligned with the curriculum, and educators do not receive assessment results in time to effectively leverage those results to guide instruction and improve student learning.

Why Assessments Matter in Math

An aligned, valid, and comprehensive system of assessment is an essential feature of effective math programs. A balanced assessment system is the tool by which teachers can continuously monitor student learning and target instructional supports as necessary to maximize learning. Assessment is such a critical feature of effective math programs that it shows up twice in NCTM’s landmark publication, Principles to Actions: Ensuring Mathematical Success for All, both as a standalone principle and as one of the eight research-informed instructional strategies.

When effectively embedded into a mathematics program, assessment becomes virtually indistinguishable from instruction. A comprehensive and balanced assessment system includes diagnostic assessments, formative assessment processes, and summative assessments.

Three Types of Assessments

Diagnostic assessments typically take place at the beginning of the school year or at the opening of a unit of instruction. Diagnostic assessment provides teachers with critical information about individual student needs, including prior knowledge or misconceptions, that identifies students who need targeted learning support in order to access and be successful in grade-level content. Implementing diagnostic assessments in an online format, and directly linking the assessment to the learning objectives of the curricular program, enhances the efficiency and effectiveness of the assessment for both teachers and students.

Effectively implemented, formative assessment is a process where teachers leverage evidence of student learning to adjust and guide their ongoing instruction and learning strategies to promote student learning. An extensive body of research supports the power of regular, ongoing formative assessment processes to positively impact student learning. Formative assessment options should permeate a math program, including activities that support students in activating prior knowledge, warm-up tasks, math centers, turn-and-talk prompts, checks for understanding, and leveled-question prompts for teachers. Most importantly, formative assessment should be linked to instructional options and materials teachers can use to shape their instruction, and to personalize and differentiate learning for students.

Summative assessment is often associated with high-stakes testing, but in an effective mathematics program, classroom-based summative assessments have a role as an additional constructive measure of students’ attainment of learning goals and can serve as an interim growth measure to show progress over time. All assessments, including summative assessments such as module tests, can be used to provide specific feedback to students about their progress and guide appropriate intervention or enrichment. Actionable feedback from assessment supports students in developing a positive mathematical identity and growth mindset through the positive experience of learning from mistakes, rather than the fear of making mistakes.

Think About It

When you go to the doctor because you don’t feel well, it is almost a certainty that the first thing she will do is administer some sort of test to determine what might be wrong with you: She checks your blood pressure and temperature, draws blood; you may have an X-ray, an EKG, and so on. Your physician doesn’t arrive at a diagnosis randomly but instead through careful assessment. A comprehensive and balanced system of assessment diagnoses student learning needs and guides effective instruction, just as medical tests diagnose illness and direct effective treatment protocols.

An effective mathematics program is more than a collection of standards, lessons, and instructional strategies. A comprehensive mathematics program embeds a balanced assessment system within it—a system that includes diagnostic, formative, and summative measures—as well as a plan and the resources necessary to ensure action can be taken from assessment results to ensure student growth. A comprehensive assessment system is indistinguishable from curriculum and instruction and is essential to propel and accelerate students’ mathematical learning and growth!

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Dr. Matthew R. Larson is an author of Into Math. Learn more about the HMH solution for K-8 students here.