# Teachers – Summative and Formative Assessment in Mathematics – What Are the Differences?

I’m a big fan of using definitions as a starting point for thinking about a topic…so let’s look at a definition of assessment from the National Council of Teachers of Mathematics (1995):

Assessment is…the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward, mathematics and of making inferences from that evidence for a variety of purposes (p. 3).

Depending on your age, this definition may describe the experience you had with assessment in mathematics during your school career, but for most readers, “testing” was really the only kind of “assessment” we knew. Like clockwork, at the end of every few sections of the math book, there would be a quiz (for a GRADE) and at the end of every chapter, there would be a TEST (for a MAJOR GRADE). Then, no matter what grades any of us received, we would go off to the next chapter, where the cycle began again.This type of testing (of which there are many varieties) is known in today’s parlance as “summative assessment,” defined as

“a culminating assessment, which gives information on student’s mastery of content” (Association for Supervision and Curriculum Development, 1996, p. 60).

The principal characteristics of summative assessment are that it:

1) occurs at the conclusion of a learning activity,

2) is to make a final judgment,

3) may compare students to other students, and

4) often results in a grade or some other ‘mark.’

In contrast, the principal characteristics of formative assessment include that it

• occurs during learning activities/experiences,
• is for the purpose of improving the learning, and
• will inform the teacher so that s/he can make adjustments if needed.

A useful definition of formative assessment is

“assessment which provides feedback to the teacher for the purpose of improving instruction” (ASCD, 1996, p. 59).

This concept of assessment meshes nicely with the NCTM definition shown above (i.e., “the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward, mathematics and of making inferences from that evidence for a variety of purposes”). Formative assessment – with or without that name – has always been around – depending on individual teacher’s attitudes towards this.  For the teacher who believes, as Grant Wiggins does, that “Good teaching is inseparable from good assessing,” there has always been an ongoing cycle of teaching, assessment, of the teaching, reteaching (as necessary), assessment, teaching, and so on. “Assessment should serve as the essential link among curriculum, teaching, and learning” (Wilcox & Zielinkski, 1997, p. 223).

So, the next time you hear others talking about assessment, ask if they are referring to formative or summative assessment. That will help you know what questions to ask next.