Exploring Formative Assessment in the Mathematics Classroom

Formative assessment is an important tool to take full advantage of, especially in this transitional era of implementing more rigorous standards.

When correctly incorporated into classroom practice, the formative assessment process provides information needed to adjust teaching and learning while they are happening. The process serves as practice for the student and a check for understanding during the learning process. The formative assessment process guides teachers in making decisions about future instruction. 

As we explore the notion of formative assessment in this blog, be reminded the use of graphic organizers are powerful tools that allow you to perform “quick checks” (a.k.a. formative assessment) during instruction.   

First of all, you want to analyze the standards to align the instruction in a more meaningful, intentional and precise manner. For example, here is one of our curriculum standards:

Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. 5.4a identify prime and composite numbers.

One of the first things we do is analyze the standard for content vocabulary. In this case, the content vocabulary is prime numbers and composite numbers. We also look at any cognitive verbs that are included in the standard. The word “identify” appears in this particular standard—so we will make sure students are identifying and we are asking questions that are inclusive of this cognitive verb. This will allow us to effectively craft questions that reinforce the language of mathematics and check our students’ facility with the language as they respond to questions either in written or spoken responses.

Thinking and Communicating in Mathematics

Next, we look for ways to make the learning experience engaging for the students, so we are able to “see” evidence of their learning that goes beyond multiple choice or memory and recall. We attempt to contextualize the content and find multiple representations so we may be able to accurately assess knowledge in a formative manner and make decisions. These decisions may include identification of students who are struggling with the task and immediately moving them into small group instruction rather than moving about the room conducting one-on-one tutorials to correct the same error. As we monitor students while they are engaged in the formative assessment activity, we use questions to elicit thinking. Our goal with questions is not merely to get a response, but to get our students thinking and communicating in mathematics.

Additionally, we focus on preplanning our questions to ask as well as thinking critically about how to phrase questions that will appear on any materials distributed to the students. This ensures a tight alignment between instruction and student learning activities.

Quick Check

An example of a “quick check” once the introduction of prime and composite has been made can be downloaded below. 

We determined a graphic organizer is better suited as a formative assessment tool so that multiple representations will be targeted. We also added a “hands-on” component so the activity supports a variety of learning styles.

1. How many students chose the one-digit numbers as two of the three choices?
2. How well were students able to identify factors?
3. Who struggled with the algebraic representation even though they were able to identify the number as prime or composite?
4. Who struggled with the visual representations?
5. Who is/isn’t able to communicate their thinking effectively and concisely in written form?

The formative assessment exemplar shared today is simple, straight to the point but also targets curriculum standards in a meaningful way. Our intent is to always have our students engaged, communicating and experiencing mathematics while we use creative ways to assess learning.