Building Identity in Classroom Assessments

May 2024

Building a positive mathematical identity should be every educator's goal for every student. When we employ classroom assessments, unfortunately, they often have the opposite effect and leave our students believing they are not capable doers of mathematics. A wide range of assessments should be given—for example, projects and interviews—to truly gauge student understanding. Still, the most common formats remain quizzes and tests. Changes to our policies on such assessments can help foster an increased sense of confidence in our students and help them realize they are capable of learning mathematics.

Educators must first carefully consider the types of questions in classroom assessments. What message do students receive when the assessment includes many multiple-choice questions? Educators frequently tell their students that mathematics is more than just getting the correct answer; critical thinking, reasoning, sense making, and communicating are also vital components of mathematics. Yet, multiple-choice questions don’t allow students to demonstrate progress in those areas because only the correct answer is measured. Additionally, students can guess and get the answer correct with very little or no understanding of the mathematics concept being assessed.

The way questions are scored is the second aspect of classroom assessments that educators should closely examine. Grading a question as completely correct or completely incorrect allows for quick grading, but does it lead to our goal of developing a positive mathematical identity? Students see the correct answer as the only valued outcome, and often believe they cannot learn mathematics when they make an error. Assigning partial credit is necessary if we want our students to recognize that they understand much of the solution process, even if they make a mistake that leads to an incorrect solution. While partial-credit grading takes longer, I learn much from examining my students’ errors. This analysis helps inform my teaching because I notice commonalities in mistakes, and then I can craft mini lessons to help them further develop their understanding of the mathematics.

Educators must allow students to retake classroom quizzes and tests. I once heard a speaker ask the audience what someone who passes the bar exam on the third attempt is called. He then wondered aloud why it was okay for law students to retake that bar exam as often as needed to pass and become a lawyer, yet retaking assessments isn’t the norm in too many classrooms. Many students struggle with anxiety, and many external factors can affect performance on a quiz or test. Allowing students to retake quizzes and tests for full credit can reduce stress and provide opportunities for educators to better gauge what students understand. I often have my students identify what type of mistake they made before they can retake the assessment. Was it a calculation error or a minor or major misunderstanding of the concept? My students are often surprised at how many of their errors were merely minor calculation errors and that they had a good understanding of the concept.

As a mathematics education community, we are having more conversations around non-traditional assessments to better gauge student understanding and allow them opportunities to demonstrate what they know. Therefore, it is vital that we continue to examine our traditional quiz and test practices and policies so that we will remain focused on fostering the development of positive mathematical identities in our students.

Kevin Dykema
NCTM President
@kdykema