Assessing math learning by asking students to explain their thinking

The Assessment Standards for School Mathematics published in 1995 by the National Council of Teachers of Mathematics describe four purposes for assessment: monitoring students’ progress, making instructional decisions, evaluating students’ achievement and evaluating programs.

Mary Lynn Vincent, New Castle Middle School, New Castle, Delaware was interested in improving the assessment practices in her algebra classes. Working with Linda Wilson, University of Delaware, she investigated strategies she could use to document observations of her students as they worked on problems. She wanted a way to record their mathematical thinking that would help her to assess their learning.

Vincent found note-taking inadequate and inconvenient. She began tape-recording her observations of students’ work as she observed them working. She quickly concluded, however, that the students’ own explanations of their thinking were more informative.

Vincent discovered that interviewing them as they worked had a profound, positive effect on their ability to explain their thinking. She found that certain activities and types of problems were superior to others for illustrating students’ mathematical reasoning. Observations were more significant if students were working in pairs or groups since their dialogue provided greater insights into their thinking. It was particularly helpful in documenting the process goals of mathematics instruction – problem solving, communication and critical thinking skills.

Vincent found she could adequately observe about four students in a class period. In this way, she was able to observe every student at least once during each marking period.

One of Vincent’s major goals was to teach students the importance of explaining their thinking, both orally and in writing, using correct mathematical language, constructing sound arguments, and giving clear justification for their solutions. She reports that her use of the tape recorder helped her students reach this goal. Many students who had not participated in class discussions gained confidence in their ability to explain their thinking.

“Informal Assessment: A Story from the Classroom” The Mathematics Teacher Volume 89, Number 3, March 1996 pp. 248-250.

Published in ERN May/June 1996 Volume 9 Number 3


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