Reviews

When is an A not an A? Assessing Levels of Mathematical Thinking

In the April 2001 issue of Mathematics Teacher, NCTM.

This delightful little book arrived just as our department was beginning to discuss grading standards. Its premise, that grades should reflect students' knowledge and their ability to perform complex tasks, not just average test percents, was one that our Board required us to begin using. We were just far enough into the discussion to realize that although we might agree with the notion in principle, figuring out how to put it into practice was going to be a difficult task. To the teachers in our department who were caught in the trap of being able to view grading standards only as a set of percents but who have been told that they must expand their viewpoints, the book has been invaluable. It has given them a series of concrete examples of tying letter grades to levels of standards-based achievement. To those who already believed that the grades should represent levels of achievement, the book gives examples that help them create their own assessment exercises. [...] It is worth your time.

In the March 2001 issue of Mathematics Teaching in the Middle School, NCTM.

This selection presents a process to evaluate students' work on the basis of mastery of levels of mathematical thinking, including the abilities to recall, apply, understand, and extend information. [...] Tests and performance tasks are designed sequentially, from recalling to extending knowledge, to facilitate scoring. Scored examples and detailed charts of percents provide grading guidelines. I recommend using this book with other teachers to share the test-design responsibilities and the scoring and interpretation of results. [...] Teachers who use 4MAT lesson design will recognize the four levels of student learning. Activities for designing level-specific tasks and tests, are given. Staff development instructors could assign practice work for teachers directly from this book rather than create instructional materials. A wide range of topics from the middle school mathematics curriculum is presented. [...] This set of activities is a valuable resource to help a teacher master the techniques of assessing students' thinking.