My field, mathematics, is a discipline in which the complexity of the subject increases with each course and each course requires a certain amount of recall from prior courses. While some students do quite well in transitioning to the next mathematical challenge, there are many who don’t bridge easily to the new content. Furthermore, students are prone to forget material learned earlier in the current course that they now need.

As a professor of mathematics, having taught for over 35 years, I am well acquainted with the reluctance of students to review material when their recall of it is imperfect. When I faced up to this issue a while back in revising my four-book Precalculus series, now in the 11^th edition, I decided to confront the problem head-on.

First some background. Mathematics texts are composed of Chapters, within which are several Sections that contain foundational content (Theorems, Definitions and explanations), Examples, and Exercises. To address the review issue, I decided to open each section with a box titled ‘Preparing For This Section.’ It lists concepts that are used in the current section but were discussed or reviewed earlier in the course. Included is an instruction (“Now Work…”) to go to the Exercises to test readiness. See below.

Recognizing that students don’t always do what they should, I added a margin note, ‘Need To Review’, at appropriate places to further guide the reader.

Lastly, to further emphasize the importance of review, I added a group of problems titled ‘Retain Your Knowledge’ that spiral back with material presented earlier in the course.

With the features cited above, students are prompted and encouraged to review and sharpen the skills learned earlier. Further, faculty are provided a means and framework for helping students bridge what they have learned to new course content.

To date I have received good marks from both students and instructors. Students say they have more confidence and feel better prepared for the final exam. Instructors indicate a decline in having to answer review-type questions and a claim in gain scores on final exams.

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Michael Sullivan has been writing textbooks for more than 35 years and currently has 15 books in print. His publishers include Pearson Education, John Wiley & Sons, and Macmillan (W H Freeman and Bedford, Freeman & Worth, high school publishers). His Precalculus, 11th edition, recently won a McGuffey Textbook Award, which recognizes textbooks whose excellence has been demonstrated over time.