The Cognitive Content of Elementary School Mathematics TextbooksAuthor(s): Leroy Callahan, Robert F. Nicely, Jr., Helen R. Fiber and Janet C. BobangoSource: The Arithmetic Teacher, Vol. 34, No. 2 (October 1986), pp. 60-61Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192998 .

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Research Report

The Cognitive Content of Elementary School Mathematics Textbooks

Students' acquisition of higher- order thinking skills has long been a goal of mathematics educators. The National Council of Teachers of Mathematics (1980), in recommending that "problem solving be the focus of school mathematics in the 1980s," noted that students must learn to "formulate key questions, analyze and conceptualize problems, define the problem and the goal, discover patterns and similarities, seek out ap- propriate data, experiment, transfer skills and strategies to new situations, and draw on background knowledge to apply mathematics" [emphasis added]. It is imperative that the re- sources teachers use to teach those skills be equal to the challenges of this goal.

In 1984, Stephen Willoughby, then President of the NCTM, reinforced Suydam's (1981) assertion that the textbook is the primary determinant of curriculum when he stated that the

Edited by Leroy Callahan State University of New York at Buffalo Buffalo, NY 14260 Prepared by Robert F. Nicely, Jr.

Helen R. Fiber Janet C. Bobango

Pennsylvania State University University Park, PA 16802

60

"most important factor in determining what mathematics is taught is the text- book used" (Willoughby 1984). Therefore, to determine the extent to which higher-order thinking skills were present in the development, practice, and acquisition of a major concept, we extended our earlier anal- yses of secondary school mathematics textbooks (Nicely 1970, 1980-81, 1985; Nicely, Bobango, and Fiber 1984) to four current elementary mathematics series.

Since the National Advisory Com- mittee on Mathematics Education (CBMS 1975) found that students read very little of the textual material in their textbooks and that the books were used primarily as a source of problems, we focused our analysis on those opportunities that students have to be actively involved with one major concept that cuts across a number of grade levels - decimals. All decimal- related problems and textual materials requiring overt student responses were analyzed - including the "devel- opment" sections of a lesson (usually the left-hand page), the "practice" section (often the right-hand page), and any word problems. A total of sixteen books, including 11 482 prob- lems, were examined.

The analytic system we used con- sisted of two scales - one to indicate the cognitive level that was required of the student and the other to indi- cate the stage of mastery of the mate- rials. The cognitive scale was ar- ranged so that behaviors such as recall, recognize, and iterate were at the lower end; compare, substitute,

categorize, and apply were toward the middle; and justify, explain, hypothe- size, generalize, prove, experiment, and design were at the upper end. The stage-of-mastery scale started with readiness; progressed through devel- opment, practice, and demonstration (test); and concluded with overlearn- ing and enrichment.

Our analysis led us to the following conclusions:

1. A significant majority (72%- 100%) of the problems in all series and at all grade levels were at the lower end of the cognitive scale. Virtually all the situations simply required stu- dents to iterate. (We used iterate to describe a situation where the only behaviors involved were chains of low-level tasks, such as repeat, copy, imitate, reproduce, recognize, and re- call. A student would repeat a learned procedure requiring no middle or higher-order behaviors, such as com- pare, substitute, categorize, apply, justify, explain, etc.)

2. Most of the iteration problems were either at the practice or overlearning stages of mastery.

3. The second most frequent cogni- tive behavior was apply. With one exception, however, less than 14 per- cent of the problems in all books were at this level. (The one exception was a third-grade book that contained 21 percent "application" problems.)

4. The total percentage of problems at the seven cognitive levels other than the iterate and application levels is insignificant. The highest percent- age - 7.7 percent for all levels other than iterate and apply - was found in just one third-grade book!

5. All four series offered enrich- ment activities in grades 4, 5, and 6. However, most of these enrichment problems required students only to iterate.

6. Readiness was not addressed in the problem sections of any of the four series.

The textbook authors and publish- ers have made an attempt to include activities at the application level of the cognitive domain but have not systematically made provisions for

Arithmetic Teacher

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students to be involved with the other important higher-order intellectual be- haviors recommended by the NCTM (1980). Therefore, teachers who value problem solving and other higher- order thinking skills will have to sup- plement the commercially available textbooks as they plan for effective mathematics instruction. They can make or purchase other instructional materials that do foster students' de- velopment of higher-order thinking, and they can develop expertise in framing questions and guiding discus- sions that will enable students to op- erate at the desired intellectual levels. Staff-development programs for these teachers must focus on both the iden- tification and selection of instructional materials and the teaching processes to be used in the classroom.

References Conference Board of the Mathematical Sci-

ences, National Advisory Committee on Mathematics Education. Overview and Anal- ysis of School Mathematics: Grades K-12. Reston, Va.: National Council of Teachers of Mathematics, 1975.

National Council of Teachers of Mathematics. An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, Va.: The Council, 1980.

Nicely, Robert F., Jr. "The Analysis of Math- ematics Instructional Materials: Concepts, Procedures, Results.** International Journal of Instructional Media 8 (1980-81): 221-32.

. "Development of Procedures for Ana- lyzing Materials for Instruction in Complex Numbers at the Secondary Level." Ph.D. diss.. University of Pittsburgh. 1970.

. "Mathematics Instructional Materials: A Decade of Change." International journal of Instructional Media 12 (1985): 127-36.

Nicely, Robert F., Jr., Janet C. Bobango, and Helen R. Fiber. "A Data-based Method for Analyzing and Selecting Secondary Mathe- matics Textbooks." Unpublished working paper, Pennsylvania State University, 1984.

Su y dam, Marilyn N. "Mathematics Educa- tion." In ASCD Curriculum Update. Alexandria, Va.: Association for Supervision and Curriculum Development, February 1981.

Willoughby, Stephen S. "Mathematics for 21st Century Citizens." Educational Leadership 41 (December 1983-January 1984): 45-50. m

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