A comparison of traditional and reform mathematics curricula in an eighth-grade classroom

This study was an action research project conducted by an eighth-grade public school mathematics teacher and a university mathematics educator. The goal of this study was to compare a traditional mathematics curriculum (Houghton-Mifflin) with a reform mathematics curriculum (Cord Applied Math) and a combination of both curricula in an eighth-grade classroom. The researchers compared three years of SAT scores including SAT total scores, SAT problem-solving scores, and SAT procedure scores. There were no significant differences found in comparing SAT total scores and SAT problem-solving scores. However, students using the Houghton-Mifflin curriculum showed a significant improvement over the Cord Applied Math and a combination of both curricula in SAT procedure scores.

Introduction

Prominent organizations such as the National Council of Teachers of Mathematics (NCTM) and the National Research Council (NRC) have identified aspects of mathematics classroom instruction that must be changed to improve mathematics instruction and increase student achievement (NCTM, 1989, 1991, 2000; NRC, 1989). One is the need to make stronger connections between mathematics and students' lives outside of the mathematics classroom. Another is a shift from lecture and transmission model, where students are expected to memorize procedure and facts, to a participation model, where students are to actively participate in constructing their own knowledge. According to McNair (2000), both of these reform efforts are supposed to change students' role in the classroom from that of a knowledge consumer to a knowledge producer.

Proponents of mathematics reform have argued that traditional mathematics instruction, the predominant form of instruction in our nation's schools, has been unsuccessful in promoting conceptual understanding and application of mathematics to real-life contexts. Battista (1999, p. 426) asserts that, "For most students, school mathematics is an endless sequence of memorizing and forgetting facts and procedures that make little sense to them." A major thrust of the current reform movement is to get students actively involved in their study of mathematics and to encourage them to see the big picture (Ross, 1996). Data suggests that most classroom instruction is geared toward the development of rote procedural skills. Existing teaching methods do not develop the high levels of conceptual understanding or the reasoning, problem solving, and communication skills that students will need to be competitive (Silver & Stein, 1996).

From the eighth-grade teacher's perspective, the transmission method of mathematics is a simpler way of teaching, predetermined and more clearly defined. In contrast, a participation-based method is more complex, demanding that he motivate students' to participate in developing math concepts; this, he cautions, is not a straightforward matter. He believes successfully motivating all students to participate may depend on the connections made between mathematics and students' experiences outside the classroom, but these connections are highly individualized, mediated by social and cultural elements of the students' environment (Lakoff & Nunez, 1997; Lave, 1988). A "daunting task" faces him in trying to reach every student, especially since there is a wide range of abilities in his classroom. He is concerned that using a reform mathematics curriculum may detract from the quality of his teaching, thus affecting student report card grades; he is troubled that parents and administrators view report card grades as a yardstick to measure the effectiveness of the curriculum and seeks a more objective criterion for making an important curriculum decision in his school district.

There is resistance towards mathematic reform from teachers, parents, administration, and school boards. What are their concerns? One, according to Ross (1996), is that the laudable focus on understanding seems to have led to some decline in mathematical skills. Since it is easier to measure and spot deficiencies in skills, than in understanding, this decline can easily be overemphasized. However, this problem is serious, especially since our future, scientists, engineers, and mathematicians must obtain both substantial understanding and fluency in their skills. This study attempts to shed light on the question of how traditional and reform mathematics curricula affect eighth-grade mathematics students' overall mathematics achievement, problem-solving ability, and skill proficiency.

Purpose

This research investigated the impact of the traditional Houghton-Mifflin Mathematics curriculum and the Cord Applied Math curriculum on students' mathematics achievement, as measured by students' yearly Stanford Achievement Test scores. Three years of data were collected from an eighth-grade general mathematics classroom. One classroom teacher and 335 students participated in the research. The question guiding this study was: Was there a significant difference in the SAT scores and sub-scores of mathematics between the three years studied?

Methods

Participants

Approximately 335 eighth-grade students from a western United States rural school district participated in this study. These students came from various socioeconomic groups and attended a public school in a predominantly farming community of about 4500 residents.

Materials

The Cord Applied Mathematics series is a set of learning materials to help students understand the mathematics needed to work and live in a technical world; it emphasizes hands-on activities and story problems. Each unit consists of content, laboratory activities, practice exercises, and glossary terminology. The series is designed to pull from the students other fields of interest and explore these interests to see where "everyday math" fits. The Houghton Mifflin series is a program designed to reflect the Curriculum and Evaluation Standards for School Mathematics issued by the NCTM. This series is traditional in that it provides direct instruction and is hierarchical in content (i.e., arithmetic, algebra, geometry, etc.).

The Stanford Achievement Test used for this study was the Stanford Achievement Test Ninth Edition (SAT 9). The SAT 9 mathematical subtests assess all of the content in mathematics recommended by the NCTM. The SAT 9 mathematical subtests are comprised of two subtests:

Mathematical Problem Solving and Mathematical Procedure.

Procedures

Individual student SAT scores were recorded for each student who attended the researcher's eighth grade general mathematics class during the 1997-1998, 1998-1999, and 1999-2000 school years. The Houghton-Mifflin series was used in the first year of the study, the Cord Applied Math in the second and a combination of both curricula in the third year. The yearly SAT scores were analyzed using an ANOVA with a 0.05 level of significance to determine if there were differences between the scores of the three school years.

Results

Tables 1, 2, and 3 summarize the analysis of the SAT Total scores, the SAT Problem Solving scores, and SAT Procedure scores.

Table 4 presents a summary of a one-way ANOVA analysis comparing the mean SAT Total scores for all three years. No significant differences (p > 0.05) were found.

Because the SAT Procedure results were statistically significant, Tukey's HSD (honestly significant difference) Test (Table 7) was used to determine where the significant differences between the means might be.

The Tukey's HSD determined, for the SAT Procedure, that each of the pair of means differed significantly, so Houghton- Mifflin series was found superior to both the Cord Applied Math as well as the combination of both series. Finally, the combination was superior to the Cord alone.

Discussion

This study investigated the impact reform mathematics has on student achievement in mathematics. Two conclusions can be drawn from the statistics reported. First, the reform methods of the Cord curriculum did not appear to improve significantly total mathematics achievement or its sub skills of procedure and problem solving. Secondly, the traditional methods of the Houghton-Mifflin curriculum seem to have a positive impact on procedural tasks (i.e., computation, equation solving, etc).

From the eighth-grade classroom teacher's perspective, these results question the cost and time being spent by teachers and his school district to implement reform math. A reform mathematics curriculum is expensive to implement; teachers must be trained and supplementary kits must be purchased. Such expenses, in his opinion, are questionable, since a reform mathematics curriculum did not promote an increase in student achievement. In his classroom a traditional mathematics curriculum was superior with regard to teaching skills and procedural competency and, thus, would help students at the high school level, since success in high-school math courses in his school district is "built upon the foundation of facts and procedures." He summarizes the results of his study in the following manner, "Over the decades educators have tried to develop more effective methods to teach mathematics. Though most educators agree that mathematics achievement needs to improve, the current reform trend does not appear to be the answer. Further, it appears to be detrimental to procedural knowledge."

References

Ball, D.L., (1996). Teacher learning and the mathematics reform: What we think we know and what we need to learn. Phi Delta Kappan. 77(7), 500-508.

Battista, M.T. (1999). The Mathematical Miseducation of America's Youth. Phi Delta Kappan. 80(6), 424-433.

Cooney, T.J. (1988). The issue of reform: What have we learned form yesteryear? Mathematics Teacher. 81(5). 352-363.

Goldman, M. (1997). Math and Learning. Education Week. 17(2). 40.

Guskey, T.R. (1990a). Integrating innovations. Educational Leadership. 47 (4),11-15.

Lakoff, G., &ez, R.E., (1997). The metaphorical structure of mathematics: Stretching out cognitive foundation for a mind based mathematics. In L.D. English (Ed).Mathematics Reasoning: Analogies, metaphors, and images (pp. 21-89). Hillsdale, NJ: Lawrence Erlbaum.

Lave, J., (1988). Cognition in Practice: Mind Mathematics and Culture in Everyday Life. Cambridge, UK: Cambridge University Press.

McNair, R.E. (2000). Life outside the mathematics classroom: Implications for mathematics teaching reform. Urban Education. 34(5). 550.

National Council of Teachers of Mathematics. (1989). Curriculum and Evaluations Standards for School Mathematics. Reston, VA: Author.

Professional Standards for Teaching Mathematics (1990. Reston, VA: Author.

Principles and Standards for School Mathematics (2000). Reston, VA: Author.

Prevost, F.J. (1993). Rethinking how we teach: Learning mathematical pedagogy. Mathematics Teacher. 86(1). 75-79.

Ross, K.A. (1996). Mathematics Reform for K - 16. The Education Teacher. 89(7), 546-547.

Silver, E.A., & Stein, M.K. (1996). The QUASAR Project: The "revolution of the possible" on mathematics instruction reform in urban middle schools. Urban Education. 30, 476-521.

Sztajn, P., (1995). Mathematics Reform: Looking for insights form nineteenth century events. School Science & Mathematics. 95(7). 377-383.

JOHN K. ALSUP

Education

Black Hills State University

Campus Box 9108

1200 University Avenue

Spearfish, SD, 57799

MARK J. SPRIGLER

275 Hillcrest Dr.

Spearfish, SD, 57783

msprig@ hotmail.com

Black Hills State University

Copyright Project Innovation Summer 2003
Provided by ProQuest Information and Learning Company. All rights Reserved