The Effect of Constructivist Mathematics on Achievement in Rural Schools

Article excerpt

International assessment data indicate American students are not competing with their counterparts in other countries. The mathematics curriculum and pedagogy are not preparing students to compete in a global economy. This study compared student achievement using sixth grade mathematics results from the Illinois Standards Achievement Test. Specifically, the study compared the results of students in three different rural school districts, all of whom were receiving instruction in three different mathematics curricula. In one district, students received seven years of the K-6 Everyday Mathematics curriculum which was compared with students who received seven years of instruction using a traditional mathematics curriculum in the second district and in the third district scores were compared with students who were taught using a traditional mathematics curriculum supplemented with Mountain Math. The results of this study indicate the constructivist K-6 elementary mathematics curriculum did not lead to higher levels in math achievement when compared with the traditional methods of instruction.

Key words: mathematics curriculum; student achievement; constructivist curriculum; traditional methods of instruction

In recent years national and international assessments have spurred America's educational and political leadership into action. Mediocre results from the 2003 and 2007 Trends in International Mathematics and Science Study (TIMSS) as well as results from the 2003, 2006, and 2009 Program for International Student Assessment (PISA) have brought intense criticism on the United States public education system to change, specifically mathematics instruction, so that students can compete with their peers from other countries. The 201 1 report published by the National Center for Education Statistics Institute of Education Sciences on the National Assessment of Educational Progress (NAEP) for fourth and eighth graders showed the average scores for fourth graders in 201 1 did not show significant change from 2009. The scores of the eighth graders did show an upward trend with a 1 point increase from 2009 and a 3 point increase from 2007. Despite this trend, 32 states and jurisdictions showed no significant change at either the fourth or eighth grade. In 2008, the National Mathematics Advisory Panel declared the delivery system in mathematics education in the United States as broken and must be fixed. The panel recommended instruction be varied and not solely studentcentered or teacher-directed (U.S. Department of Education, 2008).

Despite this call, theorists have not been able to agree on a particular approach to the teaching of mathematics. Ellis and Berry (2005) point out the lack of consensus that exists in the U.S. about how to improve mathematics education. Since the 1980's, two schools of thought have been used to address the performance short-comings: the proceduralformalist curriculum and a constructivist curriculum; more recently referred to as the cognitive-cultural curriculum by Ellis and Berry (2005). The procedural-formalist curriculum is synonymous with a more traditional approach to mathematics instruction, which emphasizes a set of logically organized facts, skills, and procedures that are perfected over time. Within this traditional approach to teaching, students practice these skills and procedures repeatedly until a minimum level of competence is attained. Assessment of learning is structured around the belief there is only one way to solve a mathematics problem. Some researchers view the traditional, procedural-formalist curriculum approach to learning as a passive process of learning facts, skills, and procedures (Stigler & Heibert, 1997; Ellis & Berry, 2005). Fifteen years ago Stigler and Heibert (1997) asserted the typical eighth-grade mathematics lesson in the United States was organized around this passive form of instruction.

The constructivist approach to mathematics instruction views learning as an active process. …