Reform-Oriented Mathematics Instruction, Achievement, and Equity: Examinations of Race and SES in 2000 Main NAEP Data

Sarah Theule Lubienski, University of Illinois, Urbana-Champaign

Eric Camburn, University of Wisconsin, Madison

Mack C. Shelley II, Iowa State University

 

Abstract

 

Utilizing restricted-use, 2000 Main NAEP mathematics data, this study investigates the distribution and impact of instructional practices advocated by the National Council of Teachers of Mathematics (NCTM).  Specifically, this report examines intersections of race/ethnicity and socioeconomic status (SES) in students’ access to reform-oriented instructional approaches, and the relationship between such approaches and student achievement.

This study is distinctive in both its development of a powerful SES variable (based on eight relevant NAEP items) that facilitates in-depth examinations of race and SES together, and its creation of nine measures of reform-oriented instruction through factor analyses involving dozens of teacher-reported instruction-related variables.

The study identifies many similarities in instruction across Black, White and Hispanic students, as well as some reform-oriented instructional practices that are implemented more with Black and Hispanic students than with White students.  However, there were ways in which White students appeared to experience more of the fundamental shifts called for in the NCTM Standards. For example, even high-SES African American students were less likely than low-SES White students to be permitted to use calculators in 8th grade.  African American and Hispanic students were assessed with multiple choice tests more often than were White students.  Additionally, White students were more likely than African American and Hispanic students to report holding beliefs about mathematics learning that are consistent with NCTM’s ideals.

Hierarchical Linear Modeling (HLM) was utilized to determine whether particular instructional practices correlated positively or negatively with achievement after controlling for relevant student- and school-level confounding variables.  Interaction effects for race, SES and gender were examined.  The HLM analyses consistently revealed that when teacher-reported reform-oriented practices significantly correlated with achievement, they did so positively.  Specifically, collaborative problem solving and teacher knowledge of the NCTM Standards were positive predictors of achievement at both grades 4 and 8.  Additionally, an emphasis on non-number mathematical strands was a positive predictor of achievement at grade 4, whereas calculator access, a de-emphasis of facts and skills, and a greater emphasis on reasoning all correlated positively with achievement at grade 8.

In contrast, student-reported calculator use and collaborative problem solving correlated negatively with achievement at grade 4.  Although the study’s overall results do not support increasing classroom-wide restrictions on calculators or collaborative group work, an examination of interaction effects suggest that teachers need to monitor whether students—particularly those who are low-SES or African American—are benefiting from calculator and collaborative group work as intended.

Additional HLM analyses revealed a strong positive relationship between student achievement and level of disagreement with the statements, “Learning mathematics is mostly memorizing facts,” and “There is only one correct way to solve a mathematics problem.”  Hence, beliefs consistent with NCTM reforms were positive predictors of achievement at both grades 4 and 8.

Although causal relationships cannot be assumed from correlations between instructional practices and outcomes, this report points to particular instructional practices that correlate with achievement, and indicates which of these are and are not being implemented equally across White, Black and Hispanic populations.  Limitations and directions for further research are discussed.