Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took mathematics courses earlier than those with lower achievement. Immediate improvement in mathematics achievement was observed right after taking particular mathematics courses (regular mathematics, prealgebra, algebra I, trigonometry, and calculus). Statistical analysis showed that all mathematics courses added significantly to growth in mathematics achievement, although this added growth varied significantly across students. Regular mathematics courses demonstrated the least regulating power, whereas advanced mathematics courses (trigonometry, precalculus, and calculus) demonstrated the greatest regulating power. Regular mathematics, prealgebra, algebra I, geometry, and trigonometry were important to growth in mathematics achievement even after adjusting for more advanced courses taken later in the sequence of students' mathematics coursework.
Xin Ma and Jesse L.M. Wilkins
Robert Reys, Barbara Reys, Richard Lapan, Gregory Holiday, and Deanna Wasman
This study compared the mathematics achievement of eighth graders in the first three school districts in Missouri to adopt NSF-funded Standards-based middle grades mathematics curriculum materials (MATH Thematics or Connected Mathematics Project) with students who had similar prior mathematics achievement and family income levels from other districts. Achievement was measured using the mathematics portion of the Missouri Assessment Program (MAP) administered to all 8th graders in the state annually beginning in the spring of 1997. Significant differences in achievement were identified between students using Standards-based curriculum materials for at least 2 years and students from comparison districts using other curriculum materials. All of the significant differences reflected higher achievement of students using Standards-based materials. Students in each of the three districts using Standards-based materials scored higher in two content areas (data analysis and algebra), and these differences were significant.
Rebecca McGraw, Sarah Thuele Lubienski, and Marilyn E. Strutchens
In this article we describe gender gaps in mathematics achievement and attitude as measured by the U.S. National Assessment of Educational Progress (NAEP) from 1990 to 2003. Analyzing relationships among achievement and mathematical content, student proficiency and percentile levels, race, and socioeconomic status (SES), we found that gender gaps favoring males (1) were generally small but had not diminished across reporting years, (2) were largest in the areas of measurement, number and operations (in Grades 8 and 12) and geometry (in Grade 12), (3) tended to be concentrated at the upper end of the score distributions, and (4) were most consistent for White, high-SES students and non-existent for Black students. In addition, we found that female students' attitudes and self-concepts related to mathematics continued to be more negative than those of male students.
Harold L. Shoen, Kristen J. Cebulla, Kelly F. Finn, and Cos Fi
We report results from a study of instructional practices that relate to student achievement in high school classrooms in which a standards-based curriculum (Core-Plus) was used. We used regression techniques to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26 schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical expectations were positively related to growth in student achievement.
In this meta-analysis I examined 26 studies on the relationship between anxiety toward mathematics and achievement in mathematics among elementary and secondary students. The common population correlation for the relationship is significant (–.27). A series of general linear models indicated that the relationship is consistent across gender groups, grade-level groups, ethnic groups, instruments measuring anxiety, and years of publication. The relationship, however, differs significantly among instruments measuring achievement as well as among types of publication. Researchers using standardized achievement tests tend to report a relationship of significantly smaller magnitude than researchers using mathematics teachers' grades and researcher-made achievement tests. Published studies tend to indicate a significantly smaller magnitude of the relationship than unpublished studies. There are no significant interaction effects among key variables such as gender, grade, and ethnicity.
Olaf Köller, Jürgen Baumert, and Kai Schnabel
A total of n = 602 students (59.5% female) from academically selected schools in Germany were tested at three time points—end of Grade 7, end of Grade 10, and middle of Grade 12—in order to investigate the relationships between academic interest and achievement in mathematics. In addition, sex differences in achievement, interest, and course selection were analyzed. At the end of Grade 10, students opted for either a basic or an advanced mathematics course. Data analyses revealed sex differences in favor of boys in mathematics achievement, interest, and opting for an advanced mathematics course. Further analyses by means of structural equation modeling show that interest had no significant effect on learning from Grade 7 to Grade 10, but did affect course selection—that is, highly interested students were more likely to choose an advanced course. Furthermore, interest at the end of Grade 10 had a direct and an indirect effect (via course selection) on achievement in upper secondary school. In addition, results suggest that, at least from Grade 7 to Grade 10, achievement affected interest—that is, high achievers expressed more interest than low achievers. The findings underline the importance of interest for academic choices and for self-regulated learning when the instructional setting is less structured.
Julie E. Riordan and Pendred E. Noyce
Since the passage of the Education Reform Act in 1993, Massachusetts has developed curriculum frameworks and a new statewide testing system. As school districts align curriculum and teaching practices with the frameworks, standards-based mathematics programs are beginning to replace more traditional curricula. This paper presents a quasi-experimental study using matched comparison groups to investigate the impact of one elementary and one middle school standards-based mathematics program in Massachusetts on student achievement. The study compares statewide standardized test scores of fourth-grade students using Everyday Mathematics and eighth-grade students using Connected Mathematics to test scores of demographically similar students using a mix of traditional curricula. Results indicate that students in schools using either of these standards-based programs as their primary mathematics curriculum performed significantly better on the 1999 statewide mathematics test than did students in traditional programs attending matched comparison schools. With minor exceptions, differences in favor of the standards-based programs remained consistent across mathematical strands, question types, and student sub-populations.
Thomas R. Post, Michael R. Harwell, Jon D. Davis, Yukiko Maeda, Arnie Cutler, Edwin Andersen, Jeremy A. Kahan, and Ke Wu Norman
Approximately 1400 middle-grades students who had used either the Connected Mathematics Project (CMP) or the MATHThematics (STEM or MT) program for at least 3 years were assessed on two widely used tests, the Stanford Achievement Test, Ninth Edition (Stanford 9) and the New Standards Reference Exam in Mathematics (NSRE). Hierarchical Linear Modeling (HLM) was used to analyze subtest results following methods described by Raudenbush and Bryk (2002). When Standards-based students' achievement patterns are analyzed, traditional topics were learned. Students' achievement levels on the Open Ended and Problem Solving subtests were greater than those on the Procedures subtest. This finding is consistent with results documented in many of the studies reported in Senk and Thompson (2003), and other sources.
Michael R. Harwell, Thomas R. Post, Amanuel Medhanie, Danielle N. Dupuis, and Brandon LeBeau
This study examined the relationship between high school mathematics curricula and student achievement and course-taking patterns over 4 years of college. Three types of curricula were studied: National Science Foundation (NSF)-funded curricula, the University of Chicago School Mathematics Project curriculum, and commercially developed curricula. The major result was that high school mathematics curricula were unrelated to college mathematics achievement or students' course-taking patterns for students who began college with precalculus (college algebra) or a more difficult course. However, students of the NSF-funded curricula were statistically more likely to begin their college mathematics at the developmental level.
Aimee J. Ellington
The findings of 54 research studies were integrated through meta-analysis to determine the effects of calculators on student achievement and attitude levels. Effect sizes were generated through Glassian techniques of meta-analysis, and Hedges and Olkin's (1985) inferential statistical methods were used to test the significance of effect size data. Results revealed that students' operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. The results for both skill types were mixed when calculators were not part of assessment, but in all cases, calculator use did not hinder the development of mathematical skills. Students using calculators had better attitudes toward mathematics than their noncalculator counterparts. Further research is needed in the retention of mathematics skills after instruction and transfer of skills to other mathematics-related subjects.