Prior Math Research Articles

Academic Self‐Concept, Interest, Grades, and Standardized Test Scores: Reciprocal Effects Models of Causal Ordering

Reciprocal effects models of longitudinal data show that academic self-concept is both a cause and an effect of achievement. In this study this model was extended to juxtapose self-concept with academic interest. Based on longitudinal data from 2 nationally representative samples of German 7th-grade students (Study 1: N = 5,649, M age = 13.4; Study 2: N = 2,264, M age = 13.7 years), prior self-concept significantly affected subsequent math interest, school grades, and standardized test scores, whereas prior math interest had only a small effect on subsequent math self-concept. Despite stereotypic gender differences in means, linkages relating these constructs were invariant over gender. These results demonstrate the positive effects of academic self-concept on a variety of academic outcomes and integrate self-concept with the developmental motivation literature.

Predictors of Young Adolescents? Math Grades and Course Enrollment Intentions: Gender Similarities and Differences

Gender differences and similarities in the relations of key constructs in Eccles and colleagues’ (Wigfield & Eccles, 2000) model of achievement were examined as predictors of math grades and enrollment intentions for Grade 9 boys (n = 263) and girls (n = 277). A number of gender similarities were found, particularly in the prediction of math grades. There were, however, two gender-specific paths: for girls, a direct path from competence beliefs to enrollment intentions, and for boys, a direct path from prior math grades to enrollment intentions. In addition, for boys, the path from utility value to enrollment intentions was stronger than it was for girls. These differential predictive patterns were found even though girls and boys reported similar levels of math utility and girls had lower math competence beliefs. For girls, competence beliefs were a significant predictor of both intentions and current math grades, which indicates the central role of competence beliefs.

Authoritative parenting, parental scaffolding of long-division mathematics, and children's academic competence in fourth grade

The current study examined the relationships among authoritative parenting, parental scaffolding of long-division math problems, and children's academic competence. In a sample of 70 two-parent middle class families participating in a longitudinal study on the transition to school, authoritative parenting was assessed globally at the beginning of fourth grade, when the children were 9–10 years old, from a broad sample of laboratory-based parent–child interactions. Microanalytic assessments of parent scaffolding were conducted during a long-division task. Teacher reports and child self-reports of the children's competence were obtained at the end of fourth grade. Extending past studies, results showed that mothers' scaffolding behavior early in the fourth grade predicted teachers' reports and children's own reports of the children's academic competence at the end of the year, after controlling for the effects of authoritative parenting and prior math achievement on those outcome variables. Discussion focuses on the role of scaffolding as a tutoring strategy that may promote academic competence in school-aged children.

Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students

This research studied the self-efficacy beliefs of 107 seventh-grade mathematics students, particularly focusing on the accuracy and predictability of their beliefs. Path analysis showed that calibration accuracy had both direct and indirect effects on math performance, with indirect effects mediated through self-efficacy beliefs. Self-efficacy played a direct role in predicting students' math performance, postperformance self-evaluation, and postperformance judgments of effort. The effects of prior math achievement on math performance were mediated largely through the students' self-efficacy beliefs. The findings also did not reveal any gender differences in self-efficacy or calibration. Although the findings supported self-efficacy predictions, they also suggested important issues for future research, including accuracy of self-efficacy training in math problem solving and assessment of effort judgments prior and post performance.

Algebra for Everyone? Benefits of College-Preparatory Mathematics for Students With Diverse Abilities in Early Secondary School

Both the research literature and the experiences of many educators indicate that unequal access to academic curricula produces inequities in student learning of mathematics. "Algebra for everyone" has become a popular slogan of reform in response to these inequalities. Do all students benefit from taking algebra, regardless of their prior math performance? If so, then systems that track students away from algebra are preventing students from realizing their potential for learning. This study uses national survey data to examine the impact of high school algebra among students who differ in their math skills prior to entering high school. Regression analysis with over 12,500 students indicates that all students benefit from taking algebra; among those with very low prior achievement, the benefits are somewhat smaller, but algebra is still worthwhile for all students. These results do not derive from unwarranted extrapolation, and they are not an artifact of ceiling effects. The analysis suggests that a given student who has not taken algebra would have achieved more by doing so, but it does not say what would happen if the whole system were changed to include all students in high school algebra. However, additional analysis indicates that students gain no less from algebra when their schools include more diverse populations of algebra-takers, compared to schools with more homogeneous populations of students taking algebra.

Longitudinal Structural Equation Models of Academic Self-Concept and Achievement: Gender Differences in the Development of Math and English Constructs

Longitudinal causal models of growth in math and English constructs (school grades, standardized tests, academic self-concept, affect and coursework selection) were based on three waves of data from the large (N = 24,599), nationally representative National Education Longitudinal Study of 1988. Math and English self-concepts had significant path coefficients leading to subsequent school grades, coursework selection, and standardized test scores. Unlike previous studies that did not consider math and English constructs in the same model, we found these relations to be very domain specific (e.g., there were significant positive paths from math self concept to subsequent math outcomes but not to subsequent English outcomes). Girls had higher scores for all English constructs and math school grades, but they had lower math self-concepts. Whereas similar studies conducted over the past 20 years found diminishing gender differences, these data show relative gains for girls in achievement and coursework selection for both mathematics and English. Path coefficients relating prior math and English constructs to subsequent outcomes, however, were similar for boys and girls. Hence, the extreme domain specificity of relations between prior self-concept and subsequent outcomes was similar for boys and girls.

Longitudinal Structural Equation Models of Academic Self-Concept and Achievement: Gender Differences in the Development of Math and English Constructs

Longitudinal causal models of growth in math and English constructs (school grades, standardized tests, academic self-concept, affect and coursework selection) were based on three waves of data from the large (N = 24,599), nationally representative National Education Longitudinal Study of 1988. Math and English self-concepts had significant path coefficients leading to subsequent school grades, coursework selection, and standardized test scores. Unlike previous studies that did not consider math and English constructs in the same model, we found these relations to be very domain specific (e.g., there were significant positive paths from math self concept to subsequent math outcomes but not to subsequent English outcomes). Girls had higher scores for all English constructs and math school grades, but they had lower math self-concepts. Whereas similar studies conducted over the past 20 years found diminishing gender differences, these data show relative gains for girls in achievement and coursework selection for both mathematics and English. Path coefficients relating prior math and English constructs to subsequent outcomes, however, were similar for boys and girls. Hence, the extreme domain specificity of relations between prior self-concept and subsequent outcomes was similar for boys and girls.

Enhancing the Validity and Usefulness of Large-Scale Educational Assessments: II. NELS:88 Science Achievement

This study is second in a series demonstrating that achievement tests are multidimensional and that using psychologically meaningful subscores in national educational surveys can enhance test validity and usefulness. NELS:88 8th- and l0th-grade science tests were subjected to full information item factor analysis. Factors reflecting everyday knowledge, scientific reasoning, chemistry knowledge, and reasoning with knowledge were obtained in 8th grade. Quantitative science, spatial-mechanical, and basic knowledge and reasoning were distinguishable factors in 10th grade. Regression analyses showed that different patterns of prior math and science achievement, and of course taking, were associated with each l0th-grade science factor. Teacher emphasis on problem solving and understanding related more to quantitative science, and basic knowledge and reasoning. Spatial-mechanical reasoning showed the strongest gender and ethnicity effects; it related also to science museum visits but not to instructional variables. It is recommended that multidimensional achievement scores be used to capture student and teacher effects that total scores used alone miss.

Students’ Help Seeking During Problem Solving: Effects of Grade, Goal, and Prior Achievement

We investigated the types of help that students request while solving math problems under the tutelage of an adult. One hundred eighteen third and sixth graders, classified as high, medium, and low math achievers and working under one of two academic goal conditions (i.e., either learning or performance goals), were asked to solve inductive reasoning problems. Students were encouraged to request whatever information they felt they needed. We found that sixth graders, in comparison with third graders, were more likely to ask for process-related hints and less likely simply to ask for the answer or express a vague lack of understanding. Students given learning goals, in comparison with those given performance goals, were more likely to request confirmation of an answer and less likely to show maladaptive patterns of questioning. Performance goals had a strong, detrimental effect on the number of problems that low achievers solved. Relations among goals, prior math achievement, help seeking, and problem-solving performance were examined.

Enhancing the Validity and Usefulness of Large-Scale Educational Assessments: II. NELS:88 Science Achievement

This study is second in a series demonstrating that achievement tests are multidimensional and that using psychologically meaningful subscores in national educational surveys can enhance test validity and usefulness. NELS:88 8th- and l0th-grade science tests were subjected to full information item factor analysis. Factors reflecting everyday knowledge, scientific reasoning, chemistry knowledge, and reasoning with knowledge were obtained in 8th grade. Quantitative science, spatial-mechanical, and basic knowledge and reasoning were distinguishable factors in 10th grade. Regression analyses showed that different patterns of prior math and science achievement, and of course taking, were associated with each l0th-grade science factor. Teacher emphasis on problem solving and understanding related more to quantitative science, and basic knowledge and reasoning. Spatial-mechanical reasoning showed the strongest gender and ethnicity effects; it related also to science museum visits but not to instructional variables. It is recommended that multidimensional achievement scores be used to capture student and teacher effects that total scores used alone miss.

Modeling test anxiety among men and women

Abstract Covariance structure modeling was used to test a model of test anxiety with a sample of 204 male and 412 female college students. Variables in the model included number of prior math courses, student course level, math self-concept, self-efficacy, achievement, and general and statistical test anxiety. Results indicated that whereas some paths differed across gender, these differences were not statistically significant according to tests of invariance. General and statistical test anxiety were found to be distinct, but related constructs, as seen in the differential relationships between these variables and other variables in the model. Lack of gender differences was discussed in light of previous research.

Structural Components of Statistical Test Anxiety in Adults

The purpose of this study was to explore the basis of test anxiety expressed when taking a statistics course using a structural modeling approach. The study involved 219 university students. The data indicated that statistical test anxiety was different from general test anxiety. The females expressed more general and statistical test anxiety than males, and students who had taken more prior math courses had higher math self-concept scores. Math self-concept and achievement in statistics were negatively related to statistical test anxiety, and the students who reported high levels of general test anxiety also reported high levels of statistical test anxiety. The structural model revealed variables not studied previously to be important in understanding statistical test anxiety.