Higher Math Achievement Research Articles

A Comparison of Learning Styles and Study Strategies Used by Low and High Math Achieving Brunei Secondary School Students: Implications for Teaching

The survey assessed the learning styles and study strategies used by 135 randomly selected Brunei secondary school students and compared them by educational level, math ability, and gender. Junior students (Forms 1-3) rely heavily on the use of the written-expressive learning style than their senior counterparts (Forms 4-5). In addition, the more able math students dominantly use the auditory-language learning style than their less able peers. Furthermore, high math achievers were better and more efficient users of the text book reading, note-taking, and memory study strategies than low achievers. Moreover, female students were more effective and superior users of the visual-language and auditory-visual-kinesthetic learning styles including the text book reading, note-taking, memory, test preparation, and concentration study strategies. These are perhaps some of the reasons why females perform better at math than males. Overall, the findings seem to have wide-ranging implications for teaching students with high support needs in mathematics.

What Affects Academic Functioning in Secondary Special Education Students with Serious Emotional and/or Behavioral Problems?

Concern is growing over the limited academic progress in special education students with emotional and/or behavioral disorders (EBD).We know little about how academic and behavioral factors interact in these students to affect their academic functioning. Therefore, potential associations were investigated over the course of one school year for 196 secondary students with EBD in a self-contained public school (SCS). Demographics, IQ and achievement testing, teacher checklist ratings for emotional/behavioral problems, and standard measures of school function were gathered. First, academic achievement was studied, and regression analyses showed that both reading and math achievement were significantly increased by higher verbal IQ and lower ADHD-inattentive symptoms (ADHD-I), and math also by higher performance IQ and younger age. Next, general academic performance was examined, and regression analysis demonstrated that major-subject GPA was significantly increased by lower ADHD-I teacher ratings, higher math achievement, and younger age. In comparison, out-of-school suspensions were significantly increased by higher conduct disorder and lower social phobia ratings. Thus, in these students with EBD in an SCS, academic functioning was primarily affected by academic parameters, and by ADHD-I but not by other emotional/behavioral problems. These results can further inform the planning of academic interventions for many students with EBD.

Examining the Association Between Implementation and Outcomes

Although there is an established literature supporting the efficacy of a variety of prevention programs, there has been less empirical work on the translation of such research to everyday practice or when scaled-up state-wide. There is a considerable need for more research on factors that enhance implementation of programs and optimize outcomes, particularly in school settings. The current paper examines how the implementation fidelity of an increasingly popular and widely disseminated prevention model called, School-wide Positive Behavioral Interventions and Supports (SW-PBIS), relates to student outcomes within the context of a state-wide scale-up effort. Data come from a scale-up effort of SW-PBIS in Maryland; the sample included 421 elementary and middle schools trained in SW-PBIS. SW-PBIS fidelity, as measured by one of three fidelity measures, was found to be associated with higher math achievement, higher reading achievement, and lower truancy. School contextual factors were related to implementation levels and outcomes. Implications for scale-up efforts of behavioral and mental health interventions and measurement considerations are discussed.

Heterogeneity in High Math Achievement Across Schools: Evidence from the American Mathematics Competition

This paper explores differences in the frequency with which students from different schools reach high levels of math achievement. Data from the American Mathematics Competitions is used to produce counts of high-scoring students from more than two thousand public, coeducational, non-magnet, non-charter U.S. high schools. High-achieving students are found to be very far from evenly distributed. There are strong demographic predictors of high achievement. There are also large differences among seemingly similar schools. The unobserved heterogeneity across schools includes a thick tail of schools that produce many more high-achieving students than the average school. Gender-related differences and other breakdowns are also discussed.

Family Socioeconomic Status and Consistent Environmental Stimulation in Early Childhood

The transition into school occurs at the intersection of multiple environmental settings. This study applied growth curve modeling to a sample of 1,364 American children, followed from birth through age 6, who had been categorized by their exposure to cognitive stimulation at home and in preschool child care and 1st-grade classrooms. Of special interest was the unique and combined contribution to early learning of these 3 settings. Net of socioeconomic selection into different settings, children had higher math achievement when they were consistently stimulated in all 3, and they had higher reading achievement when consistently stimulated at home and in child care. The observed benefits of consistent environmental stimulation tended to be more pronounced for low-income children.

The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions

This paper uses a new data source, American Mathematics Competitions, to examine the gender gap among high school students at very high achievement levels. The data bring out several new facts. There is a large gender gap that widens dramatically at percentiles above those that can be examined using standard data sources. An analysis of unobserved heterogeneity indicates that there is only moderate variation in the gender gap across schools. The highest achieving girls in the U.S. are concentrated in a very small set of elite schools, suggesting that almost all girls with the ability to reach high math achievement levels are not doing so.

Classifying Academically At-Risk First Graders into Engagement Types: Association with Long-Term Achievement Trajectories.

Based on a sample of 480 academically at-risk first graders, we used a cluster analysis involving multimethod assessment (i.e., teacher-report, peer-evaluation, and self-report) of behavioral and psychological engagement to identify subtypes of academic engagement. Four theoretically and practically meaningful clusters were identified and labeled as cooperative (n = 95), resistive (n =96), enthusiastic (n = 188), and disaffected (n = 101). The four types did not differ in IQ measured with the Universal Nonverbal Intelligence Test. The cooperative group consisted of more female and Hispanic students, whereas the resistive group consisted of more male and African American students. The cooperative group was the most popular among peers, followed by the enthusiastic group. The disaffected and resistive groups had more emotional symptoms than the cooperative and enthusiastic groups. Academic engagement types also differed in growth trajectories of academic achievement measured with Woodcock Johnson III Tests of Achievement from second to fourth grade. For reading, the cooperative and enthusiastic groups outperformed the resistive and disaffected groups at the beginning. However, the growth rate was similar across engagement types. For math, the engagement types did not differ at the beginning. However, the cooperative group developed at a faster rate and had higher math achievement by fourth grade than the other types. The findings support the importance of teaching temperament-based regulatory skills and of providing a positive psychological climate for children's academic learning.

Achievements and self-concepts in a comparison of math and science: exploring the internal/external frame of reference model across 28 countries

Marsh's (1986) Internal/External Frame of Reference (I/E) model posits a paradoxical pattern of relations between distinct school subjects, for example, math and verbal. (1) A high math achievement contributes to a positive math self-concept, and a high verbal achievement contributes to a positive verbal self-concept. (2) A high math achievement contributes to a negative verbal self-concept, and a high verbal achievement contributes to a negative math self-concept. An extension of the I/E model is proposed under which a comparison is made of the relationship between math and science, which might be regarded as distinctly different or as supplementary, and which process is termed “domain comparison”. In addition, the “supplementary” perspective (or integrating process) is a deviation from the “distinctly different” perspective (or contrasting process) that has long underpinned the I/E model. The results of exploring the I/E model for math and science across 28 countries (N = 144,069) participating in the TIMSS 2003 study revealed students from different countries undertake a contrasting or an integrating process to varying degrees. The findings suggest an incorporation of domain comparison into the I/E model.

Trajectories of career aspirations through adolescence and young adulthood: Early math achievement as a critical filter

Growth curve modelling was used to trace the trajectory of the prestige dimension of career aspirations from Grade 9 through to 3 years after high school, as a function of gender and early high school math achievement. The sample consisted of 218 university-bound adolescents (129 female, 89 male). Initial aspiration levels, the slope, and the curvature of the trajectories all differed significantly as a function of Grade 9 math performance. No significant gender or gender by achievement effects were found. These results support the notion that math achievement functions as a “critical filter” to subsequent career aspirations, with youth who performed poorly in Grade 9 math aspiring to careers that were of lower prestige. Implications of this research are discussed in terms of the development of young women's career aspirations, vocational outcomes, and involvement in higher level mathematics education.

Cognitive and Family-Support Mediators of Preschool Effectiveness: A Confirmatory Analysis

Investigated in this study were the mediators of the effects of preschool intervention on children's school achievement in sixth grade. A confirmatory structural model developed in a previous study of third graders was tested with 360 low-income, mostly black children who were available at the 3-year follow-up. The model incorporated cognitive readiness at kindergarten entry and parent involvement in school (rated by teachers and parents) as primary mediators of preschool effectiveness. In sixth grade (age 12), preschool participation at ages 3 or 4 was significantly associated with higher reading achievement, higher math achievement, and with lower incidence of grade retention. Cognitive readiness and parent involvement in school significantly mediated the estimated effects of preschool participation on school achievement and grade retention 7 years postprogram. Teacher ratings of school adjustment, school mobility, and grade retention also contributed to the transmission of effects. This integrated model fit the data better than several alternative models, including those based on the cognitive-advantage and family-support hypotheses.

Does an Extra Year Make Any Difference? The Impact of Early Access to Algebra on Long-Term Gains in Mathematics Attainment

This study investigates the lasting impact of taking algebra before high school on students ‘subsequent mathematics attainment in high school. Using a nationally representative sample of high school students, I explore the effects of early access to algebra on students’ access to advanced mathematics courses and subsequent high school math achievement. Results demonstrate that early access to algebra has an effect beyond simple increased knowledge measures and, in fact, may “socialize” a student into taking more mathematics, regulating access both to advanced coursework and increased achievement in high school. Implications for broader curriculum policy changes concerning early access to algebra are discussed.

An Experimental Study of Animation, Mathematics Achievement, and Attitude Toward Computer-Assisted Instruction

AbstractAnimation has been used in instruction for many years. However, recent advances permit the creation of desktop animations by a wider range of instructors. In order to understand the effects of animation on student learning and student reaction to it, an experimental study was conducted. A one-hour lesson on the 10th-grade mathematics topic of construction of triangles using a compass was developed in three instructional formats: (a) text only, (b) text plus static graphics, and (c) text plus animation. One hundred seventy four undergraduate elementary education majors were divided into high and low math achievement levels based on a pretest and randomly assigned to one of the three instructional groups. On a test designed to measure ability to construct triangles and identify trigonometric concepts, the animation group scored 21% and 35% higher than the graphics and text group, respectively. The graphics group scored higher than the text-only group. Attitude toward learning from CAI was equivalent...

Does an Extra Year Make Any Difference? The Impact of Early Access to Algebra on Long-Term Gains in Mathematics Attainment

This study investigates the lasting impact of taking algebra before high school on students ‘subsequent mathematics attainment in high school. Using a nationally representative sample of high school students, I explore the effects of early access to algebra on students’ access to advanced mathematics courses and subsequent high school math achievement. Results demonstrate that early access to algebra has an effect beyond simple increased knowledge measures and, in fact, may “socialize” a student into taking more mathematics, regulating access both to advanced coursework and increased achievement in high school. Implications for broader curriculum policy changes concerning early access to algebra are discussed.

The Internal/External Frame of Reference in Adolescents′ Math and Verbal Self-Concepts: A Generalization Study

This study examined the generalizability of the internal/external (I/E) frame of reference model which has been applied primarily to Australian and Canadian students. The external part of the model concerns the influence of social comparisions on the formation of math and verbal self-concepts. The internal part is when one infers one′s ability in an area (e.g., math) by comparing one′s performance in that area with one′s performance in another area (e.g., verbal). We examined whether this model was generalizable to American adolescents, across different measures of math and verbal self-concepts, and across gender. Subjects were 152 seventh and eighth graders. LISREL causal modeling and multi-sample analyses were employed. All but one of our findings were consistent with the I/E model. While higher verbal achievement made a significant contribution to lower math self-concept, higher math achievement did not make a significant contribution to lower verbal self-concept. Findings held across different self-concept instruments and across gender.

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.

Previous Experience and the Learning of Computer Programming: The Computer Helps Those Who Help Themselves

Recent developments in mathematics education indicate that previous experience is the best predictor of high school math achievement scores. Given this information we hypothesized that previous experience with computers would serve as a predictor of performance in college computer science courses. Also of interest was the possible interaction of gender, prior computing experience and computer science course performance. To examine these issues, we designed and administered a questionnaire to students across two semesters of the first year Pascal programming course at the university level. Roughly one-quarter of the students enrolled across the two semesters were female. Results show that males have more prior experience, especially in advanced computer science topics, than females, and that much of this prior experience is gained outside of school through “hacking” and unguided exploration. Amount of prior computing experience was found to predict course performance for males. For females very little prior experience was reported and this limited amount of experience was not predictive of course performance. The question of why women have so little prior experience with computers and are so sparsely represented in computer science courses is addressed.

Comparison of computer-administered and paper-administered achievement tests with elementary school children

This study compared the use of computer-administered and paper-administered versions of a classroom achievement test with elementary school children. A group of third and fourth graders was administered three forms of a 32-item arithmetic test: paper administration, computer administration with immediate item feedback, and computer administration without item feedback. No significant differences were found among the treatment groups in terms of mean test score. However, high math achievers who were administered the arithmetic test via computer with feedback showed significantly higher state anxiety than high math achievers in the other treatment conditions. These findings support the use of computers in administering classroom achievement tests. The practice of providing item feedback, however, still requires further study.

Negation, Disjunctive Syllogisms, and Mathematics Achievement

Summary It was hypothesized that high math achievement students would correctly assess syllogisms with positively and negatively worded premise statements more often than students of low math achievement, and that they would be more confident in their answers. The Mathematics Inventory I examination prepared by the School Mathematics Study Group and a disjunctive syllogism test authored by the investigator were administered to 550 male and female 8th/9th grade algebra students. Students with the top 150 and bottom 150 scores on the Mathematics Inventory made up the high and low groups. Findings revealed that students of high math achievement were not more competent in analyzing disjunctive syllogisms than students of low math achievement, nor did they express more confidence in their responses. Unexpectedly, low math achievement students were more competent with syllogisms of the form PVQ, ∼ P and PVQ, ∼ Q than high math achievement students. This was particularly true when at least one of the statements ...