Heuristic and algorithmic processing in English, mathematics, and science education

Many college students experience difficulties in basic academic skills. Recent research suggests that much of this difficulty may lie in heuristic competency--the ability to use and successfully manage general cognitive strategies. In the present study, the authors evaluated this possibility. They compared participants' performance on a practice California Basic Educational Skills Test and on a series of questions in the natural sciences with heuristic and algorithmic performance on a series of mathematics and reading comprehension exercises. Heuristic competency in mathematics was associated with better scores in science and mathematics. Verbal and algorithmic skills were associated with better reading comprehension. These results indicate the importance of including heuristic training in educational contexts and highlight the importance of a relatively domain-specific approach to questions of cognition in higher education.     

A preliminary study of achievement, attitudes toward success in mathematics, and mathematics anxiety with technology-based instruction in brief calculus

This study was designed to compare achievement, attitudes toward success in mathematics, and mathematics anxiety of college students taught brief calculus using a graphic calculator, with the achievement and attitudes and anxiety of students taught using the computer algebra system Maple, using a technology based text book. 50 men and 50 women, students in three classes at a large public university in the southwestern United States, participated. Students' achievement in brief calculus was measured by performance on a teacher-made achievement test given at the end of the study. Analysis of variance showed no significant difference in achievement between the groups. To measure change in attitudes and anxiety, responses to paper-and-pencil inventories indicated significant differences in favor of students using the computer.     

Nigerian undergraduate education majors' conceptions of mathematics

The Conceptions of Mathematics Questionnaire by Crawford, et al. was administered to 130 southwest Nigerian undergraduate education majors who took mathematics. Coefficient alphas of .86 and .84 for the Fragmented and Cohesive subscales were similar to prior values. There were no statistically significant mean differences between men and women or between undergraduates taking mathematics with science and nonscience topics.     

初中生数学焦虑的调查及其调控研究

数学焦虑既是心理科学研究的对象,又与教育、教学,特别是学科教学密切相关。本文调查发现:部分初中生存在过度的数学焦虑,并且在年级、性别等维度上具有明显差异;教师的评价方式、课堂气氛、数学考试是形成数学焦虑的主要原因。运用三条教学策略的实验研究表明,数学焦虑是可以调控的,而且数学焦虑的缓解对学生数学成绩的提高有一定的促进作用。     

Gender and mathematics anxiety: The role of math-related experiences and opinions

Abstract

Research has indicated that women may be particularly prone to experiencing mathematics anxiety and, to account for this, the sex-role socialization hypothesis posits that women are more math anxious because they have had less experience with mathematics and have more negative opinions regarding mathematics. In contrast, the math experiences hypothesis suggests that math anxiety is not truly a gender-related phenomenon, but rather is due to poor mathematical preparation, regardless of gender. The present study pitted the “sex-role” hypothesis against the “math experience” hypothesis in an examination of the relation between gender and math anxiety. One hundred and seventy-one university students completed a measure of math anxiety and a series of questions regarding their math marks, opinions, and experiences throughout their educational history. The findings clearly supported the math experience hypothesis of math anxiety, for differences in math marks, opinions, and experiences were found between non-math-anxious, moderately math-anxious, and highly math-anxious students. The few gender differences that were found indicated that the female students frequently reported higher math marks than those reported by male students. We suggest that the relation between gender and mathematics anxiety may be accounted for by gender-linked reporting biases. The limitations of the study are addressed and suggestions for future research are made.     

Locus of control, self-control, and family income as predictors of young children's mathematics and science scores

Locus of control, self-control, and family income were investigated as possible predictors of 138 young children's mathematics and science scores. The children, 60 boys and 78 girls, ranging from 4 to 8 years of age (M = 5.4, SD = 1.3) were administered the Stephens-Delys Reinforcement Contingency Interview Scale, the Self-control Rating Scale, the Comprehensive Mathematics Inventory, and a science test based on the work of D. K. Dickinson. Analysis showed mathematics scores were positively related to income, locus of control, and science scores. Mathematics and science scores were negatively related to lack of self-control. Also, science scores were positively related to locus of control. Multiple regression analysis with mathematics as the dependent variable indicated income had the greatest predictive value followed by self-control and locus of control. The multiple regression model of science was also significant, with locus of control having the greatest influence followed by self-control.     

Gender and racial differences in mathematical performance

The authors examined gender and racial differences in mathematics performance among 5th- and 8th-grade students in the United States. Math performance was assessed by scores on the math-concepts and math-computation sections of the California Achievement Test (CTB/McGraw-Hill, 1986) given at the end of the previous year. There were no significant gender differences, but in both grades, the White students scored significantly higher than the Black students. The racial differences were more pronounced in the scores for concepts than in the scores for computation. Responses to a parent questionnaire showed significant relationships between parents' self-reported math anxiety, parents' most advanced math course, and parents' education level in relation to the child's math performance. Differences in these relationships suggest that, although parents' beliefs and attitudes about math influence their child's math performance, the relationship is complex and may vary with race.     

University students' achievement goals and approaches to learning in mathematics

Background Achievement goals (AG) and students' approaches to learning (SAL) are two research perspectives on student motivation and learning in higher education that have until now been pursued quite independently. Aims This study sets out: (a) to explore the relationship between the most representative variables of SAL and AG; (b) to identify subgroups (clusters) of students with multiple AG; and (c) to examine the differences between these clusters with respect to various SAL and AG characteristics. Sample The participants were 680 male and female 1st year university students studying different subjects (e.g. mathematics, physics, economics) but all enrolled on mathematics courses (e.g. algebra, calculus). Method Participants completed a series of questionnaires that measured their conceptions of mathematics, approaches to learning, course experience, personal 2 × 2 AG, and perceived AG. Results SAL and AG variables were moderately associated and related to both the way students perceived their academic environment and the way they conceived of the nature of mathematics (i.e. the perceptual‐cognitive framework). Four clusters of students with distinctive multiple AG were identified and when the differences between clusters were analysed, we were able to attribute them to various constructs including perceptual‐cognitive framework, learning approaches, and academic performance. Conclusio This study reveals a consistent pattern of relationships between SAL and AG perspectives across different methods of analysis, supports the relevance of the 2 × 2 AG framework in a mathematics learning context and suggests that AG and SAL may be intertwined aspects of students' experience of learning mathematics at university.     

Music training and mathematics achievement

Iowa Tests of Basic Skills (ITBS) mathematics scores of eighth graders who had received music instruction were compared according to whether the students were given private lessons. Comparisons also were made between students whose lessons were on the keyboard versus other music lessons. Analyses indicated that students who had private lessons for two or more years performed significantly better on the composite mathematics portion of the ITBS than did students who did not have private lessons. In addition, students who received lessons on the keyboard had significantly higher ITBS mathematics scores than did students whose lessons did not involve the keyboard. These results are discussed in relation to previous research on music training and mathematics achievement.     

Measuring up: Academic performance of Canadian immigrant children in reading,mathematics, and science

Using the Canadian sample from the Programme for International Student Assessment, this study examined the effects of student and school characteristics on academic achievement of immigrant and non-immigrant students. No differences were found in mathematics achievement, but non-immigrant students outperformed immigrant students in both reading and science achievement. At the student level, there was more gender equity in academic achievement among immigrant than non-immigrant students. Socioeconomic inequity was related to fathers among immigrant students but to both mothers and fathers among non-immigrant students. Home language had weaker effects among immigrant than non-immigrant students. At the school level, teacher-student ratio, teacher morale, and academic pressure were predictors for immigrant students, whereas disciplinary climate for non-immigrant students. Non-immigrant students demonstrated tremendous regional differences that were absent among immigrant students.     

English learners' achievement in mathematics and science: Examining the role of self-efficacy

The goals of the current study were twofold. The first goal was to describe levels of mathematics and science self-efficacy and achievement among a sample of students with varying levels of English language proficiency. The second goal was to examine the extent to which students' self-efficacy explains the relation between their English proficiency level and mathematics and science achievement. The sample consisted of 332 fifth graders (mean age = 10.46 years, SD = 0.38) and their 63 teachers in 20 schools. The student sample was linguistically diverse with parents reporting 22 different home languages. Based on district classification procedures, each student was coded into one of three English language proficiency level categories: English proficient-speaking students (English proficient), English Learner (EL) students who are reaching proficiency, yet are still being monitored (reaching proficiency), and EL students who are receiving English for Speakers of Other Languages services (ESOL; limited English proficient). Regression analyses indicated that students identified as limited English proficient consistently demonstrated lower achievement and self-efficacy across the content areas of mathematics and science as compared to their peers who were English proficient and reaching proficiency. In addition, students' self-efficacy partially explained the relation between limited English proficiency level and achievement for science, but not for mathematics. Results indicate that educators should consider variability in students' English proficiency levels as they select supports to promote both science achievement and self-efficacy. Findings also suggest promise for practices and programs that foster self-efficacy in addition to language and content skills.     

The Kuwait University Anxiety Scale: results for 9,031 Saudi students

The Kuwait University Anxiety Scale was administered to 9,031 male (n = 4,143) and female (n = 4,888) Saudis. They were students in secondary schools (n = 4.793) and university undergraduates (n = 4,238) recruited from scattered geographical regions of the Kingdom of Saudi Arabia. Ages ranged from 15 to 26 years, mean age 19.5 yr. (SD = 2.8). The scale displayed good alphas (from .85 to .88), retest reliability (from .94 to .95), as well as good criterion-related validity (from .63 to .73) against the Trait subscale of the State-Trait Anxiety Inventory. Three highly loaded factors were extracted: Cognitive/Affective, Subjective, and Somatic anxiety. Sex differences overshadow age differences as sex-related differences were significant between the age groups from 16 to 25 years, i.e., females attained higher mean scores than their male peers. Saudi students attained means similar to those of Kuwaiti students, but both groups have significantly higher mean scores than American and Spanish college students. By and large, the scale can be recommended for use in research among students in the Saudi context.     

Spatial anxiety relates to spatial abilities as a function of working memory in children

Spatial ability is a strong predictor of students' pursuit of higher education in science and mathematics. However, very little is known about the affective factors that influence individual differences in spatial ability, particularly at a young age. We examine the role of spatial anxiety in young children's performance on a mental rotation task. We show that even at a young age, children report experiencing feelings of nervousness at the prospect of engaging in spatial activities. Moreover, we show that these feelings are associated with reduced mental rotation ability among students with high but not low working memory (WM). Interestingly, this WM?×?spatial anxiety interaction was only found among girls. We discuss these patterns of results in terms of the problem-solving strategies that boys versus girls use in solving mental rotation problems.     

Reading Proficiency and Comparability of Mathematics and Science Scores for Students From English and Non-English Backgrounds: An International Perspective

The purpose of this research is to examine the comparability of mathematics and science scores for students from English language backgrounds (ELB) and non-English language backgrounds (NELB). We examine the relationship between English reading proficiency and performance on mathematics and science assessments in Australia, Canada, the United Kingdom, and the United States. The findings indicate a strong relationship with reading proficiency accounting for up to 43% of the variance in mathematics and up to 79% in science. In all comparisons, ELB students either outperformed NELB students or performed at the same level. However, when statistical adjustments were made for reading proficiency, in both mathematics and science, the score gap between the groups became statistically non-significant in three out of the four countries. These findings point to differences in score meaning in mathematics and science assessments and limitations in comparing performances of ELB and NELB.     

Athletic self-concept and mathematics achievement in girls

Several researchers have suggested that girls' mathematics performance may be mediated by an assertive sex role or "masculine interest." The present study made the assumption that girls' athletic self-confidence reflects "masculine interest" so girls' test scores for perceived athletic competence would be related to their mathematics achievement scores. A total of 207 boys and girls in Grades 4, 5, and 6 were tested for their perceived athletic ability using the Athletic Competence subscale of Harter's 1985 Self-perception Profile, and these scores were correlated with their mathematics achievement as measured on the Metropolitan Achievement Test and term grades. A low but significant correlation with Athletic Competence scores was found for girls on both measures of mathematics achievement. Although boys scored higher on the Athletic Competence subscale, there were no sex differences on either measure of mathematics achievement. Results are discussed in terms of both sex-role theory and cognitive development.     

Verbal,mathematics, and physical education self-concepts and achievements: An extension and test of the Internal/External Frame of Reference Model

ObjectivesThe Internal/External Frame of Reference Model (I/E model; e.g., Marsh, 1986) posits that verbal achievement (Ach) produces a lower mathematics self-concept (SC) and that, conversely, mathematics Ach fosters a lower verbal SC after controlling for prior Ach in each domain. The present study extended this model by adding another school subject that has not been previously investigated, namely physical education (PE). The central goal was to verify whether Ach in PE positively or negatively predicts academic SC in the mathematics and verbal domains.DesignProspective study over one school year.MethodsParticipants were 451 French high school students (mean age = 13.5). Ach scores in mathematics, French and PE were gathered at the beginning of the school year. At the end of this one, students completed a questionnaire to assess their SC in the three school subjects. Results: Structural Equation Modelling results revealed, according to the I/E model, negative paths between mathematics Ach and verbal SC, and between verbal Ach and mathematics SC. Results also revealed singular relationship patterns between the two traditional school subjects and PE. A positive path between PE Ach and mathematics SC was observed whereas the path with the verbal SC was non-significant.ConclusionPE could have benefits to increase SC in other school subject such as mathematics. Broader implications of results for the I/E model are discussed.     

Helping parents to motivate adolescents in mathematics and science: an experimental test of a utility-value intervention

The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem.     

Math anxiety, mother's education, and the mathematics performance of adolescent boys and girls: evidence from the United States and Thailand

In this study, I investigated the relationship of mathematics performance to math anxiety, mother's education, and gender. A secondary analysis was conducted using nationally representative samples of 13-year-old children in the United States (N = 4,091) and Thailand (N = 3,613) collected as a part of the Second International Mathematics Study (Garden, 1987). Separate ANOVAs (Math Anxiety x Mother's Education x Gender) were run within each country using a 40-item math performance test as the dependent variable. Math anxiety has an inverse relationship with mathematics performance in the United States (r = -.24) and in Thailand (r = -.14). The relationship between math anxiety and mathematics performance is significant in both countries after controlling for previous achievement, mother's education, and gender, although the data suggest that there is a three-way interaction between math anxiety, mother's education, and gender in Thailand.     

小学儿童数学焦虑的潜在类别转变及其父母教育卷入效应：3年纵向考察

研究采用潜在转变分析考察小学儿童数学焦虑的类别转变以及父母教育卷入在小学儿童数学焦虑类别转变中的作用。以1720名三、四年级儿童为被试, 对其数学焦虑和感知到的父母教育卷入进行3次追踪, 每次间隔1年。结果表明：(1)小学儿童数学焦虑存在低数学焦虑组、高数学评估焦虑组和高数学获得焦虑组3种不同类别; (2)随时间的推移, 高数学评估焦虑组倾向于向低数学焦虑组转变, 高数学获得焦虑组倾向于向高数学评估焦虑组转变, 而低数学焦虑组稳定性较强; (3)父亲/母亲教育卷入对儿童数学焦虑类别转变的预测作用, 因不同的数学焦虑类别而异。上述发现为深入理解数学焦虑的形成机制以及干预措施的制定提供了重要参考。     

Attitudes toward and approaches to learning first-year university mathematics

This study examined the relationship for 180 undergraduate students enrolled in a first-year university calculus course between attitudes toward mathematics and approaches to learning mathematics using the Mathematics Attitude Scale and the Approaches to Learning Mathematics Questionnaire, respectively. Regression analyses indicated that scores for the Mathematics Attitude Scale were negatively related to scores for the Surface Approach and accounted for 10.4% of the variance and scores for the Mathematics Attitude Scale were positively related to scores for the Deep Approach to learning mathematics and accounted for 31.7% of the variance.