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.     

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.     

Graphing calculators and students' conceptions of the derivative

This study compared the effect of using graphing calculators on college students' conceptual understanding of the derivative with the traditional teaching approach in Calculus I course. Students (49 men and 52 women) in four classes at a large public university participated. On a posttest, women who were taught calculus using the graphing calculator had significantly higher scores than those taught by the traditional method.     

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.     

University students' priorities: Life goals vs. relationships

To assess the importance of life goals and relationships, a specially designed Life Goals Scale was administered to 303 university students (200 women and 103 men). Women's average ratings for relationships exceeded those of men. Men and women did not differ in average importance ratings of goals nor in tendency to sacrifice goals for a heterosexual relationship. Seventy-three percent were willing to sacrifice a majority of their goals for the relationship. The goal vs. relationship choices were influenced by sex role orientation, by dating status, and by the importance of marriage. Gender, age, year in school, parents' marital status, and grade point average were unrelated to goal vs. relationship choices. Stepwise multiple regression analyses indicated different predictors of goal vs. relationship choices for men and women.     

Relationship between students' self-assessment of their capabilities and their teachers' judgments of students' capabilities in mathematics problem-solving

The study examined the judgments made by four seventh-grade mathematics teachers of their 107 students' competence in solving mathematics problems. Simultaneously, the 107 students made self-efficacy judgments about their capability in solving mathematics problems. The two sets of judgments were tested for predicting students' mathematics performance. Also, students' prior mathematics achievement was studied for its influence on both teachers' and students' judgments and students' mathematics performance. Teachers were asked to make judgments of each student for every mathematics problem solved. Results were consistent with prior research indicating that students' mathematics self-efficacy beliefs were highly predictive of their performance. Path analysis indicated that the mathematics teachers' judgments were also highly predictive of students' performance and self-efficacy. In turn, these variables predicted students' postperformance judgments. Combining students' self-efficacy judgments and teachers' judgments of students increased predictiveness for students' mathematics performance. Educational implications were also discussed.     

Thinking styles: university students' preferred teaching styles and their conceptions of effective teachers

In the present study, the author investigated the role of thinking styles in university students' preferences for teaching styles and their conceptions of effective teachers. Students (121 men and 134 women) from the University of Hong Kong responded to 3 self-report tests: the Thinking Styles Inventory-Revised (R. J. Sternberg, R. K. Wagner, & L-F. Zhang, 2003), the Preferred Thinking Styles in Teaching Inventory (L-F. Zhang, 2003c), and the Effective Teacher Inventory (L-F. Zhang, 2003b). Results indicated that even after age, gender, and academic discipline were controlled, particular thinking styles predisposed students to particular teaching styles. Moreover, as expected, students were open to more than just teaching styles that precisely matched their own thinking styles. Results also indicated that students' thinking styles made a difference in their conceptions of effective teachers. Discussions are focused on the study's contributions to both the style literature and the growing body of knowledge on characteristics of effective teachers.     

Effect of teachers' stereotyping on students' stereotyping of mathematics as a male domain

This multilevel analysis used data from a representative sample from Grades 6, 7, and 8 in public schools in Switzerland. The data included information on (a) 6,602 students (3,307 girls, 3,295 boys) nested within 338 classes and (b) 321 mathematics teachers of these classes. The teachers and the students tended to stereotype mathematics as a male domain, and the teachers' stereotypes significantly affected the students' stereotypes after the author controlled for achievement, interest, and self-confidence in mathematics and for school grade and schooling track.     

Predicting success among first-year engineering students at the Rand Afrikaans University

160 first-year students in the Engineering Faculty at the Rand Afrikaans University completed the Study Orientation Questionnaire in Mathematics and the Senior Aptitude Test Advanced. 100 students who passed and 40 who failed the first year scored significantly differently on three subtests, Calculations, Study attitude in mathematics, and Problem-solving behaviour in mathematics. Step-wise linear regression showed a combination of three fields, namely, Calculations, Study attitude in mathematics, and Mathematics anxiety, contributed significantly (R2=25.8%) towards predicting the first-year aggregate score of first-year engineering students.     

University students' support for heterosexual women with AIDS

Support for a woman heterosexual AIDS victim was examined among 237 university students, 54% female and 54% upper division, with a mean age of 23.7 yr. A questionnaire containing one of four scenarios (AIDS resulting from unsafe sex, unsafe drug use, sex with an unfaithful husband, or a blood transfusion) measured support by people's willingness to sign or circulate a petition supporting the victim's right to attend college classes. A five-way mixed-design analysis of variance showed that victims who took risks received less support, that respondents were more willing to sign than to circulate a petition, and, while men did not discriminate among the four scenarios, women were most likely to offer support to "innocent" victims who contracted AIDS without sexual behavior. In addition, respondents who knew someone with AIDS were more likely to sign the petition. AIDS, particularly when contracted through risky behavior, is a disease with social ramifications beyond its threat to public health.     

Differences between students' estimated and attained grades in a first-year introductory psychology course as a function of identity development

Two hundred sixty-eight first-year university students were surveyed about the state of their identity development and their perceptions regarding chances for academic success in an introductory psychology course. In general, it was found that students who had an adult identity had a more accurate assessment of their chances for success in the course and also used more efficient study strategies. Students who had not completely formed an adult identity, however, were more inaccurate in estimates of their final grades and also seemed to use less productive study strategies. It was concluded that those who have formulated an adult identity might have also developed a more complete understanding of both themselves and their situation. Implications of the findings for further research regarding the effects of identity development on university life, as well as the implications for academic intervention programs, are discussed.     

University students' felt alienation and their attitudes toward African-Americans, women and homosexuals.

177 respondents attending a midwestern state university reported greater alienation from the wider society when they held more positive attitudes than negative ones toward women and homosexuals. Alienation and attitudes toward African-Americans, women, and homosexuals were not influenced by gender or religiosity.     

Lay conceptions of neuroticism

This paper is concerned with various aspects of a lay-person's conceptualization of neuroticism. Three experiments are reported which aim to investigate various determinants of the common-sense conception of neuroticism. In the first experiment subjects completed various standardized psychological tests measuring neuroticism and anxiety, while also estimating the extent of their own anxiety and neuroticism. In the second experiment subjects attempted to detect items measuring neuroticism in a standard personality questionnaire and secondly estimate the extent of their own and the ‘average’ person's neuroticism. Finally, in the third experiment subjects rated the typicality of various neurotic traits and behaviour which had been supplied by subjects in the previous two experiments. The results suggested some similarity in expert explicit theories and lay-person implicit theories, though there appeared to be systematic biases in the subjects' perception of their own neuroticism. The results are discussed in terms of the correspondence between implicit theories and explicit theories, and the functions of each theory in everyday life are considered. Problems associated with these studies and this research in general are discussed.     

Children's conceptions of Jesus

This paper presents findings from a recent study investigating young children's (aged 10–11) conceptions of Jesus in England. The overall picture revealed by the study is that whilst there was a general assent amongst pupils in our sample towards an ethical and humanistic conception of the historical Jesus, there was less of a consensus about those issues which previous research claims children find difficult to understand, namely: the divinity of Jesus; the miracles of Jesus; and Christian beliefs pertaining to Jesus' continued presence in people's lives today. The paper concludes by arguing that the variety of conceptions of Jesus which are encountered in religious education (RE) may be seen by children as a barrier to learning rather than an opportunity to grow in understanding and highlights the need for further research into the relationship between children's hermeneutical horizons and RE curriculum content.     

Psychological conceptions of randomness

This article presents a critique of the concept of randomness as it occurs in the psychological literature. The first section of our article outlines the significance of a concept of randomness to the process of induction; we need to distinguish random and non-random events in order to perceive lawful regularities and formulate theories concerning events in the world. Next we evaluate the psychological research that has suggested that human concepts of randomness are not normative. We argue that, because the tasks set to experimental subjects are logically problematic, observed biases may be an artifact of the experimental situation and that even if such biases do generalise they may not have pejorative implications for induction in the real world. Thirdly we investigate the statistical methodology utilised in tests for randomness and find it riddled with paradox. In a fourth section we find various branches of scientific endeavour that are stymied by the problems posed by randomness. Finally we briefly mention the social significance of randomness and conclude by arguing that such a fundamental concept merits and requires more serious considerations.