Variables influencing the mathematics performance of first-year tertiary students : a case study

The need to understand which factors most strongly affect performance in first-year mathematics programs at Khon Kaen University (KKU), in North Eastern Thailand, provided the main focus of the study which is described. First-year mathematics students in the 1990-1991 academic year, from four KKU faculty groups (Medicine and Nursing, Agriculture, Science and Education, and Engineering) were involved in this study. Research literatures addressing variables which were likely to influence performance in early tertiary mathematical study, and variables associated with difficulties in learning mathematics at the transition from upper secondary school to tertiary studies, were reviewed. The first major aim of the study was to identify the variables which were good predictors of first-year mathematics performance at KKU. Results from stepwise multiple regression analyses indicated that the following predictor variables were statistically significant and entered the regression equations for most Faculty groups: School Mathematics Achievement, Self-Esteem, Study Habits in Mathematics, and Faculty of Study. Other predictor variables that sometimes entered regression equations (depending on the Faculty group) were Socio-Economic-Status, Mathematics Language Competence, Mathematics Confidence, Attitude Towards Mathematics, and Gender. Depending on Faculty group, the statistically significant variables accounted for between 11% and 74% of scores on fist-year KKU mathematics examinations. The predictor variables contributed much more to the variance of scores on first-semester mathematics examinations than to the variance of scores on second-semester mathematics examinations. It was also found that scores on the Direct Entry Examination Mathematics test (administered by KKU) and the School Mathematics Achievement test (developed and administered by the author) had stronger correlations with first-year KKU mathematics performance than did scores on the National Entry Examination Mathematics tests (administered by the Thai Ministry of University Affairs). Scores on the three pre-university mathematics achievement test instruments were better predictors of first-semester mathematics performance than of second-semester mathematics performance. It was found that the mean Mathematics Confidence of male students was statistically significantly higher than that of female students, but there were no statistically significant gender differences in Mathematics Misplaced Confidence. Only about 30% of the main sample ( 30% of the male and 30% of the female sample groups) had appropriate confidence in mathematics, that is, they thought their answers were correct when they were, in fact, correct, and they thought they were wrong when they were, in fact, incorrect. So far as Faculty performance differences were concerned, Engineering students had the highest Mathematics Confidence scores, followed by the Medicine and Nursing group of students and the Science and Education group students. Agriculture students had the lowest mean Mathematics Confidence score. No statistically significant differences occurred in Mathematics Misplaced Confidence between different Faculty groups. The second main aim of the study was to investigate why many first-year students experienced difficulties in coping with their mathematics units. A small group of senior secondary mathematics teachers, university mathematics lecturers, and first-year mathematics students were interviewed during the first semester of the 1990-1991 academic year. Interviews were conducted by the author according to a questionnaire format, and were aimed at identifying factors causing difficulty in the transition from senior secondary to university mathematical study. The analysis of the quantitative data together with the interview data indicated that the major sources of difficulty were associated with: (a) students' mathematical abilities; (b) curriculum content; (c) course organisation; (d) students' study habits; (e) instructional styles; and (f) assessment procedures. The results of the investigation are discussed in the light of the relevant literature and related research. The study concludes with recommendations which are addressed to mathematics teachers and education administrators in senior secondary schools in Thailand, to the Thai Ministry of Education, and to the KKU Department of Mathematics.

Implementing cooperative learning in grade four mathematics classes in Thailand

This study showed that successful implementation of cooperative learning in Thai primary mathematics classrooms requires three components: preparation of teachers, preparation of instructional materials and the preparation of pupils. In addition, cooperative learning was found to have a positive effect on pupils' mathematics achievement and their attitude towards mathematics.

The "strugglers" in selected computer based mathematics classrooms

In this paper, the experiences of lower achieving mathematics students in two secondary mathematics classrooms in which computers were regularly used are described. A year 8 and a year 9 mathematics class from one secondary school participated in the ethnographic study. The results show that in these two classrooms the learning relationships and power relationships did not, in general, support the learning and engagement of lower achievers in mathematics. Research into computer based teaching methods that engage low achieving students in computer based mathematics is needed.

Trends and factors concerning gender and mathematics in Australasia

For many years now gender differences in average mathematics achievement in Australia and New Zealand have not been significant in large-scale domestic and international studies. However there is some recent evidence, from Australia at least, that gender differences in achievement favouring males may be re-emerging and, despite some positive affective findings and trends with respect to affect and participation leading up to the turn of the century, a pattern of lower interest and declining participation in mathematics among girls is evident. In this paper, trends in gender equity with respect to participation, achievement and affect reported in the literature over the past decade will be presented and analysed. Of particular interest are the factors that may have influenced these trends. Findings from recent research will be discussed. However it would seem that the attempts made by researchers to explain these trends are either limited in their capacity to establish an explanation or imply a deficit view of girls. An alternate position on gender equity and explanation of these trends will be presented in this paper with the purpose of making a contribution to the debate on curriculum and pedagogy in mathematics education.

Technology for mathematics education : equity, access and agency

In this chapter, issues of equity – including gender, access, and agency – with respect to the learning of mathematics with technology are examined. Research findings are not equivocal. Compared to late developing countries, where issues of access to technology can be complicated by educational and cultural values and beliefs, there seems to be greater access to technology to be used for the learning of mathematics in developed nations. There also appears to be some disparity in findings on the relationship between technology use and gender differences in mathematics achievement; in some countries the gender gap favoring males may be closing, while in other countries, where there have been little or no gender differences in the past, the gap may be widening. Areas in which more research is needed have been identified.

Using assessment data : does gender make a difference?

Since 2000 gender differences in mathematics achievement in Australia have reappeared. In this paper we report on the achievement outcomes of girls and boys in a longitudinal study of reform in low economic school communities. Analysis of student data to inform teaching was one element of student centred approaches implemented by teachers. Teachers targeted students’ next point of learning and more girls than boys participated in mathematics intervention programs. Growth in achievement was greater for boys than for girls in the primary years, and so the achievement gap that favours males widened. It is concluded that student centred approaches need to be gender inclusive.

Student centred approaches : teachers' learning and practice

Student-centred approaches to teaching and learning in mathematics is one of the reforms currently being advocated and implemented to improve mathematics outcomes for students from low SES backgrounds. The models, meanings and practices of student-centred approaches explored in this paper reveal that a constructivist model of student-centred teaching and learning is being promoted and implemented with some success. The ways in which teachers and leaders are being supported through network and school-based professional learning are described.

The role of attention in the academic attainment of children with autism spectrum disorder

Academic attainment in children with Autism Spectrum Disorder (ASD) is under-studied, with associated factors largely undetermined. Parent-reported attention symptoms, attentional-switching and sustained-attention tasks were examined to determine relationships with mathematics and reading attainment in 124 children aged 7–12 years; sixty-four with high-functioning ASD, half girls, and sixty age- and gender-matched typical children (TYP). With full-scale IQ controlled there were no differences in mathematics, reading, attentional switching or sustained attention. In regression analysis, attentional switching was related to mathematics achievement in ASD but not TYP children. Findings highlight attentional switching difficulties are linked with poorer mathematics outcomes in ASD.

Sex differences in achievement in year 12 mathematics and non-routine problem solving

In 1991 all Victorian year 12 students undertook the new Victorian Certificate of Education Mathematics Study designed by the Victorian Curriculum and Assessment Board. This paper presents the results of a study into sex difference in achievement in the new VCE Mathematics study in Victoria. An important goal of the study designers was to encourage more equal participation in senior secondary mathematics by females and males and to include assessment of mathematical skills previously not assessed in a year 12 course in Victoria. These new tasks could conceivably change the degree and direction of sex difference in achievement in senior secondary mathematics.

Large-scale mathematics assessment : looking globally to act locally

In this paper, I will argue that it is possible to use data from large-scale international and national mathematics assessment programmes, whose attention is on summative achievement, to provide formative information that informs teachers about the effects of their classroom practice. However, to have impact on, and be useful for, classroom practitioners, these achievement data need to be reworked and re-presented in ways that are plausible, provide a basis for inferences about practice, and be appropriate for the intended audience. This paper examines achievement-focused assessment programmes in terms of their aims and approaches, and develops the argument that formative assessment possibilities are present, within these programmes, although usually hidden. Examples are drawn from several sources to support this argument, and demonstrate a variety of approaches that have been taken in the past. Suggestions for further action are made.

Towards an integration of theories of achievement motivation

This thesis investigated children's school achievement in terms of an integration of three theories of achievement motivation. The three theoretical outlooks were expectancy-value theory (EVT), implicit theories of intelligence (ITI), and flow theory (FT). The first of two studies was an exploratory investigation of the effectiveness of each theory independently and combined to predict children's achievement in four school subjects. The subject areas were maths, reading, instrumental music and sport. Participants were 84 children (40 females and 44 males) aged 9 to 10 years, one of each child's parents, and school teachers of each child in the four subject areas. All data were collected through questionnaires based on the three models. The results indicated that EVT and FT but not ITI accounted for a significant amount of the variance in children's achievement, including effects for subject area and gender. A second confirmatory study tested EVT, FT and an integrated model for the prediction of achievement in maths, reading and instrumental music. The participants were a further 141 children (74 females and 67 males) aged 10 to 11 years, and a parent and teachers of each child. Data collection using questionnaires occurred early in the school year (Timel) and approximately five months later (Time2). For EVT, children and parents’ competence beliefs were significant predictors of children's achievement in each subject area. Females tended to believe themselves more competent at reading and instrumental music and also valued these subjects more highly than boys. Modeling results for flow theory indicated that children's emotional responses to classes (happiness and confusion) were significant predictors of achievement, the type of emotion varying between subject areas and time periods. Females generally had a more positive emotional reaction to reading and instrumental music classes than males did. The integrated model results indicated significant relationships between EVT and flow theories for each subject area, with EVT explaining most achievement variance in the integrated model. Children's and parents’ competence beliefs were the main predictors of achievement at Timel and 2, Subject area and gender differences were found which provide direction for future research. Anecdotal reports of parents and teachers often attest to individual differences in children's involvement in various school domains. Even among children of apparently similar intelligence, it is not uncommon to find one who likes nothing better than to work on a mathematics problem while another much prefers to read a novel or play a musical instrument Some children appear to achieve good results for most of the activities in which they are engaged while others achieve in a less consistent manner, sometimes particularly excelling in one activity. Some children respond to failure experiences with a determination to improve their performance in the future while others react with resignation and acceptance of their low ability. Some children appear to become totally absorbed in the activity of playing sport while others cannot wait for the game to end. The primary research objective guiding the current thesis is how children's thoughts and feelings about school subjects differ and are related to their school achievement. A perusal of the achievement motivation literature indicates several possible models and concepts that can be applied to explain individual differences in children's school achievement. Concepts such as academic self-concept, multiple intelligences, intrinsic and extrinsic motivation, self-beliefs, competence beliefs, subjective task values, mastery and performance goals, ‘Flow’ experiences and social motivation are just some of the constructs used to explain children's achievement motivation, both within and between various activity domains. These constructs are proposed by researchers from different theoretical perspectives to achievement motivation. Although there is much literature relevant to each perspective, there is little research indicating how the various perspectives may relate to each other. The current thesis will begin by reviewing three currently popular theoretical orientations cited in achievement motivation research: subjective beliefs and values; implicit theories of intelligence, and flow experience and family complexity. Following this review, a framework will be proposed for testing the determinants of children's school achievement, both within each of the three theoretical perspectives and also in combination.

Improving middle years mathematics and science

The overall aim of the Improving Middle Years Mathematics and Science (IMYMS) project was to explore the explore the nature and significance of subject cultures in framing teacher and school practice in mathematics and science and to develop a middle years school improvement model that takes account of these subject cultures in influencing school and teacher change. The project also investigated ways in which effective pedagogies in mathematics and science can be monitored; and ways in which higher order learning outcomes in mathematics and science can be reliably assessed.

The project has worked with more than 30 schools in four clusters to support them in planning for and implementing change. A framework describing effective mathematics and science pedagogies was developed, and used as the basis for auditing procedures that track classroom practice. Instruments were developed and used to probe: teacher classroom practice; student perceptions of classroom practice and learning preferences; knowledge outcomes; reasoning in science and mathematics; understanding of the nature of science and mathematics; and performance skills in mathematics and science investigations. Data sources have also included questionnaire data, interviews, school reports and field notes. Video data was also collected and used for stimulated recall interviews concerning teacher beliefs and practices.

In order to support teachers and schools to improve their practice, the project team worked with cluster educators in each of the clusters, and with school coordinators, through a number of network meetings including an initial ‘leading change’ workshop, through cluster visits, and the provision of auditing and planning instruments supported by data analysis support. The nature of the subject cultures of, and effective pedagogies in, mathematics and science, was explored using interview data with effective teachers, literature exploration, interviews with project teachers to map characteristics of their practice, the team’s experience of the construction and analysis of achievement tests, a video and interview study of teachers of mathematics and science, and student perceptions data.