Abstracts
The ubiquitousness of the Internet and communication technologies is having a significant influence on teaching and learning practices both in terms of what is learnt and how it is learnt. Mathematics teaching and learning in vocational education is also facing new challenges due to the enormous influence of new technologies on workplace practices. This study makes an attempt to design and implement a web-based learning environment to facilitate and enhance the teaching and learning of mathematics in a TAFE setting. The design and development of the web-based learning environment aimed at providing opportunities for more engaging and authentic learning activities and promoting the use of new learning technologies in mathematics teaching and learning. The study included a practical orientation of action to bring about a change in the practice of teaching of mathematics in vocational education. Using a design-based research approach the study comprised two cycles. In the first cycle three mathematics teachers were involved in exploring Internet based mathematics resources and participated in the design of a website that consisted of twelve units of basic mathematical topics with facilities for both synchronous and asynchronous communication. This web-based learning environment known as Maths Concurrent Assistance (MCA) Online was then trialled with a number of mathematics teachers and students in mainly workshop mode. In the second cycle, the web-based learning environment was customised for a business mathematics module in a diploma course and trialled with a semester long course taught on campus in a blended learning format. Data obtained through classroom observation, WebCT logs, discussion board postings, test results and interviews were used to explore and analyse issues concerned with students' participation, access and use and the role of teacher in facilitating mathematics learning. The study also included a quasi-experimental research design to compare achievement and attitude of students who participated in this experiment with another group of students taught the same content by the same teacher in a traditional face-to-face mode with no Internet activities. Results from the study indicate that students' successful participation in web-based mathematics learning in vocational education is contingent upon factors including learner readiness, interface design and course design. Students' attitude towards mathematics appeared to influence their participation in web-based mathematical activities. Although computer skills and confidence are necessary for successful participation in web-based activities, students' attitude towards mathematics played a more important role in determining their participation.
According to previous research, mathematics anxiety tends to increase in early adolescence, in addition to general decreases in academic motivation. Concurrent with these trends, adolescence is also the time when peers begin to play a larger part in the social development of the individual. The objective of this thesis was to explore adolescent mathematics anxiety from two broad perspectives. Two studies were conducted that examined affective (Study 1) and relational (Study 2) factors associated with the mathematics anxiety of Year 8 students from two co-educational schools in Victoria, Australia. A two-wave, two-school design allowed extensive analyses of these factors from both cross-sectional and longitudinal positions. Part one of the thesis focuses on the affective basis of adolescent mathematics anxiety. Study 1 explored trait mathematics anxiety in addition to the state or on-task anxiety that arose as participants completed a mathematics problem-solving task. Assessment of on-task anxiety was achieved via the use of the computer program Between the Lines (BTL). The two dimensions of emotionality and worry were found within trait responses but not state responses. Trait mathematics anxiety was also found to be distinct from general test anxiety. Consistent with research trends, girls reported higher levels of mathematics anxiety, and anxiety was negatively correlated with achievement. Person-centred analysis of on-task engagement produced profiles that showed a unique association of anxiety and interest with performance patterns on the BTL tasks; in turn, these profiles were related to particular trends of regulatory compatibility. Finally, relationships between anxiety and motivation, namely value and competence beliefs, were examined according to the control-value theory of achievement emotions. These associations varied for trait and state (pre- and post-task) models and also according to school. Part two of the thesis offers a relational perspective on adolescent mathematics anxiety by focusing on the role that peer networks play in its aetiology. While the dyadic effects of peer relationships on motivation and learning have been investigated, less attention has been directed to the influence of different types of peer networks. Study 2 used a social network approach and contemporary modelling techniques to explore peer interactions and their effects on mathematics anxiety and motivation. This thesis provided the first application of the two modelling techniques in the area. A cross-sectional analysis extended trends observed within Study 1 data to emphasize the impact of contextual factors, with peer influence and peer culture varying according to school, type of peer relationship, and the specific attribute considered, namely, mathematics anxiety, value or competence beliefs. Social influence modelling allowed for the exploration of different mechanisms of social influence – broadly, contagion and activity processes – within time, help-seeking and close-friend networks. Longitudinal modelling of these three networks, along with mathematics anxiety and gender, again revealed between school variation and differences across peer relationships. No evidence of social influence was found, however, social selection effects were observed in varying networks across the two schools.
Shirazian, Zahra Parvanehnezhad
The purpose of this study was to explore of the role of language switching in a group of Iranian bilingual students while they were involved in mathematical problem solving. Language switching has been viewed as a common practice in bilingual students in their classroom, particularly for mathematics learning. In bilingual students, using their first language to solve at least part of a problem may facilitate mathematical thinking and lead to a successful problem solving process. The bilingual children in this study were comprised of sixteen Iranian non-English speaking background (NESB) Year 4 and 5 students who attended state schools on weekdays and participated in two Persian schools on weekends during term 4, 2005. To address the main aim of the study, four research questions were posed; (i) To what extent do Year 4/5 Iranian NESB students use language switching while solving different types of mathematical problems?, (ii) What factors prompt language switching (if any) in this sample of bilingual students?, (iii) Is there any relationship between proficiency in the L1 (Persian) and L2 (English) languages and mathematics performance/ competency?, and (iv) What, if any, relationship exists between students’ background and language switching?
After completing a pilot study and reviewing the results, a qualitative case study methodology was chosen as the most appropriate means of providing in-depth data for the main aim of this research. Based on Clarkson’s (1996) study, data was derived from the transcripts of a semi-structured interview, two language comprehension tests, and a questionnaire administered to parents. The interview was comprised of two phases; a mathematical problem solving phase which involved three different types of mathematical questions (word problems, symbolic and open-ended questions) and an associated Language Switching Checklist; and, in phase 2, a series of questions about the student’s problem solving strategies, their use of language switching, and home background. Language comprehension tests comprised of an English reading comprehension (TORCH) test in a cloze format, and a Persian reading comprehension test in a short-answer format, were used to determine the level of students’ proficiency in English (L1) and Persian (L2). The parent questionnaire contained items regarding home status and background, such as parents’ expectation for their children’s education, and the language spoken most of the time at home.
Results showed that a large proportion of Iranian NESB students used language switching to solve the three types of mathematics problems, particularly word problems. In focussing on the type of questions attempted, language switching occurred more frequently in solving word problems. The main reason for language switching in this group of bilingual children was problem difficulty. An in-depth investigation of the data showed that difficulty in comprehending the problem and/ or implementing an appropriate strategy, prompted language switching. Other factors influencing language switching were: familiarity with particular numbers used habitually, and being in the Persian school or interview environment. Findings indicated that high proficiency in both languages may be associated with high competency in mathematics. Parents’ attitudes and speaking Persian at home may contribute to the event of language switching in Iranian NESB students when solving mathematical problems.
The number of students involved in this study was far too small to generalize the findings. However, consistent with the findings of Clarkson (1996) and Latu (2005), the phenomenon of language switching by bilingual students should be considered in mathematics classrooms. Improvement of both L1 and L2 proficiency appears to be associated with the level of mathematical performance, as presented in the literature (Clarkson, 1996; Clarkson & Dawe, 1996; Erktin & Akyel, 2005). Presenting mathematical questions in a simple or reworded format could assist bilingual students to comprehend and solve a problem properly. It is suggested that these findings should be taken into account in developing an appropriate mathematics curriculum for bilingual students in an Australian context.
Brenda Bicknell
2009
This study examines multiple perspectives on the education of a group of fifteen Year 6 and Year 8 students identified as mathematically gifted and talented. The students’ mathematical experiences, both past and present are examined using evidence from school policy documents; student, teacher, and parent interviews; questionnaires; and classroom observations. The purpose of this case study was to seek understandings about awareness of the characteristics of mathematically gifted and talented students, the identification of and educational provisions for mathematically gifted and talented students, parental involvement, and school transfer.
The group of fifteen students consisted of ten Year 6 students who transferred from primary school to a new school for Year 7, and five Year 8 students who moved to secondary schools for Year 9. These students had been identified by their school and teachers as gifted and talented in mathematics.
This predominantly qualitative study is underpinned by an interpretive paradigm and influenced by a sociocultural philosophy of learning and teaching. The literature review presents the dilemmas, similarities, and differences that prevail in the field of gifted education. A more specific focus is given to the education of mathematically gifted students to highlight gaps in the field. This two-year study tracking a group of students provides a cohesive approach to understanding the educational provisions for students identified as mathematically gifted and talented in the New Zealand setting. The multiple case studies included interviews, questionnaires, documents, and observations.
The research findings show that there is not a comprehensive understanding by schools and teachers about the characteristics of mathematically gifted students. Despite the documentation of a range of identification processes in school policies, a multiple method approach is not practised in many schools. Provision of appropriate programmes is variable and determined by factors such as school organization, identification, teacher knowledge and expertise, and resources. Parents play a key role in their children’s mathematics education as motivators, resource providers, monitors, mathematics content advisers, and mathematical learning advisers. Schools, teachers, parents, and peers all contribute to the success of a student’s transfer from one phase of schooling to another; they support a student’s social and emotional well being and influence curriculum continuity in mathematics.
This study provides insights into the various determinants of the development of mathematical talent. For New Zealand schools and teachers, it provides evidence that understanding the characteristics of mathematical giftedness is important and that identification processes must reflect this understanding. Provisions must be well considered and evaluated; the role of parents should be understood and valued; and home-school communications strengthened. Together, all stakeholders share a critical role in the education of mathematically gifted and talented students.