Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.

Changes in how prospective teachers anticipate secondary students’ answers

This study focuses on how prospective teachers learn about students’ mathematical thinking when (i) anticipating secondary students’ answers reflecting different characteristics of understanding and (ii) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school teachers enrolled in an initial training programme. The results indicate three changes in how the prospective teachers anticipate secondary students’ answers in relation to the role given to a perceptual or relational perspective of the classification of quadrilaterals. These changes are described considering how prospective teachers grasp the students’ understanding of the inclusive relation among quadrilaterals as a conceptual advance. We argue that prospective teachers’ learning was promoted after participating in a structured environment where they had the opportunity to discuss how to recognize the features of student’s understanding.

Secondary teachers’ conceptions of teaching and learning

This paper presents a phenomenographic analysis of the conceptions of teaching and learning held by a sample of 16 secondary school teachers in two Australian schools. It provides descriptions of four categories, derived from pooled data, of the ways in which these teachers thought about teaching and about learning, their teaching strategies, and their focus on student or content. The categories for teaching and learning are described with each teacher allocated to the category most typical of their conceptions of teaching and of learning. The lack of congruence, in some cases, between the conceptions of teaching and of learning held by these teachers is discussed.

Support teachers, learning difficulties and secondary school culture

This thesis will report on mixed method research which examined secondary Support Teachers Learning Difficulties (STLDs) and their modes of operation in New South Wales (NSW) government schools, Australia. Four modes of operation were identified in the literature as consultancy, team teaching, in-class support and withdrawal. An additional area of other duties was also included to examine the time when STLDs were not functioning in the four identified modes of operation. NSW government policy is in keeping with the literature as it recommends that STLDs should spend the majority of their time in consultancy and team teaching while in class with a minimum of withdrawal of students from their main classrooms for individual or small group instruction. STLDs, however, did not appear to be functioning in the recommended way. A number of factors identified in the literature, which may influence the modes of operation, can be grouped under the heading of school culture thus this research involved the examination of the effects of school culture on the modes of operation with the aim of expanding our understanding of the functioning of STLDs and providing suggestions for improvement. The theoretical base of social constructionism has informed this research which included survey and case study methods. Case studies of the STLDs in three secondary schools led to the conclusion that, in conjunction with factors such as flexibility and commitment, the involvement of the STLD in a sub-culture of learning support may lead to functioning in the recommended modes of operation.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The new Australian Curriculum and national standardised testing have placed the teaching of numeracy across the curriculum at the forefront of what Australian schools must do. However, it has been left to schools to determine how they do this. Although there is a growing body of literature giving examples of pedagogies that embed numeracy in various learning areas, there are few studies of cross-curricular numeracy from the management perspective. This paper responds to the research question: How do selected Queensland secondary schools interpret and apply the Australian Curriculum requirement to embed numeracy throughout the curriculum? A multiple case study design was used to investigate the actions of the senior managers and mathematics teachers in three large secondary schools located in outer Brisbane. The numeracy practices in the three schools were interpreted from asocial constructivist perspective. The study found that in each school key managers had differing constructions of numeracy that led to confusion in administrative practices, policy development and leadership. The lack of coordinated cross-curricular action in numeracy in all three schools points to the difficulty that arises when teachers do not share the cross-curricular vision of numeracy present in the Australian Curriculum. The managers identified teachers’ commitment, understanding, or skills in relation to numeracy as significant barriers to the successful implementation of numeracy in their school. Adoption of the Australian Curriculum expectation of embedding numeracy across the curriculum will require school managers to explicitly commit to initiatives that require persistence,time and, most importantly, money.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The Australian Curriculum identified seven General Capabilities, including numeracy, to be embedded in all learning areas. However, it has been left to individual schools to manage this. Whilst there is a growing body of literature about pedagogies that embed numeracy in various learning areas, there are few studies from the management perspective. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and mathematics teachers in three Queensland secondary schools, in order to investigate how they meet the Australian Curriculum requirement to embed numeracy throughout the curriculum. The study found a lack of coordinated cross-curricular approaches to numeracy in any of the schools studied. It illustrates the difficulties that arise when teachers do not share the Australian Curriculum cross-curricular vision of numeracy. Schools and curriculum authorities have not acknowledged the challenges for teachers in implementing cross-curricular numeracy, which include: limited understanding of numeracy; a lack of commitment; and inadequate skills. Successful embedding of numeracy in all learning areas requires: the commitment and support of school leaders, a review of school curriculum documents and pedagogical practices, professional development of teachers, and adequate funding to support these activities.

The professional development, resource and support needs of rural and urban ICT teachers

This paper presents findings from the SiMERR National Survey concerning the need priorities of secondary ICT teachers for professional development, resources and student learning experiences. The findings - drawn from a survey of 237 secondary ICT teachers across Australia - provide an opportunity to compare the needs of teachers working in metropolitan, provincial and remote schools. The study found that vacant ICT positions are difficult to fill ond that the novel on dynamic nature of ICT requires teachers to have more extensive opportunities for on-the-job training, collegial collaboration and mentoring than is the case for teachers of more traditional subjects like science and mathematics. The study also found that ICT teachers are commonly required to manage and maintain ICT resources and to assist other staff to use ICT resources, while being allocated insufficient time in which to do these additional activities. The implications of these and other findings are discussed along with recommendations to help address the needs of ICT teachers in different parts of Australia.

An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

Teachers' perceptions of effects of terminal examinations on teaching and learning at the secondary school level in Zimbabwe

This study was particularly aimed at the examinations and the effect they have on schooling at the secondary school level in Zimbabwe. The views and opinions of teachers on the use of terminal examinations for certification and the influence they are seen to have on teachers' approach to the curriculum were examined. The literature has shown that there is widespread criticism of the justice and effects of terminal examinations. It is argued that they lead to an over-emphasis of that which is measured, knowledge and intellectual ability, at the expense of that kind of education progress which is almost impossible to measure in an end-of-the-course assessment. Three hundred and six secondary school teachers responded to a survey which asked for teachers' perceptions of examinations and the curriculum. The findings of this study indicated that teaching is structured towards examinations. Although teachers are trying to teach and develop reasoning skills and other activities, the pressure of examinations and the importance of doing well in them force teachers to restrict themselves to examination requirements.

A conceptual analysis of research literature on teachers' ideology and literacy practices: extending the dialogue through a secondary analysis of high school English as an additional language contexts /

This thesis provides a conceptual analysis of research literature on teachers' ideology and literacy practices as well as a secondary analysis of three empirical studies and the ways in which the ideologies of the English as an Additional Language (EAL) (Street, 2005) teachers in these contexts impact the teaching of literacy in empowering/disabling ways. Several major theoretical components of Cummins (1996, 2000), Gee (1996, 2004) and Street (1995, 2001) are examined and integrated into a conceptual triad consisting of three main areas: power and ideology, validation of students ' cultural and linguistic backgrounds, and teaching that empowers. This triad provides the framework for the secondary analysis of three empirical studies on the ideologies of secondary EAL teachers. Implications of the findings from the conceptual and secondary analyses are examined in light of the research community and secondary school teachers of EAL.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Teachers' conceptions about students' mathematical reasoning : Gendered or not?

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking.