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Current teaching practice has been greatly enriched through valuable research into students’ acquisition of deep understanding and skills in early multiplication and division. Research in multi-digit multiplication and division is still relatively undeveloped. This proposed study will explore how students achieve computational fluency in multiplication and division. This paper outlines the background literature and research into multiplication and division. It then proposes questions to be explored and the intended methodology to determine effective pedagogical approaches that encase both mental and written computational methods.

The Numeracy Development Project has been systematically introduced into New Zealand schools since its conception in 2001. For many teachers, successful implementation of this mathematics education reform required a transformation of long held beliefs and practices. This shift involved moving from a view of mathematics learning as individualistic and passive, towards one in which students come to do and understand mathematics through participating in collaborative activity. This change in pedagogy and the required content knowledge has brought a range of challenges for many teachers. The purpose of this short presentation is to share the journey of two lead teachers (coaches) working with a mentor to enhance their understanding of number in the mathematics classroom. The mentor was a school adviser and the coaches came from schools that had previously been involved in the Numeracy Development Project. The process took place over six months and was aimed at improving both pedagogy and content knowledge of the in-school coaches and other teachers within their schools. A particular emphasis was placed on improving student learning in multiplicative and proportional thinking.

This presentation documents the learning journey of a group of six Year 5/6 students from a low decile school. These students worked with the first author over several sessions to build their understanding of fractions (i.e., tenths, hundredths), and the links between these fractions and the corresponding decimal places. Structured materials (plastic tubing cut to different lengths) based on a linear measurement model of the number line were used to help students appreciate the relationships between 1 whole, 1/10, and 1/100. Selected excerpts from the learning sessions are used to illustrate the insights that emerged during learning sessions. The findings are interpreted using the theoretical frameworks of Piaget and Vygotsky.

Learning to write good test items is an important aspect of the teacher preparation programmes in Singapore. This paper reports on the types of errors in writing test items in mathematics made by student teachers who were following the pre-service course for teaching at primary level. An analysis of the errors reveals that student teachers demonstrate some key shortcomings in: Use of language, mastery of content knowledge, use of diagrams as support, and use of appropriate context when writing the items.

Financial modelling is an accessible and practical way to expose students to the power of mathematical modelling and the Excel spreadsheet with its extensive collection of financial functions is often incorporated into courses on financial mathematics. At AUT University we have chosen to focus on the Excel spreadsheet for our introductory courses and this has served us well as students have developed modelling skills and Excel skills at the same time as being exposed to financial functions. In our more advanced course we have introduced students to the financial toolbox in Matlab. In this study we report on some experiences of this initial group of students as they grapple with the different mindset needed to relearn from a Matlab perspective functions they had mastered using Excel and explore the potential that Matlab offers to move beyond what Excel can offer. Our report will also identify some of the limitations we have uncovered as we have developed our course and allow us to demonstrate why financial modelling provides a fruitful source of worthwhile examples to help students to develop modelling skills.

This study proposes to look at the nature of language required in a middle school mathematics classroom through a teaching experiment. The teaching intervention proposes to provide explicit teaching of the mathematical and non-mathematical language and orchestrate subsequent opportunities for students to engage in substantive communication through cooperative groupwork. The emphasis will be on conceptual understanding through language acquisition rather than solely through learning procedures. The study proposes to examine the impact of the teaching intervention on student motivation and engagement in mathematics.

In this study, a sample of 73 pre-service secondary mathematics teachers, enrolled in the PGDE programme at the National Institute of Education in Singapore, completed a survey about their views on their practicum experience. Preliminary results show that most of the student teachers acknowledged that the practicum was a good learning experience but they differed in what they reported was the most important aspect of their learning about the teaching of mathematics and about what they perceived as their most and least memorable experiences while teaching mathematics during the practicum.

This research will examine factors affecting engagement in Mathematics as students make the transition from primary and secondary schooling. This presentation will consider the background literature and include discussions on factors affecting motivation, engagement, and student learning in the middle years of schooling, such as teacher-student relationships, teacher content knowledge, and pedagogy. The research questions will be presented and an outline of the proposed methodology will be provided. Understanding the factors that affect students’ learning at this significant stage of education will better inform educators about the issues that may influence their subject choices beyond middle schooling.

A pilot study, analysing twenty-one Year 10 students’ reflections on a unit on exponential functions taught using real-world problems, and supported by the use of CAS calculators. The real-world contexts explored during the unit provided a focus for follow-up interviews. Detailed analysis of the transcripts revealed four themes: Impact of technology; difficulty in expression; prediction; choice of scenario. Findings support results from related research reported in the literature and highlight the importance of the choice of real-world scenarios. Analysis revealed variation in students’ preference relating to scenarios. This variation provides a challenge in the preparation of appropriate material.

Significant technological tools have impacted on students’ learning of Mathematics. In this study, I wish to seek evidence that dynamic geometry enhances students’ understanding of certain geometric properties and can serve as a vehicle for discovering unknown properties. The aim of the study is to explore the impact of dynamic geometry on 40 Year 9 high school students’ understandings of geometric properties. A mixedmethodology will be utilized in order to confirm the findings from different data sources; such as interview, video and audio recordings, computer savings, students’ workbooks, and pre- and post-tests.

Schools are rapidly adopting Interactive White Boards (IWBs) [or alternatively termed Smart Boards]. The rapidity of uptake has not been in step with any well designed, comprehensive research effort that might inform patterns of adoption and implementation by teachers, nor any sufficient understanding about the impact IWBs might have on students and their learning in mathematics and other areas of the curriculum. This is not the first time that attractive resources have been rapidly taken up into the teaching of mathematics, based more on faith. Whether this matters is an interesting question to ask. In this short communication, I concentrate on insights from some of the relevant IWB research literature, noting gaps and deficiencies that need to be addressed. In particular it is noted that usually only self-report methods are used, there is a lack of studies that describe the impact of IWB use on cognition and that document actual changes in classroom interaction. As well studies often do not clearly focus on IWBs. These shortcomings make it difficult to assess the impact of IWB technology, if not impossible, in terms of any changes in the quality of student learning. Teachers certainly like them, but is this enough?

What role do competitions play in a mathematics programme? This question is examined from the multiple perspectives of fifteen students (11-13 year olds) identified as mathematically gifted and talented, and their teachers and parents. A variety of different types of mathematics competitions were subscribed to including local, national, and international competitions. There was varied access to the competitions and differing perspectives; students and parents shared similar views about the value of competitions but there was a difference of opinion among the teachers.

An evaluation study aims to validate a new conceptual framework for mathematics learning based on the development of pattern and structure. It will evaluate the effectiveness of a school-entry mathematics program built on this framework using classroom observations and an interview-based student assessment. The Pattern and Structure Mathematics Awareness Program (PASMAP) focuses on unit of repeat, multiplicative reasoning, spatial structuring, and congruence and similarity. The program will be evaluated in Kindergarten classes from four large primary schools in Brisbane and Sydney.

MERGA has enjoyed a strong and rich history since its inception over 30 years ago. In that time it has been instrumental in supporting and developing a prominent group of mathematics education researchers who have made a significant contribution to the field. The purpose of this Round-Table Discussion is to consider how MERGA and its members might continue to promote, support and encourage mathematics educators from generation X and generation Y (and beyond), so they can stand on the shoulders of those who have gone before, and continue to build the stellar reputation of mathematics education research in Australasia. This discussion is open to both experienced and novice researchers, and hopefully it will lead to some strategies and ideas for succession planning that will ensure the health of MERGA and mathematics education research into the future.

The New Zealand Numeracy Development Project (NDP) was introduced to combat the disparity between high and low achieving students. It originated as a pilot project in 1999 as an extension and modification of the Australian ‘Count Me In Too’ project, and was implemented by the Ministry of Education in 2001. Whilst some improvements have been noted, there is evidence of continuing disparity between Maori and Pakeha student achievement, and underachievement of these students remains a concern. A vital component of NDP was that teachers were provided opportunities for professional development. A Ministry of Education Quality Teacher Research and Development (QTRD) program was introduced in 2007, supporting teachers in action research to raise student achievement. This presentation analyses the experiences of a group of teachers who undertook the QTRD course to develop more effective teaching practices to enhance the learning of low achieving Maori and Pasifika students. We provide complementary perspectives on our participation in the project, and the dual benefits of increased student achievement and ongoing professional learning for the teachers. We argue that quality, theory-based professional development and reflective practice are necessary to enhance the teaching and learning of disadvantaged students. In the Round Table we hope to stimulate discussion with Australian, New Zealand, and other international colleagues about: • The nature of successful professional development partnerships between teachers and university researchers; • Characteristics of effective numeracy education programs for disadvantaged students; • Challenges in working with teachers and students in low socio-economic or disadvantaged areas.

The Home School Partnership Numeracy facilitators will start the round table discussion by presenting the findings from three small studies: i) Two case studies investigating if schools change the way they communicate student achievement to parents as a result of participating in the Home School Partnership project. ii) A small research project involving all of the schools across the Waikato region that have been involved in Home School Partnership projects in the last three years. The international evidence cited in Alton-Lee (2003) positively supports the enhancement of student learning through home and school partnerships. In New Zealand, two Best Evidence Syntheses research also highlight the importance of establishing effective relationships between home and school (Alton-Lee, 2003; Biddulph, Biddulph, & Biddulph, 2003). The Home School Partnership project reflects the acknowledgement of parents as first teachers and the desire to continue to encourage parents to confidently interact and communicate with their children about mathematics. Effective relationships within the school community encourage parents to take an active role in the shared responsibility of their children’s education. Aspects that might be considered in this discussion include: Background information about home and school partnerships; successful learning communities involving facilitators, lead teacher and lead parents; and communication of student achievement to parents. Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best evidence synthesis. Wellington: Ministry of Education. Biddulph, F., Biddulph, J. & Biddulph, C. (2003). The complexity of community and family influences on children’s achievement in New Zealand: Best evidence synthesis. Wellington: Ministry of Education.

The purpose of this roundtable is to describe a research proposal and seek feedback and advice on the proposed study. The research project aims to investigate current concerns of a downturn in motivation and engagement levels as students move through the middle years of schooling (Years 5 to 8 in New South Wales). Current research has shown at this time of transition from primary schooling to secondary many of these students begin to perceive mathematics to be a special domain in which smart students succeed and others merely get by or fail. Although students feel mathematics is important, many are not pursuing mathematics in the later years of school. This choice is seriously influenced by attitudes towards and performance in mathematics and significantly shaped by school mathematical experiences. While there is a wealth of research investigating issues surrounding the motivation and engagement of students in mathematics during the middle years, there is a gap in the research in terms of longitudinal studies. Through this longitudinal study there will be opportunity investigate if and how levels of motivation and engagement change within students as they progress through the transition from primary to secondary schooling. Within the study factors affecting any changes in motivation and engagement will be investigated and factors that play a role in increasing or sustaining levels motivation and engagement in mathematics will be identified.