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In recent years there has been growing concern as to how to bridge the gap between the theory preservice teachers engage with as part of their learning in their tertiary classrooms and the profession. To enable pre-service teachers to make stronger connections with the profession, a mathematics teacher educator worked collaboratively with a practicing teacher by co-teaching one cohort of preservice teachers studying primary mathematics education. In this paper, we present two snapshots of the co-teaching experience and a framework that was used to describe how the co-teaching partnership helped the pre-service teachers to elicit mathematical thinking make connections between theory and practice, when engaged in mathematical discourse.

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when teaching. The focus of this paper is second-year Australian primary pre-service teachers' MCK of real number items related to ratio, rate, proportion and proportional reasoning. This paper reports on strengths and weakness of pre-service teachers' MCK when responding to test items; including a method suitable for analysing responses to five items and ranked by three levels of difficulty. The results revealed insights into their correct methods of solutions and common incorrect responses, identifying difficulty, where multiplication and division were required. The method of coding test items by difficulty ranking may assist with developing an appropriate learning trajectory, which will assist pre-service teachers develop their MCK of this and other difficult topics. (Contains 7 tables and 4 figures.)

This paper describes the mathematical journey of a mature aged nursing student as she struggles to become more academically numerate. Within the paper, academic numeracy is defined around three features: competence, confidence and critical awareness of both the context of mathematics and students' own relationship with mathematics. It then uses this definition to describe a course for 1st year nursing students to develop their mathematics skills needed for their degree. A conceptual framework, based on Valsiner's Human Development Theory, is used to trace students' developing understanding of academic numeracy. Finally the paper describes one student, Sally, as she struggles to become more numerate.

To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete examples of what lapses of integrity look like in this context. The intent is to lay groundwork for discussion and a response to this issue from within our discipline.

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students' understanding of functions and variables, as well as the use of technology in their last year of school (Year 12). Did their teachers discourage the use of CAS for algebra? Did the students actually learn how to use CAS to support their work in algebra or to support their learning of algebra? Did they find that, given the level of algebra, it was faster to work with pen-and-paper than to correctly enter algebraic expressions? The results reported in this paper are based on items included in a pilot survey. They raise questions rather than provide answers. The results do however tell us that, at least from these first year university students' recollection of their Year 12 experience, most or their VCE mathematics teachers made little use of CAS as a pedagogical tool in their classes, despite the institutional approval and encouragement indicated by both the State's curriculum and assessment for the past decade. A better understanding of the barriers to teachers using CAS technology to enhance their pedagogy is needed and then perhaps more effective professional learning programs can be provided for teachers.

This paper reports on an investigation into pre-service teachers' mathematical content knowledge and their ability to interpret students' responses to a multi-digit multiplication task and make subsequent appropriate teaching decisions. Using a combination of quantitative and qualitative methods, the researchers tested aspects of the mathematical knowledge held by a volunteer group of twenty final year preservice primary teachers. A volunteer sample of seven pre-service teachers were involved in a follow-up interview, where they were provided with hypothetical student work samples, including one using the long multiplication algorithm, and asked to analyse the student's mathematical thinking and make suggestions as to appropriate teaching approaches. The results indicated that the pre-service teachers in the study had an instrumental understanding of the long multiplication process that impacted on their ability to both recognise and address students' mathematical errors. This study provides an insight into the lack of content knowledge of a small sample of pre-service teachers with respect to multiplication of two and three digit numbers and subsequent lack of pedagogical content knowledge for teaching this topic.

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students' development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards biology degrees and so on. This paper considers the phases of transitions that students experience as they embark on a course of study and then go on to professional life. We make inferences about the ways the curriculum should be designed to alleviate the difficulties of these phases as well as to take account of the capabilities that graduates will require in the workplace. It is not only where students are coming from that affects their learning but where they are heading to, in combination with their perceptions of that destination. (Contains 1 table and 1 figure.)

An event based on "find the rule" problems has been part of the University of Canberra Maths Day since 1985. In this paper, the authors describe the Swiss event, its context, its aims, its logistics, and gives examples of problems used in past events. The type of problems used, how they are used in an event at the maths day, and how the event evens out the competition and stops strong schools dominating are also discussed.

Teaching and learning of mathematics is challenging when lecturer and students are separated geographically. While student engagement and interaction with the course, with other students and with the lecturer is vital to mathematics learning, it is difficult to facilitate this electronically, because of the nature of mathematics. With tablet technology now becoming ubiquitous and many new and inexpensive models entering the market, it is timely to investigate how the distance student experience in mathematics can be impacted by the use of tablet technologies. This paper reports on a case study of a first year mathematics course at a regional Australian university, where distance students were provided with affordable tablet PCs. An investigation of the impact of this technology on engagement and interaction is at the centre of this study. Evidence from journals, students' assessment submissions, screen snippets, student communication and formal student evaluations is analysed. It was found that distance students acknowledged the value of tablets for communicating mathematics, particularly for assignment submission and feedback, but they also recognized the potential for easier interaction with content and the lecturer. This paper highlights the specific benefits and challenges tablet PCs present to the learning experiences in mathematics within the distance context. (Contains 10 figures.)

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematics with a reliance on the development of visual explanation while providing audio narration. In this paper, we report on a study undertaken at an Australian university, to investigate the perceived level of usefulness of captions and their automatic translations in a mathematics course. We discovered that students broadly agreed that captions are a useful learning feature: to allow flexibility of where and when a video is watched, but also to help understand speaker accents, and clarify explanations that are difficult to hear in the recording. Due to the high levels of use and perceived educational benefits of closed captions in online video but limited literature, there is a significant need for new research in this area. An urgent discussion is needed to explore how students engage with closed captions, how they may support learning, and to investigate implications on instructional design of mathematical videos.

This paper explores how a secondary school in western Sydney used educational research as an impetus to change its mathematical education culture over a three year period. Key changes occurred in four areas: leadership; pedagogy; structures for teaching and learning; and mathematical environments. These included increased professional conversations, adoption of a numeracy lesson structure, regular use of manipulatives and open ended tasks and a structured intervention program for mathematically vulnerable students. Critical to the development of these changes were partnerships with a university academic and the CEDP system leadership team as well as school leadership participation in professional learning.

This project aimed to quantitatively measure the ability of first year science students to transfer their mathematical skills and knowledge to a physical context. An instrument used in earlier studies to measure transfer of mathematical knowledge was modified for this project, and tested with 49 student volunteers. This paper presents the Transfer Index, a novel way of measuring the degree of transfer of the students' mathematics skills and knowledge. It is demonstrated that the Transfer Index is a useful way of quantifying transfer and that it has predictive validity in a natural educational setting. (Contains 7 tables, 4 figures and 5 footnotes.)

On her death in 1910, Florence Nightingale left a vast collection of reports, letters, notes and other written material. There are numerous publications that make use of this material, often highlighting Florence's attitude to a particular issue. In this paper we gather a set of quotations and construct a dialogue with Florence Nightingale on the subject of statistics. Our dialogue draws attention to strong points of connection between Florence Nightingale's use of statistics and modern evidence-based approaches to medicine and public health. We offer our dialogue as a memorable way to draw the attention of students to the key role of data-based evidence in medicine and in the conduct of public affairs.

Learning and teaching in higher education is framed by curriculum models. Over the past decade constructive alignment (Biggs & Tang, 2009, 2011) has become widely accepted as the curriculum planning model for Australian higher education. Constructive alignment privileges learning outcomes in curriculum design, learning and teaching and assessment. In this paper we reflect on the selection and adoption of particular curriculum frameworks in higher education in relation to the purposes and aims of the intended learning experience and the intended future professional. Our reflection is contextualised within the discipline area of mathematics. We argue that the journey towards becoming a member of a professional community is complex and that alternative curriculum models that facilitate a focus on that journey may be more appropriate under certain circumstances. We suggest that when designing a learning experience, it is necessary firstly to consider the type of learner or future professional you are trying to enable and secondly, to choose a curriculum design framework that best supports that goal. [ABSTRACT FROM AUTHOR]

There is international agreement that quantitative skills (QS) are an essential graduate competence in science. QS refer to the application of mathematical and statistical thinking and reasoning in science. This study reports on the use of the Science Students Skills Inventory to capture final year science students’ perceptions of their QS across multiple indicators, at two Australian research-intensive universities. Statistical analysis reveals several variables predicting higher levels of self-rated competence in QS: students’ grade point average, students’ perceptions of inclusion of QS in the science degree programme, their confidence in QS, and their belief that QS will be useful in the future. The findings are discussed in terms of implications for designing science curricula more effectively to build students’ QS throughout science degree programmes. Suggestions for further research are offered. [ABSTRACT FROM PUBLISHER]