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.

Facilitating growth in prospective teachers’ knowledge : teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

Engaging students in authoring and playing computer games

Computer games have become a commonplace but engaging activity among students. They enjoy playing computer games as they can perform larger-than-life activities virtually such as jumping from great heights, flying planes, and racing cars; actions that are otherwise not possible in real life. Computer games also offer user interactivity which gives them a certain appeal. Considering this appeal, educators should consider integrating computer games into student learning and to encourage students to author computer games of their own. It is thought that students can be engaged in learning by authoring and using computer games and can also gain essential skills such as collaboration, teamwork, problem solving and deductive reasoning. The research in this study revolves around building student engagement through the task of authoring computer games. The study aims to demonstrate how the creation and sharing of student-authored educational games might facilitate student engagement and how ICT (information and communication technology) plays a supportive role in student learning. Results from this study may lead to the broader integration of computer games into student learning and contribute to similar studies. In this qualitative case study, based in a state school in a low socio-economic area west of Brisbane, Australia, students were selected in both junior and senior secondary classes who have authored computer games as a part of their ICT learning. Senior secondary students (Year 12 ICT) were given the task of programming the games, which were to be based on Mathematics learning topics while the junior secondary students (Year 8 ICT) were given the task of creating multimedia elements for the games. A Mathematics teacher volunteered to assist in the project and provided guidance on the inclusion of suitable Mathematics curricular content into these computer games. The student-authored computer games were then used to support another group of Year 8 Mathematics students to learn the topics of Area, Volume and Time. Data was collected through interviews, classroom observations and artefacts. The teacher researcher, acting in the role of ICT teacher, coordinated with the students and the Mathematics teacher to conduct this study. Instrumental case study was applied as research methodology and Third Generation Activity Theory served as theoretical framework for this study. Data was analysed adopting qualitative coding procedures. Findings of this study indicate that having students author and play computer games promoted student engagement and that ICT played a supportive role in learning and allowed students to gain certain essential skills. Although this study will suggest integrating computer games to support classroom learning, it cannot be presumed that computer games are an immediate solution for promoting student engagement.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

Student understandings of numeracy problems: Semantic alignment and analogical reasoning

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all curriculum areas are responsible for numeracy. This general capability approach confuses what numeracy should look like, especially when compared to the structure of numeracy as defined on standardised national tests. In seeking to define numeracy, schools tend to look at past NAPLAN papers, and in doing so, we do not find examples drawn from the various aspects of school curriculum. What we find are more traditional forms of mathematical worded problems.

Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

Teacher aides and their pedagogical contributions in the underachieving Indigenous mathematics classroom

This study examines the pedagogical contributions made by teacher aides in underperforming Indigenous mathematics secondary classrooms. Three teaching teams, each consisting of a teacher and their teacher aide, responded to semi-structured interviews. Their mathematics classrooms were observed for details of pedagogical contributions to the mathematics lessons. It was found that the pedagogical contributions of the teacher aides varied from co-teaching contributions, to the provision of menial support and behaviour management. The techniques used by the teacher aides to provide student feedback, to support behaviour management and to undertake questioning vary greatly, and this variance is also evident in the classroom atmosphere. Teacher aides are providing pedagogical contributions, and are engaged in instructional interactions, and are in a sense “teaching”.