An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

Primary alkaline battery cathodes a three-scale model

A mathematical model for the galvanostatic discharge and recovery of porous, electrolytic manganese dioxide cathodes, similar to those found within primary alkaline batteries is presented. The phenomena associated with discharge are modeled over three distinct size scales, a cathodic (or macroscopic) scale, a porous manganese oxide particle (or microscopic) scale, and a manganese oxide crystal (or submicroscopic) scale. The physical and chemical coupling between these size scales is included in the model. In addition, the model explicitly accounts for the graphite phase within the cathode. The effects that manganese oxide particle size and proton diffusion have on cathodic discharge and the effects of intraparticle voids and microporous electrode structure are predicted using the model.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

A thematic approach to integrating maths and science for pre-service primary teachers via sustainability

Efforts to improve mathematics and science content knowledge have in many institutions required redefining teacher education through new teaching and learning. See, for example, Peard & Pumadevi (2007) for an account of one such attempt involving the development of a Foundations Unit, Scientific and Quantitative Literacy. This unit is core for all first year pre-service primary teacher education students at Queensland University of Technology (QUT) and two Education Institutes in Malaysia, Institute Perguruan Raja Melewar (IPRM), and Institute Perguruan Teknik (IPT) Kuala Lumpur. Since then, QUT has modified the unit to adopt a thematic approach to the same content. An aim of the unit rewrite was the development of a positive attitude and disposition to the teaching and learning of mathematics and science, with a curiosity and willingness to speculate about and explore the world. Numeracy was specifically identified within the mathematics encountered and appropriately embedded in the science learning area. The importance of the ability to engage in communication of and about mathematics and science was considered crucial to the development of pre-service primary teachers. Cognisance was given to the appropriate selection and use of technology to enhance learning - digital technologies were embedded in the teaching, learning and assessment of the unit to avoid being considered as an optional extra. This was achieved around the theme of “the sustainable school”. This „sustainability‟ theme was selected due to its prominence in Australia‟s futures-oriented National Curriculum which will be implemented in 2011. This paper outlines the approach taken to the implementation of the unit and discusses early indicators of its effectiveness.

A thematic approach to integrating maths and science for pre-service primary teachers via sustainability

Efforts to improve mathematics and science content knowledge have in many institutions required redefining teacher education through new teaching and learning. See, for example, Peard & Pumadevi (2007) for an account of one such attempt involving the development of a Foundations Unit, Scientific and Quantitative Literacy. This unit is core for all first year pre-service primary teacher education students at Queensland University of Technology (QUT) and two Education Institutes in Malaysia, Institute Perguruan Raja Melewar (IPRM), and Institute Perguruan Teknik (IPT) Kuala Lumpur. Since then, QUT has modified the unit to adopt a thematic approach to the same content. An aim of the unit rewrite was the development of a positive attitude and disposition to the teaching and learning of mathematics and science, with a curiosity and willingness to speculate about and explore the world. Numeracy was specifically identified within the mathematics encountered and appropriately embedded in the science learning area. The importance of the ability to engage in communication of and about mathematics and science was considered crucial to the development of pre-service primary teachers. Cognisance was given to the appropriate selection and use of technology to enhance learning - digital technologies were embedded in the teaching, learning and assessment of the unit to avoid being considered as an optional extra. This was achieved around the theme of “the sustainable school”. This ‘sustainability’ theme was selected due to its prominence in Australia’s futures-oriented National Curriculum which will be implemented in 2011. This paper outlines the approach taken to the implementation of the unit and discusses early indicators of its effectiveness.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Culture-fair assessment : challenging Indigenous students through effortful mathematics teaching

This paper reports on a mathematics education research project centred on teachers’ pedagogical practices and capacity to assess Indigenous Australian students in a culture-fair manner. The project has been funded by the Australian Research Council Linkage program and is being conducted in seven Catholic and Independent primary schools in north Queensland. Our Industry Partners are Catholic Education and the Association of Independent Schools, Queensland. The study aims to provide greater understanding about how to build more equitable assessment practices to address the issue of underperforming Aboriginal and Torres Strait Islander (ATSI) students in regional and remote Australia. The goal is to identify ways forward by attending to culture-fair assessment practice. The research is exploring the attitudes, beliefs and responses of Indigenous students to assessment in the context of mathematics learning with particular focus on teacher knowledge in these educational settings in relation to the design of assessment tasks that are authentic and engaging for these students in an accountability context. This approach highlights how teachers need to distinguish the ‘funds of knowledge’ (González, Moll, Floyd Tenery, Rivera, Rendón, Gonzales & Amanti, 2008) that Indigenous students draw on and how teachers need to be culturally responsive in their pedagogy to open up curriculum and assessment practice to allow for different ways of knowing and being