Problematising the mathematics curriculum : some examples from Australia and Japan

Problem solving is often seen as being the core of mathematics. While there are many examples of teaching for and about problem solving, there are relatively few examples of teaching mathematical content through problem solving. This paper uses data from three, apparently quite different, mathematics lessons from Australia and Japan to explore different ways in which mathematics can be taught successfully through problem solving and to analyse some of the characteristics of such lessons. It also attempts to identify some of the supports and constraints for adopting a problem solving approach to the teaching of mathematics that exist in the quite different contexts of Japan and Australia.

Students' and teachers' use of ICT in primary mathematics

This paper reports on the findings of a research project that investigated the use of Information and Communication Technologies (ICT) in Primary mathematics in an urban and rural network. Surveys and semi structured interviews were held to obtain insight into teachers’ and students’ perceptions and attitudes towards the usage of ICT in the teaching and learning of mathematics. The presentation will highlight the findings and include a discussion on the types of ICT that students use in and out of school to learn mathematics.

Questions in primary mathematics classrooms

In this paper the types of questions that primary teachers use when teaching mathematics are discussed. Teachers from five primary schools participated in a professional development program designed to improve the quality of questioning in mathematics classrooms. Changes in their practice as they perceived them are presented.

Mathematics curriculum reform : reproducing social inequalities

This book is essential reading for Australasian mathematics educators and other researchers with an interest in the history of mathematics curriculum, the culture of mathematics, gender, and social justice issues in mathematics. Drawing on the results of research conducted by the Educational Outcomes Research Unit at the University of Melbourne and historical documents, Richard Teese argues that the education system fails to diffuse the economic and cultural benefits assumed to flow from the completion of secondary schooling.

A comparative study of content settings of mathematics curriculum standards from China, Australia, and Finland

The study investigated the mathematics curricula standards set by the governments in China, Australia(Victoria) and Finland in the aspects of the amount of content statements, the structure of content areas, level of details, level of requirement, the distribution of content, and the changes of content areas. The results show that China's mathematics standard has the biggest amount of and the most detailed content statements; that of Australia is in the second place; and Finnish standard has the least amount of content statements that are very general. The standards in all three countries emphasize numbers and operation and geometry.However,China's standards present a dynamic change, with different focus for different grades; Australian standards have similar proportion of each part of content for different grades and the amount of each part increases with grade; there is no fixed setting and proportion of content in Finnish standard, which is not confined by any mode.

A framework for primary teachers’ perceptions of mathematical reasoning

Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.

The place of place-based education in the Australian primary geography curriculum

The idea for this paper emerged from a recent qualitative investigation which examined the ways in which six Australian primary teachers conceptualised geography and geography teaching (Preston, 2014b). A finding of this research was a strong correlation between the breadth of geographical understandings and the years of experience and age of participants. For early career teachers, conceptions of geography were narrowly confined to information-oriented perceptions. Whereas, the two teachers, with more than 30 years in primary schools, portrayed much more complex understandings. Their conceptions depicted geography as process-oriented and in relational terms, that is, understandings of geography that recognise the interactions and interdependence of people and environments (Bradbeer, Healey, & Kneale, 2004). Both these experienced teachers were also committed to place-based, inquiry approaches to geography teaching and had been using placebased methodologies long before it became a new movement in education (Morgan, 2009, p. 521 ). This prompted me to question why geography education seldom features in discourses of place-based education and to contemplate the oft-cited argument (at least in the United States) that the recent focus on curriculum standards is incompatible with locally responsive curriculum (Jennings, Swidler, & Koliba, 2005).
In order to answer these questions, I explore the intersections and divergences between place-based education and geography education in the Australian context. Drawing on Smith's (2002) and Gruenewald's (2003) conception of place-based education, and the new. Australian geography curriculum document, I argue that primary geography education has strong synergies with place-based education methodologies and aims. I further suggest that a geographical perspective can augment placebased education to enrich and broaden students' understandings of the complex interactions between and within places. This argument is balanced with a critical examination of the practice of geography education acknowledging that the tradition of fieldwork might benefit from placebased education approaches that enable more embodied, socially engaged interactions with places. Thus, I contend, place-based education and geography education are mutually supportive and each can extend the other. The paper concludes with a reflection on the challenges in Australia in preparing primary teachers for the implementation of the new (place-based) geography curriculum.

Team: Bee Me. A formulative evaluation of a negative eating attitudes and behaviors primary prevention curriculum targeted at 5 th grade elementary school girls

Objective. To evaluate a school-based intervention aimed at the primary prevention of negative eating attitudes and behaviors among preadolescent girls, and to revise curriculum lessons based on quantitative and qualitative findings. ^ Intervention Design. A formative evaluation was conducted on four Team: Bee Me curriculum lessons at a Houston elementary school. Evaluation focused on program satisfaction and short-term effect on knowledge and eating attitudes and behaviors. ^ Results. Sixteen girls participated in the five-day project. Statistically significant improvements in overall knowledge were observed (p<0.05), however only modest changes were observed in eating attitudes and behaviors. Program satisfaction was high among student participants and the teacher who implemented it. Insight for future modifications to this program and for similar interventions was provided by the students and teacher. ^ Conclusions. This program led to positive trends in outcome variables; however longer and more intensive testing of this program is needed to better evaluate its effectiveness.^

Forging futures? Engineering in the primary school curriculum

Starting with the research question, "How can the Primary School Curriculum be developed so as to spark Children's Engineering Imaginations from an early age?" this paper sets out to critically analyse the issues around embedding Engineering in the Primary School Curriculum from the age of 5 years. Findings from an exploratory research project suggest that in order to promote the concept of Engineering Education to potential university students (and in doing so begin to address issues around recruitment / retention within Engineering) there is a real need to excite and engage children with the subject from a young age. Indeed, it may be argued that within today's digital society, the need to encourage children to engage with Engineering is vital to the future sustainable development of our society. Whilst UK Government policy documents highlight the value of embedding Engineering into the school curriculum there is little or no evidence to suggest that Engineering has been successfully embedded into the elementary level school curriculum. Building on the emergent findings of the first stage of a longitudinal study, this paper concludes by arguing that Engineering could be embedded into the curriculum through innovative pedagogical approaches which contextualise project-based learning experiences within more traditional subjects including science, history, geography, literacy and numeracy.

Development of a Game-Based Mathematics Curriculum for Preschool

America’s deficiency in mathematics can be benefitted by an emphasis in mathematics from an early age. An effective math curriculum for preschool should consist of the most important aspects of early childhood mathematics, including number writing and identification, one-to-one correspondence, cardinality, number comparison, ordinality, number sequence, and number bonds.

Learning to 'understand backwards' in time: children's temporal cognition and the primary history curriculum

This study examines children’s temporal ways of knowing and it highlights the centrality of temporal cognition in the development of children’s historical understanding. It explores how young children conceptualise time and it examines the provision for temporal cognition at the levels of the intended, enacted and received history curriculum in the Irish primary school context. Positioning temporality as a prerequisite second-order concept, the study recognises the essential role of both first-order and additional second-order concepts in historical understanding. While the former can be defined as the basic, substantive content to be taught, the latter refers to a number of additional key concepts that are deemed fundamental to children's capacity to make meaningful sense of history. The study argues for due recognition to be given to temporality, in the belief that both sets of knowledge, the content and skills, are required to develop historical thinking (Lévesque, 2011). The study addresses a number of key research questions, using a mixed methods research design, comprising an analysis of history textbooks, a survey among final year student teachers about their teaching of history, and school-based interviews with primary school children: What opportunities are available for children to develop temporal ways of knowing? How do student teachers experience being apprenticed into the available culture for teaching history and understanding temporality at primary level? What insights do the cognitive-developmental and sociocultural perspectives on learning provide for understanding the dynamics of children’s temporal ways of knowing? The study argues that the skill of developing a deeper understanding of time is a key prerequisite in connecting with, and constructing, understandings and frameworks of the past. The study advances a view of temporality as complex, multi-faceted and developmental. The findings have a potential contribution to make in influencing policy and pedagogy in establishing an elaborated and well-defined curriculum framework for developing temporal cognition at both national and international levels.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Le développement d’une séquence d’enseignement/apprentissage basée sur l’histoire de la numération pour des élèves du troisième cycle du primaire

Notre contexte pratique — nous enseignons à des élèves doués de cinquième année suivant le programme international — a grandement influencé la présente recherche. En effet, le Programme primaire international (Organisation du Baccalauréat International, 2007) propose un enseignement par thèmes transdisciplinaires, dont un s’intitulant Où nous nous situons dans l’espace et le temps. Aussi, nos élèves sont tenus de suivre le Programme de formation de l’école québécoise (MÉLS Ministère de l'Éducation du Loisir et du Sport, 2001) avec le développement, notamment, de la compétence Résoudre une situation-problème et l’introduction d’une nouveauté : les repères culturels. Après une revue de la littérature, l’histoire des mathématiques nous semble tout indiquée. Toutefois, il existe peu de ressources pédagogiques pour les enseignants du primaire. Nous proposons donc d’en créer, nous appuyant sur l’approche constructiviste, approche prônée par nos deux programmes d’études (OBI et MÉLS). Nous relevons donc les avantages à intégrer l’histoire des mathématiques pour les élèves (intérêt et motivation accrus, changement dans leur façon de percevoir les mathématiques et amélioration de leurs apprentissages et de leur compréhension des mathématiques). Nous soulignons également les difficultés à introduire une approche historique à l’enseignement des mathématiques et proposons diverses façons de le faire. Puis, les concepts mathématiques à l’étude, à savoir l’arithmétique, et la numération, sont définis et nous voyons leur importance dans le programme de mathématiques du primaire. Nous décrivons ensuite les six systèmes de numération retenus (sumérien, égyptien, babylonien, chinois, romain et maya) ainsi que notre système actuel : le système indo-arabe. Enfin, nous abordons les difficultés que certaines pratiques des enseignants ou des manuels scolaires posent aux élèves en numération. Nous situons ensuite notre étude au sein de la recherche en sciences de l’éducation en nous attardant à la recherche appliquée ou dite pédagogique et plus particulièrement aux apports des recherches menées par des praticiens (un rapprochement entre la recherche et la pratique, une amélioration de l’enseignement et/ou de l’apprentissage, une réflexion de l’intérieur sur la pratique enseignante et une meilleure connaissance du milieu). Aussi, nous exposons les risques de biais qu’il est possible de rencontrer dans une recherche pédagogique, et ce, pour mieux les éviter. Nous enchaînons avec une description de nos outils de collecte de données et rappelons les exigences de la rigueur scientifique. Ce n’est qu’ensuite que nous décrivons notre séquence d’enseignement/apprentissage en détaillant chacune des activités. Ces activités consistent notamment à découvrir comment différents systèmes de numération fonctionnent (à l’aide de feuilles de travail et de notations anciennes), puis comment ces mêmes peuples effectuaient leurs additions et leurs soustractions et finalement, comment ils effectuaient les multiplications et les divisions. Enfin, nous analysons nos données à partir de notre journal de bord quotidien bonifié par les enregistrements vidéo, les affiches des élèves, les réponses aux tests de compréhension et au questionnaire d’appréciation. Notre étude nous amène à conclure à la pertinence de cette séquence pour notre milieu : l’intérêt et la motivation suscités, la perception des mathématiques et les apprentissages réalisés. Nous revenons également sur le constructivisme et une dimension non prévue : le développement de la communication mathématique.

Primary students' success on the structured number line

Number lines are part of our everyday life (e.g., thermometers, kitchen scales) and are frequently used in primary mathematics as instructional aids, in texts and for assessment purposes on mathematics tests. There are two major types of number lines; structured number lines, which are the focus of this paper, and empty number lines. Structured number lines represent mathematical information by the placement of marks on a horizontal or vertical line which has been marked into proportional segments (Figure 1). Empty number lines are blank lines which students can use for calculations (Figure 2) and are not discussed further here (see van den Heuvel-Panhuizen, 2008, on the role of empty number lines). In this article, we will focus on how students’ knowledge of the structured number line develops and how they become successful users of this mathematical tool.