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"primary mathematics"
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Conceptualising mathematics teacher noticing as a perception/action cycle
Most studies of mathematics teacher noticing employ information-processing-based models of noticing. While information processing has been used productively to research the cognitive requirements of noticing, critics have argued that these accounts conceptualise noticing as a relatively passive and mental act. This paper demonstrates how an alternative perception/action cycle model of noticing can draw attention to how teacher noticing is supported by active interaction with the classroom environment mid-lesson. Data from two primary mathematics lessons were gathered using a head-mounted camera technique. These data are analysed using the perception/action cycle model to demonstrate the model’s capacity to enable productive research. The model draws attention to aspects of teacher behaviour that support noticing that are given little weight when information processing informs analysis. By contrasting the noticing of one experienced and one beginning teacher, differences in the way that each teacher deployed their attention and looked for information mid-lesson can be ascertained. The experienced teacher took action that increased the likelihood that students would create mathematical representations that enabled perception of students’ mathematical thinking and deployed their attention so that they were more likely to be in the right place at the right time to notice. The perception/action cycle model draws attention to these under-researched aspects of mathematics teacher noticing.
Journal Article
Supporting teachers in structuring mathematics lessons involving challenging tasks
The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary
teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers responded to survey items in both Likert and free format style after teaching the ten lessons. The responses of the teacher
participants indicate that the lesson structure proposed was helpful, and the elements of the lessons suggested to teachers were both necessary and sufficient for supporting students in engaging with the challenging tasks. Implications
for teacher educators and curriculum developers are offered. [Author abstract, ed]
Journal Article
The really useful maths book : a guide to interactive teaching
\"A rich resource which will help a teacher who likes to take risks to enable, inspire and support. - TES magazineThe Really Useful Maths book has been written for all those who want children to enjoy the challenge of learning mathematics. It presents teachers and students with exciting and varied ideas for introducing mathematics to children. With suggestions about the best ways to use resources and equipment to support learning, it describes in detail how to make learning the easy option for children. This accessible and comprehensive book covers both the practical side of mathematics and the theory and practice of mathematics teaching. Packed with ideas and activities, it is the perfect tool to help you to improve your teaching strategies. Topics covered include:numbers and the number system what teachers need to know about interactive teaching calculating consolidating new ideas and developing personal qualities shape and space measures, statistics and data handling consolidation and practice for accuracy, speed and fluency.Fully updated to take into account changes in mathematics teaching and curriculum, this new edition offers a host of new ideas for teaching, new topics, a glossary of mathematical terms and an activity matrix for easy navigation of the books practical activities. It is the perfect tool to support training and practicing primary teachers, subject specialists and mathematics coordinators in schools\"-- Provided by publisher.
Book
Using expectancy-value theory to explore aspects of motivation and engagement in inquiry-based learning in primary mathematics
Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory provides a framework through which children's beliefs about their mathematical competency and their expectation of success are able to be examined and interpreted, alongside students' perceptions of task value. In this paper, Eccles and Wigfield's expectancy-value model has been adopted as a lens to examine a complete unit of mathematical inquiry as undertaken with a class of 9-10-year-old students. Data were sourced from a unit (~10 lessons) based on geometry and geometrical reasoning. The units were videotaped in full, transcribed, and along with field notes and student work samples, subjected to theoretical coding using the dimensions of Eccles and Wigfield's model. The findings provide insight into aspects of IBL that may impact student motivation and engagement. The study is limited to a single unit; however, the results provide a depth of insight into IBL in practice while identifying features of IBL that may be instrumental in bringing about increased motivation and engagement of students in mathematics. Identifying potentially motivating aspects of IBL enable these to be integrated and more closely studied in IBL practises. [Author abstract, ed]
Journal Article
Teaching and learning about whole numbers in primary school
This book offers a theory for the analysis of how children learn and are taught about whole numbers.
Book
Assessing students’ understanding of time concepts in Years 3 and 4: insights from the development and use of a one-to-one task-based interview
Time is an important but complex area of learning for students in the primary years. This study sought to develop a tool which would provide a clear picture of students’ understanding of what constitutes time and how time is related to clock and calendar use. Four major components of time, Awareness of time, Succession, Duration, and Measurement of time, with related key ideas, formed the basis for a Framework for the Learning and Teaching of Time. This Framework underpinned the development of a 69-item, one-to-one task-based interview to assess students’ understanding of time. Data from interviews of Year 3 and 4 students gave a clear picture of how they experienced the mathematics of time. The range of scores across all assessed areas of the Framework revealed a considerable spread of students’ understandings of time concepts. This paper focuses on the development of the Framework and interview, the interview data, and the general benefits of the use of the task-based assessment interview in assessing the mathematical understanding and thinking of children regarding time.
Journal Article
Inclusive practices in the teaching of mathematics: some findings from research including children with Down syndrome
Children with Down syndrome can and do learn important mathematics and increasingly, this is occurring in regular school classrooms. The research literature offers little about the practices of effective primary school teachers who are including children with Down syndrome in the teaching of mathematics. In this paper we present findings from a project that followed teachers’ journeys through a school year as they taught mathematics in primary classrooms including a child with Down syndrome. In particular, we focus on one aspect of the project: the nature of the teachers’ practice and the specific challenges that emerged during teaching and planning. Data were collected through classroom observations, interviews with teaching team members and examining learning artefacts such as work samples and reflection journals. Classroom experiences in such contexts often require adjustments both in the planning and in the implementation. Vignettes illustrate such adjustments and provide insights into the teacher decision-making involved. Themes that emerged from analysis of the data are discussed. These themes were based on researcher reflections and meetings following each round of observations and were reported back to the teachers for verification. We explore the themes, reflecting on current policy influencing inclusive education in Australia and internationally, highlighting challenges that emerged in seemingly straightforward concepts. Our aim in this paper is to explore examples of an innovative approach to mathematics education for students with Down syndrome—the technique of teaching all students the mathematics from their year level, with adjustments. The careful study of the practices of teachers offers implications for effective inclusive mathematics education for the diverse classrooms that are increasingly the norm across Australia and around the world.
Journal Article