Gaye Williams

Abstracting in the Context of Spontaneous Learning

There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii’s mental activities. Using video-stimulated interviews, the model was then used to analyse the behaviour of two Year 8 students who had demonstrated spontaneous abstracting. The analysis highlighted the crucial role of synthetic and evaluative analysis, two processes that seem unlikely to occur under guided construction.

Studying learners in intercultural contexts

Researchers have increasingly recognized that learning mathematics is a cultural activity. At the same time, research aims, technological advances, and methodological techniques have diversified, enabling more detailed analyses of learners and learning to take place. Increased opportunities to study learners in different cultural, social and political settings have also become available, with ease of access to results of international benchmark testing online. Large-scale quantitative studies in the form of international benchmark tests like Trends in International Mathematics and Science Study (TIMSS), the Programme for International Student Assessment (PISA), and detailed multi-source (including video) qualitative studies like the international Learners’ Perspective Study (LPS), have enabled a broad range of research questions to be investigated. This chapter points to the usefulness of large-scale quantitative studies for stimulating questions that require qualitative research designs for their exploration. Qualitative research has raised awareness of the importance of socio-cultural and historical cultural perspectives when considering learning. This raises questions about uses that could be made of “local” theories in undertaking intercultural analyses.

Building Optimism in Prospective Mathematics Teachers

This three-task sequence, which interconnects congruency, similarity, geometric constructions, and deductive proof, can be accessed by prospective mathematics teachers possessing limited understanding of these topics. Creative thinking is stimulated during work within this sequence: experimenting, recognizing relevant mathematics from earlier in the sequence to progress this experimenting, and connecting mathematical understandings. This chapter focuses on how the implementation of this complex task sequence provided opportunities for successes that theory suggests should contribute to developing psychological factors to increase future teachers’ ability to think flexibly when encountering mathematical and pedagogical challenges.

Learning and Cognition in Mathematics

Learning and cognition is a classical and very vital area in research on mathematics education. Researchers have published many valuable research findings that have contributed to significant development in this area. The continued efforts of researchers now and in the future will, we hope, lead to extensive ‘pay-offs’. Different to many other special and related TSGs, such as teaching and learning of algebra, geometry, measurement, statistics, calculus, reasoning, proving and problem solving, to mention a few, TSG22’s participants will contribute a more general focus on learning and cognitive activity, and insights into students’ characteristics; their strengths and weaknesses in the process of mathematics learning.

Enlivening STEM Education Through School-Community Partnerships

A major response to the growing concern with diminishing engagement and participation of students in STEM pathways, in Australia and internationally, has been the involvement of the STEM community in school outreach activities. In Australia there has been a proliferation of links between scientists and schools, with the aim of engaging students in authentic activities and providing models of what STEM work pathways might entail. This chapter will draw on a series of projects studying partnerships between the professional science/mathematics communities and schools, to explore a range of partnership models, the experience and outcomes for students and teachers, and challenges for crossing the boundary between school and STEM professional communities. Such school/STEM community partnerships are particularly suited to studies related to environmental and sustainability issues, a focus explored in the chapter. Further, we will draw on a recent evaluation of the Australia-wide, CSIRO-led Scientists and Mathematicians in Schools (SMiS) program. That study provided insight into the use and outcomes of the SMiS model. We will explore some of the challenges of working across the school-STEM professional practice boundary, implications for curriculum, and differences in partnerships for mathematics compared to science.

Topic Study Group No. 27: Learning and Cognition in Mathematics

Deakin Research Online, Deakin University’s Research Repository Deakin University CRICOS Provider Code: 00113B Topic study group no. 27: learning and cognition in mathematics Citation: Williams, Gaynor, Van Dooren, Wim, Dartnell, Pablo, Lindmeier, Anke and Proulx, Jérôme 2017, Topic study group no. 27: learning and cognition in mathematics, in ICME-13 : Proceedings of the 13th International Congress on Mathematical Education, Springer, Cham, Switzerland, pp. 501505. DOI: 10.1007/978-3-319-62597-3_54