54,713 research outputs found
Development Of 10-Year-Olds’ Mathematical Modelling
No full textThis paper addresses the developments of a class of fifth-grade children as they worked modelling problems during the first year of a 3-year longitudinal study. In contrast to usual classroom problems where students find a brief answer to a particular question, modelling activities involve students in authentic case studies that require them to create a system of relationships that is generalisable and re-usable. The present study shows how 10-year-olds, who had not experienced modelling before, used their existing informal mathematical knowledge to generate new ideas and relationships, and how these developments were fuelled by significant social interactions within small group settings
Mathematical and Analogical Reasoning in Early Childhood
No full textThe chapters of this book provide further evidence of young children's reasoning abilities. We draw on rich sets of data from a longitudinal and cross-cultural study of young children’s reasoning development as they progressed from preschool through to the end of second grade. The participants included the children and their teachers from schools in Australia and the United States. We pay special attention to the children’s development of mathematical and analogical reasoning in their informative years, given that our earlier studies had highlighted the importance of analogical reasoning in children's mathematical development (Alexander, White, & Daugherty, 1997). The purpose of this first chapter is to provide background information on analogical and mathematical reasoning, and to highlight the issues that are the focus of this book. Consideration is given first to the nature, role, and development of analogical reasoning
Promoting the Development of Young Children's Mathematical and Analogical
No full textThis concluding chapter begins with a brief overview of the main findings of our study. The remainder of the chapter offers suggestions for fostering the development of mathematical and analogical reasoning in the early school years. I also acknowledge the valuable input from the authors of the commentary chapters (8 and 9)
Theoretical, conceptual, and philosophical foundations for mathematics education research : timeless necessities
No full textSurveying theories and philosophies of mathematics education
No full textAny theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the \ud
foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions:\ud
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(1) What is reality? Or what is the nature of the world around us?\ud
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(2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and,\ud
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(3) How can we be certain in the “truth” of what we know? [the epistemological question]\ud
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Politicizing mathematics education : has politics gone too far? Or not far enough?
No full textIn this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.\ud
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Changing agendas in international research in mathematics education
No full textHandbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies..
Problem solving in a 21st century mathematics curriculum
No full textResearch on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)..
Perspectives on Reconceptualizing Early Mathematics Learning
No full textThis introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters
Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure
No full textThe Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning.\ud
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A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed
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