Kindergarten students' understanding of probability concepts

This study explored kindergarten students’ intuitive strategies and understandings in probabilities. The paper aims to provide an in depth insight into the levels of probability understanding across four constructs, as proposed by Jones (1997), for kindergarten students. Qualitative evidence from two students revealed that even before instruction pupils have a good capacity of predicting most and least likely events, of distinguishing fair probability situations from unfair ones, of comparing the probability of an event in two sample spaces, and of recognizing conditional probability events. These results contribute to the growing evidence on kindergarten students’ intuitive probabilistic reasoning. The potential of this study for improving the learning of probability, as well as suggestions for further research, are discussed.

Militarising the body politic : new media as weapons of mass instruction

As militarization of bodies politic continues apace the world over, as military organizations again reveal themselves as primary political, economic and cultural forces in many societies, we argue that the emergent and potentially dominant form of political economic organization is a species of neo-feudal corporatism. Drawing upon Bourdieu, we theorize bodies politic as living habitus. Bodies politic are prepared for war and peace through new mediations, powerful means of public pedagogy. The process of militarization requires the generation of new, antagonistic evaluations of other bodies politic. Such evaluations are inculcated via these mediations, the movement of meanings across time and space, between formerly disparate histories, places, and cultures. New mediations touch new and different aspects of the body politic: its eyes, its ears, its organs, but they are consistently targeted at the formation of dispositions, the prime movers of action.

Leading learning within a PLC : implementing new mathematics content

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Reunitising hundredths: prototypic and nonprototypic representations

This paper reports on a study in which 29 Year 6 students (selected from the top 30% of 176 Year 6 students) were individually interviewed to explore their ability to reunitise hundredths as tenths (Behr, Harel, Post & Lesh, 1992) when represented by prototypic (PRO) and nonprototypic (NPRO) models. The results showed that 55.2% of the students were able to unitise both models and that reunitising was more successful with the PRO model. The interviews revealed that many of these students had incomplete, fragmented or non-existent structural knowledge of the reunitising process and often relied on syntactic clues to complete the tasks. The implication for teaching is that instruction should not be limited to PRO representations of the part/whole notion of fraction and that the basic structures (equal parts, link between name and number of equal parts) of the part/whole notion needs to be revisited often.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

Surveying theories and philosophies of mathematics education

Any 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 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: (1) What is reality? Or what is the nature of the world around us? (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, (3) How can we be certain in the “truth” of what we know? [the epistemological question]