Dialogues on Numbers: Script-Writing as Approximation of Practice (original) (raw)
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Script writing in the mathematics classroom: Imaginary conversations on the structure of numbers
Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the characters attempted to convince each other of their point of view. They had to imagine and articulate fictional characters' reasoning, as well as design a potential pedagogical intervention. We outline what script writing revealed about the participants' understanding of the structure of natural and rational numbers and of mathematical argumentation, and discuss the affordances of this methodological tool in teacher education.
Educational Studies in Mathematics, 2002
Number theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge. Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction.
Using scenes of dialogue about mathematics with adult numeracy learners - what it might tell us
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How might we characterise the discussion following reading of scenes of dialogue? The idea for this work came from two broad areas, one of which concerns learner-learner interactions and the other concerns the use of participants in verbalising the words of others. A few years ago, I was involved in a project in which discussion of mathematical concepts by learners was a key part of the learning intervention. What interested me was that learner-learner interactions were at times rather minimal. The reports from the sessions contained very few records of learner-learner interactions. A search around learner interactions in the literature produced more teacher-learner interactions than learner-learner. Indeed most of these were concerned with school learners rather than adults, the area which was of most interest to me. A second influence for me began in an observation that I made when attending a research seminar. I had noted that in one session participants were asked to read out th...
Reflections on mathematics education research questions in elementary number theory, 2002
Learning and Teaching Number Theory: Research in Cognition and Instruction, ). S. R. Campbell and R. Zazkis (Eds.), (pp. 213-230), Monograph Series of the Journal of Mathematical Behavior Vol. 2, Westport, CT, Ablex Publishing, 2002.
This is the summary chapter of the monograph. It begins: This monograph intentionally raises more questions than it answers. Indeed the editors' aims included convincing readers that many interesting questions in the teaching and learning of number theory await their attention, and that there are engaging number theory tasks with which to investigate students' mathematical sense making. Number theory appears to be a rather neglected area in the mathematics education research literature. Whether one looks at the NCTM Handbook of Research on Mathematics Teaching and Learning (Grouws, 1992) or the NCTM Yearbook, Developing Mathematical Reasoning in Grades K-12 (Stiff, 1999), one finds almost nothing on students' engagement with number theory topics. By number theory we mean, as do the monograph editors, results concerning the structure of the integers that are not primarily computational, for example, questions about factorization or the distribution of primes. Whatever the reasons for this research lacuna, this monograph, devoted entirely to various number theory investigations and reports, should help fill this void and heighten the community's awareness of the potential for fruitful investigations. These might concern individual students' cognitions on a variety of topics from divisibility and prime factorization to number theoretic generic proofs and mathematical induction, or they might be more socio-cultural studies.
Using dialogue in Mathematics classes: Could it aid Mathematicsal reasoning?
2012
Students studying for a language module for an Advanced Certificate in Education in Mathematics and Science Education (ACE:MST) at Nelson Mandela Metropolitan University (NMMU) were asked to answer a questionnaire about their perceptions concerning language, language policy and their experiences in multilingual classes. Very often students give answers that would satisfy the lecturer. In order to open windows to their souls they were first asked to write poetry about their language experiences before they answered the questionnaire. The results opened a common ground of trust and sharing in the class that could not have been evident in a normal lecture environment
Creating numbers: Participationist discourse on mathematics learning
The point of departure for this article is that the language in which researchers conduct their investigations influences their ability to ask questions and interpret data. The traditional language of research on numerical thinking implies that the child is aware of the existence of the abstract objects called numbers prior to being able to apply them in any way. Those who adopt discursive approach conceptualize thinking at large and numerical thinking in particular as forms of communication. In this way, they remove the assumption about the pre-existence of numbers: by portraying them as discursive constructs, they imply that numbers are products rather than pre-given objects of human communication. In this paper, after presenting the basic tenets of the discursive approach to cognition, I explore the question of how the proposed reconceptualization impacts our understanding of numerical thinking and the practice of fostering children’s numerical development. Theoretical arguments is supported with empirical examples coming from my own and other researchers’ recent studies.