This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their properties. The prospective teachers’ reflections upon the process they underwent indicate that they developed awareness of various aspects of creativity while deepening their mathematical and didactical knowledge.
Paulus Gerdes has written an article called Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education. This article was recently published online in ZDM. In this article, Gerdes provides an interesting overview of how the cultural practices of African mathematics (teacher) education has developed, and he makes a seemingly (to me) impossible connection between traditional basket weaving and exploration of technologies.
Here is the abstract of the article:
The study at teacher education institutions in Africa of mathematical ideas, from African history and cultures, may broaden the horizon of (future) mathematics teachers and increase their socio-cultural self-confidence and awareness. Exploring educationally mathematical ideas embedded in, and derived from, technologies of various African cultural practices may contribute to bridge the gap between ‘home’ and ‘school’ culture. Examples of the study and exploration of these technologies and cultural practices will be presented. The examples come from cultural practices as varied as story telling, basket making, salt production, and mat, trap and hat weaving.
A new book, entitled Theories of Mathematics Education, is about to be published by Springer (due October 2009). One of the editors, Bharath Sriraman (also editor of The Montana Mathematics Enthusiast) has been kind enough to give me permission to post the book cover and the table of contents here on my blog. Thanks, Bharath!
Looking at the table of contents is enough to make me believe that this is definitely going to be an important book, and it will make an impact on our field of research! If you won't take my word for it, please take the time to read through the table of contents yourself:
I especially like the way it is built up, with introductions and commentaries to all the parts of the book. This will give the reader a feeling of how the field has evolved, and how it is still in a process of evolving.
The publisher has given the following description of the book:
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.
This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbooks to which the teachers were accustomed. However, variation emerged when considering the ways in which the teachers interacted with the materials for their learning of mathematics. Whereas some teachers accepted and even embraced changes to the teaching–learning process that accompanied use of the curriculum materials, other teachers experienced discomfort and frustration at times. Nonetheless, each teacher considered that use of the curriculum materials improved her mathematical understandings in significant ways. Implications of these results for mathematics teacher education are discussed.
A new newsletter has been published from ICMI, and, as usual, it contains lots of interesting information. I would have liked to post the entire newsletter here, but since it is freely available online, I am only going to point to the table of contents:
Editorial: Continuing Professional Development and Effective integration of Digital Technologies in Teaching and Learning Mathematics: Two Challenges for ICMI
A XXIst century Felix Klein's follow up workshop
Deadline Extended: ICMI / ICIAM STUDY
EARCOME5: First Announcement
Chilean Journal of Statistics (ChJS)
Calendar of Events of Interest to the ICMI Community
ICMI encounters: Hassler Whitney, Laurence C. Young and Dirk J. Struik: Personal recollections
Subscribing to ICMI News
You can also check out the archive for a complete listing of previous (and current) newsletters!
Eleanor Chute has written an interesting article about the importance of algebra in school mathematics. It is not a scientific article, but I think it is worth reading even though! (It was published on September 1st in the Pittsburgh Post-Gazette.) The article is part of a series related to school mathematics, and the two previous articles in the series raise interesting questions about early math and fractions.
Although algebra to many represents a hurdle, or even the graveyard in their mathematical careers, the article claims that:
Algebraic thinking is done even by people who don't realize they're using algebra.
After a series of examples, Chute goes on to quote Michele Burgess, who claims that students should not be confronted with algebra for the first time in the Algebra 1 course. This leads me to think about the debate (and research) concerning early algebra, although this is not referred to in this article in particular. If you are interested, I recommend the chapter on early algebra by David Carraher and Analucia Schliemann in NCTM's Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007), or even Carolyn Kieran's chapter on algebra in the same handbook.
Reference:
Lester, F. K. (Ed.) (2007). Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age Pub.
Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an individual's desire, power, and tendency to act in particular ways. We characterize details of motivation in mathematical learning through qualitative analysis of honors calculus students’ extended, collaborative problem solving efforts within a longitudinal research project in learning and teaching. Contextual Motivation Theory emerges as an interpretive means for understanding the complexities of student motivations. Students chose to act upon intellectual-mathematical motivations and social-personal motivations that manifested simultaneously. Students exhibited intellectual passion in persisting beyond obtaining correct answers to build understandings of mathematical ideas. Conceptually driven conditions that encourage mathematical necessity are shown to support the growth of intellectual passion in mathematics learning.
Susanne Prediger has written an article about How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign. The article was published online in Journal of Mathematics Teacher Education on Thursday last week. Point of departure in her article is the very important question about what mathematical (content) knowledge prospective teachers need. A main claim which is raised already in the introduction is: "Listen to your students!" In the theoretical background, Prediger takes Shulman's classic conceptualization of three main categories of content knowledge in teaching as point of departure:
Subject-matter knowledge
Pedagogical-content knowledge
Curricular knowledge
She continues to build heavily on the work done by Hyman Bass and Deborah Ball (e.g. Ball & Bass, 2004), and she goes on to place her own study in relation to the work of Bass and Ball:
Whereas Bass and Ball (2004) concentrate on the first part of their program, namely, identifying important competences, this article deals with both parts, the analytical study of identifying, and the developmental study of constructing a sequence for teacher education, exemplified by a sequence in the course entitled school algebra and its teaching and learning for second-year, prospective middle-school teachers.
Here is the abstract of Prediger's article:
What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for pre-service middle-school mathematics teachers.
References: Bass, H., & Ball, D. L. (2004). A practice-based theory of mathematical knowledge for teaching: The case of mathematical reasoning. In W. Jianpan & X. Binyan (Eds.), Trends and challenges in mathematics education (pp. 107–123). Shanghai: East China Normal University Press.
Professional development comes in many forms, some of which are deemed more useful than others. However, when groups of teachers are excluded, or exclude themselves, from professional development opportunities, then there is an issue of social justice. This article examines the experiences of a group of teachers from a Māori-medium school who attended a mathematics teacher conference. By analysing the teachers’ sense of belonging through their ideas about engagement, alignment and imagination, we are able to describe how different kinds of relationships influence the inclusion/exclusion process. This leads to a discussion about what can be done by the teachers as well as conference organisers to increase these teachers’ likelihood of attending further conferences in the future.
My name is Reidar Mosvold, and I am Associate Professor in Mathematics Education at University of Stavanger, Norway. This blog is my attempt to follow my field: mathematics education research. I hope you might find this site interesting too!
If you want to send me an e-mail rather than making direct comment to articles, you can reach me at: reidar.mosvold@uis.no
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