Just before Christmas, I wrote about a forthcoming issue of TMME. This issue has now appeared, and (as usual) all the articles are freely available for anyone! I am not going to repeat the rather impressive list of authors and titles for this issue, since you can easily find that for yourself. I would only like to point you to the excellent editorial by the main editor (Professor Bharath Sriraman), entitled: Opening 2011’s Journal Treasure Chest. And this issue truly is a treasure chest! So, point your cursor towards the journal’s home page, and dig into the chest!
Argumentation and proofs in elementary calculus
Ferdinando Arzarello and Cristina Sabena have written an article entitled Semiotic and theoretic control in argumentation and proof activities. This article was recently published online in Educational Studies in Mathematics. Here is an abstract of their article:
We present a model to analyze the students’ activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin’s structural description of arguments, Peirce’s notions of sign, diagrammatic reasoning and abduction, and Habermas’ model for rational behavior. Based on empirical qualitative analysis we identify three different kinds of semiotic actions featuring the organization of the argumentations, and related to different epistemological status of the arguments. In such semiotic actions, the students’ argumentation and proof activities are managed and guided according to two intertwined modalities of control, which we call semiotic and theoretic control. The former refers to decisions concerning the selection and implementation of semiotic resources; the latter refers to decisions concerning the selection and implementation of a more or less explicit theory or parts of it. The structure of the model allows us to pinpoint a dialectical dynamics between the two.
Imagining mathematics teaching practice
Sandra Crespo, Joy Ann Oslund and Amy Noelle Parks have written an article that was recently published online in ZDM – The international journal on mathematics education. The article is heading towards an interesting topic: that of mathematics teaching practice. The title of their article is Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion. Here is the abstract:
Prospective teachers work with a variety of representations of mathematics teaching (i.e., narrative cases, transcripts, video clips) in teacher preparation courses. Generally, they are considered the audience, not producers, of those artifacts. In this article, however, we focus on representations produced by prospective teachers when they were asked to generate a hypothetical classroom dialogue for the equality task: “What goes in the box: 8+4=[ ]+5?” We discuss the nature and quality of the representations produced by four different cohorts of teacher preparation students—prior to admission, at the beginning, middle, and end of their program. Prospective teachers within and across all cohorts produced an unexpected diversity of representations of class discussions. Of special interest to us were their hybrid representations, those that combined multiple images of mathematics teaching practices. These representations not only provide a lens into prospective teachers’ development as mathematics teachers but could also become tools to support novices as they learn more complex forms of mathematics teaching.
Two interesting articles on teachers’ knowledge
In the recent issue of Journal for Research in Mathematics Education, two interesting articles about teachers’ mathematical knowledge for teaching are published. One of these articles, “The nature and predictors of elementary teachers’ mathematical knowledge for teaching“, was written by Heather C. Hill. Here is the abstract of her article:
This article explores elementary school teachers’ mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.
The other article was written by Courtney A. Bell, Suzanne Wilson, Traci Higgins and D. Betsy McCoach, and this article is entitled “Measuring the effects of professional development on teacher knowledge: the case of developing mathematical ideas“. The abstract of their article can be found below:
This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers’ specialized knowledge for teaching mathematics and illustrates how such research could be conducted. This study adds to our understanding of the ways in which professional development program features, facilitators, and issues of scale interact in the development of teachers’ mathematical knowledge for teaching. Study limitations and challenges are discussed.
Preschoolers’ notion of chance and probability
Zoi Nikiforidou and Jenny Pange have written an article about The notions of change and probabilities in preschoolers, which was published in the most recent issue of Early Childhood Education Journal. Here is the abstract of their article:
Chance, randomness and probability constitute statistical notions that are interrelated and characterize the logicomathematical thinking of children. Traditional theories support that probabilistic thinking evolves after the age of 7. However, recent research has underlined that children, as young as 4, may possess and develop basic notions, through mental mechanisms and/or through intuitive processes. In the current study, preschoolers (N = 200) aged 4–6, participated in two diverse probability tasks related to the likelihood of events and the graphical representation of randomness. The aim of this study was to test whether children, at this young age, have the ability to predict the most probable outcome in a probabilistic game with animal cards and whether they can mark symbols randomly distributed in a 5 × 5 matrix. Preschoolers infered correctly the most likely outcome and showed a minimal understanding of randomness by preferring the uniform rather than random distribution of items. Such findings have both methodological and educational implications for further research as already the notions of chance and probabilities are integrated in Preschool Mathematics Curricula worldwide.
Mathematical Thinking and Learning, issue 4
Mathematical Thinking and Learning is one of the major journals within mathematics education research, and the fourth issue of the journal has now been published. This issue contains the following three articles:
- Advanced mathematical knowledge in teaching practice: perceptions of secondary mathematics teachers, by Rina Zazkis and Roza Leikin.
- Understanding the development of flexibility in struggling algebra students, by Kristie Jones Newton, Jon R. Star and Kathleen Lynch.
- Mathematics majors’ perceptions of conviction, validity, and proof, by Keith Weber.
To learn more about these articles, visit the links above to read their abstracts!
Critical Mathematics Education – Special issue of Philosophy of Mathematics Education Journal
Philosophy of Mathematics Education Journal is Paul Ernest’s online (and open access) journal. New issues of the journal have been infrequently released over the last years, and I have many times feared that Ernest has given up on his journal. Quite recently, however, a new and interesting special issue has been released. The focus of this special issue is on “Critical Mathematics Education”. Ole Skovsmose, who must be considered as one of the main figures within this particular area of our field, has written two articles in this issue. Here is a complete list of authors and titles:
- Ole Skovsmose Mathematics: A Critical Rationality?
- Ole Skovsmose Can Facts be Fabricated through Mathematics?
- Paul Ernest The Scope and Limits of Critical Mathematics Education
- D. F. Almeida Are there Viable Connections between Mathematics, Mathematical Proof and Democracy?
- Ubiratan D’Ambrosio Ethnomathematics: A Response to the Changing Role of Mathematics in Society
- Annica Andersson Can a Critical Pedagogy in Mathematics lead to Achievement, Engagement and Social Empowerment?
- Ieda Maria Giongo & Gelsa Knijnik School Curriculum and Different Mathematics Language Games: A Study at a Brazilian Agricultural-Technical School
- Mario Sánchez & Morten Blomhøj The Role of Mathematics in Politics as an Issue for Mathematics Teaching (pdf)
- Hilary Povey Teaching for Equity, Teaching for Mathematical Engagement
- Randall Collins & Sal Restivo Robber Barons and Politicians in Mathematics: A Conflict Model of Science
- Sal Restivo & Randall Collins Mathematics and Civilization
- Marilyn Frankenstein Critical Mathematics Education: An Application of Paulo Freire’s Epistemology
- Michael W. Apple Reform through Conservative Modernization: Standards, Markets, and Inequality in Education
- Peter Appelbaum Sense and Representation in Elementary Mathematics
- Maria Nikolakaki Investigating Critical Routes: The Politics of Mathematics Education and Citizenship in Capitalism
- Tony Brown Cultural Continuity and Consensus in Mathematics Education
- M. Sencer Corlu A Historical Analysis of Democracy in Mathematics and Mathematics Education in European Culture
- Laura J. Jacobsen Embedding Mathematics in the Elementary Teacher Education Curriculum Network
- Lawrence M. Lesser The Necessity of Equity in Teaching Statistics
If you head to the journal home page, you can freely download each of the articles (in Word format).
December issue of JMTE
The December issue of Journal of Mathematics Teacher Education has recently been published. This issue constitutes the second part of a theme issue on “Mathematics teacher and mathematics teacher educator change” (see also my post about the October issue, which constituted part 1 in this theme issue!). This issue contains six interesting articles:
- Observing the process of mathematics teacher change: part 2, by David Reid and Vicki Zack
- Understanding change through a high school mathematics teacher’s journey to inquiry-based teaching, by Olive Chapman and Brenda Heater
- Challenges of critical colleagueship: examining and reflecting on mathematics teacher study group interactions, by Lorraine M. Males, Samuel Otten and Beth A. Herbel-Eisenmann
- Teachers’ and researchers’ collaboration in analysing mathematics teaching: A context for professional reflection and development, by Despina Potari, Haralambos Sakonidis, Roula Chatzigoula and Alexandros Manaridis
- Mathematics pedagogical change: rethinking identity and reflective practice, by Margaret Walshaw
- Theoretical perspectives on mathematics teacher change, by Merrilyn Goos and Vince Geiger
If you just have the time to read one of these articles, I recommend that you start with the last one, by Merrilyn Goos and Vince Geiger. This article is a discussion essay, where the authors discuss issues that have been raised in all the articles in these two special issues of JMTE. They used a socio-cultural lens in order to analyze this.
New issue of ZDM – handheld technology
A new issue of ZDM has been published, and this issue has a focus on “Handheld technology in the mathematics classroom – theory and practice”. The theme issue presents 12 articles, including an editorial by Paul Drijvers and Hans-Georg Weigand:
- Handheld technology for mathematics education: flashback into the future, by Luc Trouche and Paul Drijvers
- Examining the didactic contract when handheld technology is permitted in the mathematics classroom, by Robyn Pierce, Kaye Stacey and Roger Wander
- Towards a competence model for the use of symbolic calculators in mathematics lessons: the case of functions, by Hans-Georg Weigand and Ewald Bichler
- Multimodality in multi-representational environments, by Ferdinando Arzarello and Ornella Robutti
- Handheld calculators between instrument and document, by Gilles Aldon
- Emergent pedagogies and the changing role of the teacher in the TI-Nspire Navigator-networked mathematics classroom, by Alison Clark-Wilson
- Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-Nspire in Scottish secondary schools, by Allan Graham Duncan
- Influences of CAS and GC in early algebra, by Matthias Zeller and Bärbel Barzel
- MobileMath: exploring mathematics outside the classroom, by Monica Wijers, Vincent Jonker and Paul Drijvers
- Hoyles, C. and J.-B. Lagrange (eds.) (2010): Mathematics Education and Technology—Rethinking the Terrain. The 17th ICMI Study. Springer: New York a. o., by Hans-Georg Weigand
- Ivor Grattan-Guinness: Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics. The John Hopkins University Press, Baltimore, 2009. 386 pp. ISBN 978-0801892486 Paperback, by Gilda de La Rocque Palis
Using video in teacher education
Rosella Santagata and Jody Guarino have written an interesting article about Using video to teach future teachers to learn from teaching. The article was recently published online in ZDM. Rosella, the main author of the article, used to work at LessonLab in Santa Monica (LessonLab closed in 2009), but now works at the University of California, Irvine. One of her particular areas of focus is to use technological tools (like video) to foster teacher learning, and she has written lots of articles about this. (See her publication list for more!)
In this particular article, they present results from the “Learning to Learn from Mathematics Teaching” project. The main focus in the article is on how they have used video in a particular course for pre-service teachers. The project is linked with lesson study, and it seems to build upon the previous studies (like the TIMSS Video Studies) that Santagata and her previous colleagues (like Jim Stigler and James Hiebert) at the LessonLab conducted some years ago. The “Lesson Analysis Framework” is presented and discussed in detail, and so is their use of videos to develop analytic skills with the teachers. So, if you want to learn more about the use of videos in teacher education, this is a great opportunity to learn from one of the masters in this field. And the article is Open Access too, so it should be freely available for everyone to read!!!