Teachers’ beliefs arguably have an impact on their teaching practice (see for instance Leder et al., 2002), but often, beliefs appear to be resistant to change. It is therefore an interesting topic that is being raised by Peter Grootenboer in his article: Mathematical belief change in prospective primary teachers. The article was recently published online in Journal of Mathematics Teacher Education.

Grootenboer provides a nice overview of previous research in this area, and that alone is reason enough to read this article. In addition, the study he reports is very interesting. Unlike many other studies of teachers’ beliefs, Grootenboer has conducted a naturalistic study (in his own classroom), and he collected data from different sources: observation, interviews and assignments. If, like me, you are interested in teachers’ beliefs in mathematics education, you should definitely read this article! Here is the abstract:

The development and influence of beliefs in teacher education has been a topic of increasing interest for researchers in recent years. This study explores the responses of a group of prospective primary teachers to attempts to facilitate belief change as part of their initial teacher education programme in mathematics. The students’ responses seemed to fall into three categories: non-engagement; building a new set of beliefs and; reforming existing beliefs. In this article the participants’ responses are outlined and illustrated with stories from three individuals. This study suggests that belief reform is complex and fraught with ethical dilemmas. Certainly there is a need for further research in this area, particularly given the pervasive influence of beliefs on teaching practice.

Blake E. Peterson and Steven R. Williams (both from Brigham Young University) have written an interesting article about Learning mathematics for teaching in the student teaching experience: two contrasting cases. This article was published two days ago in Journal of Mathematics Teacher Education. In their article, they deal with important topics like learning and knowing mathematics, pedagogical content knowledge (Shulman), mathematical knowledge for teaching (Ball and others), and they also discuss the influence of beliefs on teaching. All in all, this is very much in line with my own research interest, and I think the article gives a nice overview of the relevant literature in the field. The study presented is also interesting. So, if you are interested in any of the above mentioned topics, you should definitely take a closer look at this article!

Here is the abstract:

Student teaching (guided teaching by a prospective teacher under the supervision of an experienced “cooperating” teacher) provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching. The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur. We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the lesson and on mathematics from the students’ point of view. These contrasting experiences suggest that student teaching can have a profound effect on prospective teachers’ understanding of mathematics in and for teaching.

Luis Radford has written an article that was recently published online in Educational Studies in Mathematics. The article is concerned with aspects related to” the role of gestures and bodily actions in the learning of mathematics”, and the article provides some interesting theoretical perspectives together with some practical examples. The article is entitled: Why do gestures matter? Sensuous cognition and the palpability of mathematical meaning, and here is the abstract:

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed “sensuous cognition.” The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal “material” conception of thinking. The very texture of thinking, it is suggested, cannot be reduced to that of impalpable ideas; it is instead made up of speech, gestures, and our actual actions with cultural artifacts (signs, objects, etc.). As illustrated through an example from a Grade 10 mathematics lesson, thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools.

Luis Radford is a distinguished scholar, and he has published a large number of important articles over the years. If you want to read more about his work, you should visit his list of publications. Most of his articles are freely available in pdf-format!

Olof Bjort Steinthorsdottir and Bharath Sriraman have written an article that was published in ZDM recently. The article is entitled: Exploring gender factors related to PISA 2003 results in Iceland: a youth interview study. Here is the abstract of the article:

Students’ mathematical achievement in Iceland, as reported in PISA 2003, showed significant and (by comparison) unusual gender differences in mathematics: Iceland was the only country in which the mathematics gender gap favored girls. When data were broken down and analyzed, the Icelandic gender gap appeared statistically significant only in the rural areas of Iceland, suggesting a question about differences in rural and urban educational communities. In the 2007 qualitative research study reported in this paper, the authors interviewed 19 students from rural and urban Iceland who participated in PISA 2003 in order to investigate these differences and to identify factors that contributed to gender differences in mathematics learning. Students were asked to talk about their mathematical experiences, their thoughts about the PISA results, and their ideas about the reasons behind the PISA 2003 results. The data were transcribed, coded, and analyzed using techniques from analytic induction in order to build themes and to present both male and female student perspectives on the Icelandic anomaly. Strikingly, youth in the interviews focused on social and societal factors concerning education in general rather then on their mathematics education.

Laurie D. Edwards has written an article that was recently published in Educational Studies in Mathematics. The article is entitled Gestures and conceptual integration in mathematical talk. Here is the abstract:

Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately.

A key idea in the article is that mathematics is seen as “an embodied, socially constructed human product”, and gestures therefore might provide a relevant contribution to the mathematical thinking and communication. Edwards provides a nice explanation for the role of research on gestures:

(…) gesture constitutes a particular modality of embodied cognition, and, along with oral speech, written inscriptions, drawings and graphing, it can serve as a window on how learners think and talk about mathematics.

The article provides a good overview of the theoretical framework for this area of research, and the study itself is also interesting. The participants (all women) were twelve volunteers from a course for prospective elementary school teachers, and the course was taught by Edwards herself. The participants were interviewed in pair, and the interview sessions were videotaped. The gestures that were caught on videotape were classified by McNeill’s scheme.

Jae Hoon Lim has written an article called Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom, which was recently published in ZDM. Here is the abstract of the article:

This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant’s class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as “I,” “we,” “they,” and “should/shouldn’t” elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.

Research in Mathematics Education has released its September issue (Volume 10, Issue 2), and the issue includes a number of interesting articles. Here are the headlines:

• How persuaded are you? A typology of responses Authors: Matthew Inglis; Juan Pablo Mejia-Ramos
• To be or to become: how dynamic geometry changes discourse Authors: Nathalie Sinclair; Violeta Yurita
• A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end Author: Ian Jones
• Paradoxes as a window to infinity Authors: Ami Mamolo; Rina Zazkis
• The effect of graphic calculators on Negev Arab pupils’ learning of the concept of families of functions Author:Muhammad Abu-Naja
• The mathematical competence of adults returning to learning on a university
  foundation programme: a selective comparison of performance with the
  CSMS study Author: Mary Dodd
• Mathematics and dyslexics: classroom management skills and children’s response to noise Author: Mari Palmer
• A synthesis of existing frameworks used to analyse mathematics curricula Author: Nusrat Fatima Rizvi
• Beginning elementary teachers’ use of representations in mathematics teaching Author: Fay Turner
• Observing students’ use of images through their gestures and gazes Author: Tracy Wylie

A new article has appeared in Educational Studies in Mathematics with the long and interesting title: On semiotics and subjectivity: a response to Tony Brown’s “signifying ‘students’, ‘teachers’, and ‘mathematics’: a reading of a special issue”. The article is written by two celebrated researchers within the field of mathematics education research: Norma Presmeg and Luis Radford. Here is the abstract of their article:

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of Educational Studies in Mathematics on “Semiotic perspectives in mathematics education” (Sáenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1–2), 2006). Among these issues are conceptualizations of subjectivity and the notion that particular readings of Peircean and Vygotskian semiotics may limit the ways that authors define key actors or elements in mathematics education, namely students, teachers and the nature of mathematics. To deepen the conversation, we comment on Brown’s approach and explore the theoretical apparatus of Jacques Lacan that informs Brown’s discourse. We show some of the intrinsic limitations of the Lacanian idea of subjectivity that permeates Brown’s insightful analysis and conclude with a suggestion about some possible lines of research in mathematics education.

Charlene Morrow and Inga Schowengerdt have written an article in ZDM where they report on a case-study of high school women. The article is entitled Stepping beyond high school mathematics: a case study of high school women, and here is a copy of the abstract:

The Summer Explorations and Research Collaborations for High School Girls (SEARCH) Program, held annually since 2004 at Mount Holyoke College in the US, was created for talented high school girls to explore mathematics beyond that taught in high school. Our study, which focuses on factors that facilitate or inhibit the pursuit of higher level mathematics by girls, is centered on the 2006 SEARCH Program. We present a combination of qualitative and quantitative data drawn from student journals written during SEARCH, program evaluations written at the end of SEARCH, post-program interviews, and comparisons with two peer group samples. From this data we point to important factors, such as developing a mathematical voice, gaining a broader view of advanced mathematics, being challenged in a supportive atmosphere, and having a positive stance toward risk-taking, that may help to maintain the interest of talented girls in advanced mathematical studies.