William H. Schmidt et al. have written an article entitled Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries. The article was recently published online in ZDM. Here is the abstract of the article:

Cross-national research studies such as the Program for International Student Assessment and the Third International Mathematics and Science Study (TIMSS) have contributed much to our understandings regarding country differences in student achievement in mathematics, especially at the primary (elementary) and lower secondary (middle school) levels. TIMSS, especially, has demonstrated the central role that the concept of opportunity to learn plays in understanding cross-national differences in achievement Schmidt et al., (Why schools matter: A cross-national comparison of curriculum and learning  2001). The curricular expectations of a nation and the actual content exposure that is delivered to students by teachers were found to be among the most salient features of schooling related to academic performance. The other feature that emerges in these studies is the importance of the teacher. The professional competence of the teacher which includes substantive knowledge regarding formal mathematics, mathematics pedagogy and general pedagogy is suggested as being significant—not just in understanding cross-national differences but also in other studies as well (Hill et al. in Am Educ Res J 42(2):371–406, 2005). Mathematics Teaching in the 21st Century (MT21) is a small, six-country study that collected data on future lower secondary teachers in their last year of preparation. One of the findings noted in the first report of that study was that the opportunities future teachers experienced as part of their formal education varied across the six countries (Schmidt et al. in The preparation gap: Teacher education for middle school mathematics in six countries, 2007). This variation in opportunity to learn (OTL) existed in course work related to formal mathematics, mathematics pedagogy and general pedagogy. It appears from these initial results that OTL not only is important in understanding K-12 student learning but it is also likely important in understanding the knowledge base of the teachers who teach them which then has the potential to influence student learning as well. This study using the same MT21 data examines in greater detail the configuration of the educational opportunities future teachers had during their teacher education in some 34 institutions across the six countries.

Donna Kotsopoulos and Michelle Cordy have written an article with an interesting angle: Investigating imagination as a cognitive space for learning mathematics. The article was published online in Educational Studies in Mathematics on Monday. Abstract:

Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.

Leone Burton has written an article that was recently published in ZDM. The article is entitled Moving towards a feminist epistemology of mathematics. Here is the article abstract:

There is, now, an extensive critical literature on gender and the nature of science, three aspects of which, philosophy, pedagogy and epistemology, seem to be pertinent to a discussion of gender and mathematics. Although untangling the inter-relationships between these three is no simple matter, they make effective starting points in order to ask similar questions of mathematics to those asked by our colleagues in science. In the process of asking such questions, a major difference between the empirical approach of the sciences, and the analytic nature of mathematics, is exposed and leads towards the definition of a new epistemological position in mathematics.
This is a version of a paper first presented at the ICME7 theme group of the International Organisation on Women and Mathematics Education, Quebec, 1992. Its present content owes much to discussion with and comments from members of that network. In addition, I would particularly like to thank Mary Barnes, Leonie Daws, Stephen Lerman and the anonymous reviewers for challenging and provoking re-working of the ideas.

Joke Torbeyns, Bert De Smedt, Pol Ghesquière and Lieven Verschaffel have written an article entitled Acquisition and use of shortcut strategies by traditionally schooled children. The article was published online in Educational Studies in Mathematics this week. The development of strategies among children is an important aspect of mathematics education, and this article has a particular focus on the shortcut strategies children develop within the number domain 20-100. Here is the abstract of the article:

This study aimed at analysing traditionally taught children’s acquisition and use of shortcut strategies in the number domain 20–100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions and subtractions that maximally elicit the use of the compensation (45 + 29 = _; 45 + 30 – 1 = 75 – 1 = 74) and indirect addition strategy (71 – 68 = _; 68 + 2 = 70, 70 + 1 = 71, so the answer is 2 + 1 or 3). In the first task, children were instructed to solve all items as accurately and as fast as possible with their preferred strategy. The second task was to generate at least two different strategies for each item. Results demonstrated that children of all grades and all achievement levels hardly applied the compensation and indirect addition strategy in the first task. Children’s strategy reports in the second task revealed that younger and lower achieving children did not apply these strategies because they did not (yet) discover these strategies. By contrast, older and higher achieving children appeared to have acquired these strategies by themselves. Results are interpreted in relation to cognitive psychological and socio-cultural perspectives on children’s mathematics learning.

Shelly Sheats Harkness has written an article called Social constructivism and the Believing Game : a mathematics teacher’s practice and its implications. This article was published in Educational Studies in Mathematics on Monday. Here is the abstract of the article:

The study reported here is the third in a series of research articles (Harkness, S. S., D’Ambrosio, B., & Morrone, A. S.,in Educational Studies in Mathematics 65:235–254, 2007; Morrone, A. S., Harkness, S. S., D’Ambrosio, B., & Caulfield, R. in Educational Studies in Mathematics 56:19–38, 2004) about the teaching practices of the same university professor and the mathematics course, Problem Solving, she taught for preservice elementary teachers. The preservice teachers in Problem Solving reported that they were motivated and that Sheila made learning goals salient. For the present study, additional data were collected and analyzed within a qualitative methodology and emergent conceptual framework, not within a motivation goal theory framework as in the two previous studies. This paper explores how Sheila’s “trying to believe,” rather than a focus on “doubting” (Elbow, P., Embracing contraries, Oxford University Press, New York, 1986), played out in her practice and the implications it had for both classroom conversations about mathematics and her own mathematical thinking.

The September issue of Journal of Mathematics Teacher Education has been released. The issue contains a number of interesting articles:

How can research be used to inform and improve mathematics teaching practice? by Anne D. Cockburn

Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom, by Megan E. Staples

Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers, by Shari L. Stockero

What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems, by Sandra Crespo and Nathalie Sinclair

Mathematical preparation of elementary teachers in China: changes and issues, by Yeping Li, Dongchen Zhao, Rongjin Huang and Yunpeng Ma

Two new articles have been published online in International Journal of Mathematical Education in Science and Technology:

• Extraction of roots of quintics by division method. Author: Raghavendra G. Kulkarni
• Modelling and inverse-modelling: experiences with O.D.E. linear systems in engineering courses. Author: Victor Martinez-Luaces

Melissa Gresalfi, Taylor Martin, Victoria Hand and James Greeno have written an article called:
Constructing competence: an analysis of student participation in the activity systems of mathematics classrooms. The article was published online in Educational Studies in Mathematics a couple of days ago. Here is the abstract of the article:

This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that agency and accountability were distributed in the classrooms through interactions between the teachers and students as they worked on mathematical content. In doing so, we problematize the assumption that competencies are simply attributes of individuals that can be externally defined. Instead, we propose a concept of individual competence as an attribute of a person’s participation in an activity system such as a classroom. In this perspective, what counts as “competent” gets constructed in particular classrooms, and can therefore look very different from setting to setting. The implications of the ways that competence can be defined are discussed in terms of future research and equitable learning outcomes.

Gerd Brandell from Sweden has written an article that was published in ZDM on Wednesday. The article is entitled Progress and stagnation of gender equity: contradictory trends within mathematics research and education in Sweden, and here is the abstract:

During the last decade women in Sweden have reduced men’s lead in participation in mathematics education and in professional careers as mathematicians. However, the development is uneven and slow overall. In some areas and at the highest levels women have increased their participation only marginally. Why, one may ask, is progress so slow after almost 20 years of active work from the Women and Mathematics movement in Sweden and within a society in which gender equity is highly valued at the societal and political levels? The development is described in quantitative measures going back 20 years. Several concrete and successful initiatives from the last decade intended to “de-gender” mathematics and to involve women and men alike in mathematics are described. In contrast a gender-blind position or a view of women as problems in mathematics seems to reign within some influential bodies.

David Clarke and Li Hua Xu has written an article with a very interesting focus, and a very long title: Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation: public oral interactivity and mathematical orality. The research reported in this article appears to be connected with both the Learner’s Perspective Study (which Clarke has been involved with for a long time), and the TIMSS Video Study. The article was recently published online in ZDM. Here is the abstract:

The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study documented the voicing of mathematical ideas in public discussion and in teacher–student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher–student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons studied in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation and to student learning ourcomes are central to the development of any theory of mathematics instruction and learning.