Viktor Freiman and Nicole Lirette-Pitre have written an article entitled Building a virtual learning community of problem solvers: example of CASMI community that was recently published online in ZDM. Here is the article abstract:

Virtual multidisciplinary learning communities can become an important resource helping school teachers and students to foster a culture of communication, problem solving, and technology integration. Not only does the community concept virtually enlarge the mathematical learning space, it also opens several innovative ways to connect mathematics to other subjects, namely science and language arts. This article reflects on theoretical foundations of the new interactive virtual science and mathematics learning community, CASMI, as well as the first results of its implementation. The process of designing, enacting, and analyzing virtual problem solving communities, their technological, pedagogical and social aspects as a common ground for integrating mathematical, science and reading literacy into classroom practice and pre-service teacher training in an innovative and efficient way will be discussed.

Lara Alcock and Matthew Inglis have written an article entitled Doctoral students’ use of examples in evaluating and proving conjectures. This article was published in Educational Studies in Mathematics on Saturday. Here is the abstract of the article:

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and semantic reasoning strategies relative to a representation system of proof. We then use this conceptualisation as a basis for contrasting the behaviour of two successful mathematics research students whilst they evaluated and proved number theory conjectures. We observe that the students exhibited strikingly different degrees of example use, and argue that previously observed individual differences in reasoning strategies may exist at the expert level. We conclude by discussing implications for pedagogy and for future research.

Patrick Barmby, Tony Harries, Steve Higgins and Jennifer Suggate have written an article that was recently published online in Educational Studies in Mathematics. The article is entitled The array representation and primary children’s understanding and reasoning in multiplication, and here is a copy of the abstract:

We examine whether the array representation can support children’s understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a ‘representational-reasoning’ model of understanding, where understanding is seen as connections being made between mental representations of concepts, with reasoning linking together the different parts of the understanding. We examine in detail the implications of this model, drawing upon the wider literature on assessing understanding, multiple representations, self explanations and key developmental understandings. Having also established theoretically why the array representation might support children’s understanding and reasoning, we describe the results of a study which looked at children using the array for multiplication calculations. Children worked in pairs on laptop computers, using Flash Macromedia programs with the array representation to carry out multiplication calculations. In using this approach, we were able to record all the actions carried out by children on the computer, using a recording program called Camtasia. The analysis of the obtained audiovisual data identified ways in which the array representation helped children, and also problems that children had with using the array. Based on these results, implications for using the array in the classroom are considered.

Wolff-Michael Roth and Jennifer S. Thom have written an article entitled Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization. This article was recently published in Educational Studies in Mathematics. Here is the abstract of the article:

Mathematical concepts and conceptions have been theorized as abstractions from—and therefore transcending—bodily and embodied experience. In this contribution, we re-theorize mathematical conceptions by building on recent philosophical work in dialectical phenomenology. Accordingly, a conception exists only in, through, and as of the experiences that the individual realizes it. To exemplify our reconceptualization of mathematical conceptions, we draw on an episode from a study in a second-grade classroom where the students learned about three-dimensional geometrical objects.

Berinderjeet Kaur from the National Institute of Education in Singapore has written an article with the interesting title: Teaching and learning of mathematics: what really matters to teachers and students? This article was recently published in ZDM. In some previous articles, Kaur has reported on studies concerning the expectations that Singapore students have of their “best” mathematics teacher. In this article, Kaur draws upon data from The learner’s perspective study (LPS), and in particular data from the interviews of students and teachers in Singapore, and the main research questions are related to what students and teachers attach importance to in a mathematics lesson. The Singapore study used a similar research design as that of the LPS. This paper reports on the analysis of data from a part of the study that involved interviews of from the classrooms of three competent teachers.

Here is the abstract:

The learner’s perspective study, motivated by a strong belief that the characterization of the practices of mathematics classrooms must attend to learner practice with at least the same priority as that accorded to teacher practice, is a comprehensive study that adopts a complementary accounts methodology to negotiate meanings in classrooms. In Singapore, three mathematics teachers recognized for their locally defined ‘teaching competence’ participated in the study. The comprehensive sets of data from the three classrooms have been used to explore several premises related to the teaching and learning of mathematics. In this paper the student interview data and the teacher interview data were examined to ascertain what do students attach importance to and what do teachers attach importance to in a mathematics lesson? The findings of the student interview data showed that they attached importance to several sub-aspects of the three main aspects, i.e., exposition, seatwork and review and feedback of their teachers’ pedagogical practices. The findings of the teacher interview data showed that they attached importance to student’s self assessment, teacher’s demonstration of procedures, review of prior knowledge and close monitoring of their student’s progress in learning and detailed feedback of their work. It was also found that teachers and students did attach importance to some common lesson events.

Henrik Winkelmann, Marja van den Heuvel-Panhuizen and Alexander Robitzsch have written an article called Gender differences in the mathematics achievements of German primary school students: results from a German large-scale study. The article was recently published in ZDM. Here is the article abstract:

In Germany, national standards for mathematics for the end of primary school were established in 2004. In the present study, data were collected to evaluate these standards, and were used to compare the mathematical skills of girls and boys. Many studies have shown that gender differences are strongest at the highest levels of education. The findings from primary school are less consistent. Thus, in our study we analyzed achievement differences in a sample of approximately 10,000 third and fourth graders, representative of the German elementary school population. Gender-specific competencies were compared in the different content domains, both for the general mathematical competence, and for the cognitive levels of the tasks. Overall, boys outperformed girls, but substantial variation was found between the content domains and general mathematical achievement. Differences were higher in grade three than in grade four. The proportion of boys in the classroom did not appear to affect the individual level of performance. Analysis of the items on which boys or girls clearly outperformed each other reproduced a pattern of specific item characteristics predicting gender bias consistent with those reported in previous studies in other countries.

Katrina Piatek-Jimenez has written an article called: Images of mathematicians: a new perspective on the shortage of women in mathematical careers, which was recently published in ZDM. Here is the abstract:

Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore, each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to pursue mathematical careers.

Robert K. Sembiring, Sutarto Hadi and Maarten Dolk have written an article about an interesting experimental study related to the current reform movement in Indonesia, where the theory of Realistic Mathematics Education (RME) is being adopted. The article is entitled Reforming mathematics learning in Indonesian classrooms through RME, and it was published online in ZDM on Sunday, August 24. Here is the abstract of the article:

This paper reports an experimental study on the development of exemplary curriculum materials for the teaching of fractions in Indonesian primary schools. The study’s context is the current reform movement adopting realistic mathematics education (RME) theory, known as Pendidikan Matematika Realistik Indonesia (PMRI), and it looked at the role of design research in supporting the dissemination of PMRI. The study was carried out in two cycles of teaching experiments in two primary schools. The findings of the design research signified the importance of collaboration between mathematics educators and teachers in developing RME curriculum materials. The availability of RME curriculum materials is an important component in the success of the PMRI movement, particularly in supporting students and teachers in activity-based mathematics learning. Most of the students and teachers in the two schools positively appraised teaching and learning with the developed materials. Since the teachers were actively involved in developing the materials, they felt a sense of ownership and recognised that their students’ classroom experiences of the materials helped them avoid standard difficulties. That appears to be a particular benefit of the bottom-up approach characteristic of the PMRI movement.

Sigrid Blömeke, Lynn Paine, Richard T. Houang, Feng-Jui Hsieh, William H. Schmidt, M. Teresa Tatto, Kiril Bankov, Tenoch Cedilll, Leland Cogan, Shin Il Han, Marcella Santillan and John Schwille have written an article entitled Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education. The article was published online in ZDM last week. The paper presents data from four countries in relation to the study called: “Mathematics Teaching in the 21st Century (MT21)” (see webpage!). The entire MT21 report is available for free download at the project webpage. Here is a copy of the abstract:

The study “Mathematics Teaching in the 21st Century (MT21)” focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.

Demetra Pitta-Pantazi and Constantinos Christou have written an article called Cognitive styles, dynamic geometry and measurement performance. The article was recently published online in Educational Studies in Mathematics. Here is the abstract of the article:

This paper reports the outcomes of an empirical study undertaken to investigate the effect of students’ cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students’ learning. A total of 49 6th grade students were tested using the VICS and the extended CSA-WA tests (Peterson, Verbal imagery cognitive styles and extended cognitive style analysis-wholistic analytic test—Administration guide. New Zealand: Peterson, 2005) for cognitive styles. The same students were also administered a pre-test and a post-test involving 20 measurement tasks. All students were taught a unit in measurement (area of triangles and parallelograms) with the use of dynamic geometry, after a pre-test. As expected, the dynamic geometry software seems to accommodate different cognitive styles and enhances students’ learning. However, contrary to expectations, verbalisers and wholist/verbalisers gained more in their measurement achievement in the environment of dynamic geometry than students who had a tendency towards other cognitive styles. The results are discussed in terms of the nature of the measurement tasks administered to the students.