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.