Dor Abrahamson has written an article in Educational Studies in Mathematics about Embodied design: constructing means for constructing meaning:

Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains under-conceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students’ observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants’ compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.

Michael Weiss, Patricio Herbst and Chialing Chen (all from University of Michigan, Ann Arbor) have written an interesting article about Teachers’ perspectives on “authentic mathematics” and the two-column proof form. The article was published online in Educational Studies in Mathematics on Friday. Here is the abstract:

We investigate experienced high school geometry teachers’ perspectives on “authentic mathematics” and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it, provided he return to complete the argument later. Prompted by this episode, the teachers in our focus groups revealed two apparently contradictory dispositions regarding the use of the two-column proof form in the classroom. For some, the two-column form is understood to prohibit a move like that shown in the video. But for others, the form is seen as a resource enabling such a move. These contradictory responses are warranted in competing but complementary notions, grounded on the corpus of teacher responses, that teachers hold about the nature of authentic mathematical activity when proving.

Mette Andresen and Lena Lindenskov have written an article that was published in ZDM just before the weekend. The article is entitled New roles for mathematics in multi-disciplinary, upper secondary school projects, and here is the abstract:

A new concept, compulsory multi-disciplinary courses, was introduced in upper secondary school curriculum as a central part of a recent reform. This paper reports from a case study of such a triple/four-disciplinary project in mathematics, physics, chemistry and ‘general study preparation’ performed under the reform by a team of experienced teachers. The aim of the case study was to inquire how the teachers met the demands of the introduction of this new concept and, to look for signs of new relations established by the students between mathematics and other subjects, as a result of the multi-disciplinary teaching. The study revealed examples of good practice in planning and teaching. In addition, it served to illuminate interesting aspects of how students perceived the school subject mathematics and its relations to other subjects and to common sense.

Tim Rowland has written an article about The purpose, design and use of examples in the teaching of elementary mathematics. This article was recently published (online) in Educational Studies in Mathematics. The article describes an interesting study that featured video recordings of 24 lessons that were taught by prospective teachers. Here is the abstract of the article:

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

Journal of Mathematics Teacher Education has released the August Issue (Number 4, Volume 11). This issue contains five interesting articles:

1. Researchers and their roles in teacher education, by Konrad Krainer
2. Investigating changes in prospective teachers’ views of a ‘good teacher’ while engaging in computerized project-based learning, by Ilana Lavy and Atara Shriki
3. Teaching experiments and professional development, by Anderson Hassel Norton and Andrea McCloskey
4. Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving, by Andreas J. Stylianides and Deborah L. Ball
5. Expanding the instructional triangle: conceptualizing mathematics teacher development, by Kelli Nipper and Paola Sztajn

Garrod Musto has written an article that was recently published in Teaching Mathematics and its Applications. The article is entitled Showing you’re working: a project using former pupils’ experiences to engage current mathematics students, and here is the abstract:

To help students view mathematics in a more favourable light, a number of former pupils were contacted and asked to give details of how they use mathematics in their daily lives. This information was gathered through an online questionnaire or visits to the school to talk to pupils—a booklet of responses was also given to students. Attitudinally pre- and post-testing students suggested that this initiative helped address pupils’ concerns regarding the purpose of classroom mathematics. The diversity of professions also helped dispel many myths about the usefulness of mathematics. Subsequently, the project has proven to be a catalyst for a range of cross-curricular projects and events inspired by the former pupils’ case studies, all of which serve to continue to address the initial aims of the project regarding pupil perception of the subject, in the light of both workplace and everyday life.

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.