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.

Thilo Höfer and Astrid Beckmann have written an article that was recently published in ZDM. The article is entitled Supporting mathematical literacy: examples from a cross-curricular project. Here is the abstract:

Mathematical literacy implies the capacity to apply mathematical knowledge to various and context-related problems in a functional, flexible and practical way. Improving mathematical literacy requires a learning environment that stimulates students cognitively as well as allowing them to collect practical experiences through connections with the real world. In order to achieve this, students should be confronted with many different facets of reality. They should be given the opportunity to participate in carrying out experiments, to be exposed to verbal argumentative discussions and to be involved in model-building activities.
This leads to the idea of integrating science into maths education. Two sequences of lessons were developed and tried out at the University of Education Schwäbisch Gmünd integrating scientific topics and methods into maths lessons at German secondary schools. The results show that the scientific activities and their connection with reality led to well-based discussions. The connection between the phenomenon and the model remained remarkably close during the entire series of lessons. At present the sequences of lessons are integrated in the European ScienceMath project, a joint project between universities and schools in Denmark, Finland, Slovenia and Germany (see www.sciencemath.ph-gmuend.de).

Gallit Botzer and Michael Yerushalmy have written an article that was recently published in International Journal of Computers for Mathematical Learning. The article is entitled Embodied Semiotic Activities and Their Role in the Construction of Mathematical Meaning of Motion Graphs. Here is the abstract:

This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of interaction: 2D freehand motion and 2D synthesized motion, designed by the composition of single variable function graphs. Our theoretical framework combines two perspectives: the embodied approach to the nature of mathematical thinking and the Vygotskian notion of semiotic mediation. The article describes in detail the actions, gestures, graph drawings, and verbal discourse of one pair of high school students and analyzes the social semiotic processes they experienced. Our analysis shows how the computerized artifacts and the students’ gestures served as means of semiotic mediation. Specifically, they supported the interpretation and the production of motion graphs; they mediated the transition between an individual’s meaning of mathematical signs and culturally accepted mathematical meaning; and they enable linking bodily actions with formal signs.

The article gives a nice introduction to the theoretical foundations concerning the connections between bodily movement and semiotics. The study being described in the article was a learning experiment, and the use of illustrative photos and figures in the article makes it easy to understand the discussion of the different motions and pointing gestures that were used.

International Journal of Science and Mathematics Education has already published the September issue. This issue contains the following 8 articles:

1. Effects of advance organiser strategy during instruction on secondary school students’ mathematics achievement in Kenya’s Nakuru district, by Bernard N. Githua and Rachel Angela Nyabwa.
2. Examining Reflective Thinking: A Study of Changes in Methods Students’ Conceptions and Understandings of Inquiry Teaching, by Jing-Ru Wang and Sheau-Wen Lin
3. Following Young Students’ Understanding of Three Phenomena in which Transformations of Matter Occur, by Lena Löfgren and Gustav Helldén
4. Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems, by Salvador Llinares and Ana Isabel Roig
5. Cognitive Incoherence of Students Regarding the Establishment of Universality of Propositions through Experimentation/Measurement, by Mikio Miyazaki
6. Differentials in Mathematics Achievement among Eighth-Grade Students in Malaysia, by Noor Azina Ismail and Halimah Awang
7. Thai Grade 10 and 11 Students’ Understanding of Stoichiometry and Related Concepts, by Chanyah Dahsah and Richard Kevin Coll
8. The Inquiry Laboratory as a Source for Development of Metacognitive Skills, by Mira Kipnis and Avi Hofstein

It might be dangerous to pick only a few articles for further comment, as all these articles raise interesting issues, but I will still make a few comments about some of them.

The article by Llinares and Roig has a focus on students’ problem solving, with a particular focus on word problems. Connections are made with research on mathematical modelling (e.g. the research of Danish colleague and editor of NOMAD, Morten Blomhøj), and the article gives a nice overview of research concerning problem solving and mathematical modelling. The study that is reported in the article is a survey/test where students were faced with five questions/problems. Llinares and Roig discuss the problem-solving strategies that were used to solve the three word problems in this test.

The article by Githua and Nyabwa provides insight into mathematics teaching in Kenya, and the article builds heavily on Ausubel’s theory of advance organisers. The objectives of the reported study were to investigate whether or not there were statistical significant differences in mathematics achievement between students who had been taught using advance organisers or not, and they also wanted to investigate whether gender affected achievement when advance organisers were used.

Another interesting article was the one by Ismail and Awang, which provides more insight into factors that influenced the achievement of Malaysian students in the TIMSS 1999 student assessment.

Three new articles have been published by International Journal of Mathematical Education in Science and Technology:

• A note on variance components model, by Anant M. Kshirsagar and R. Radhakrishnan
• An elementary proof of a converse mean-value theorem, by Ricardo Almeida
• Bionomic exploitation of a ratio-dependent predator-prey system, by Alakes Maiti, Bibek Patra and G.P. Samanta

The August issue of ZDM is available, and it has a special focus on “Didactical and Epistemological Perspectives on Mathematical Proof”. This issue contains 14 articles:

1. Introduction to the special issue on didactical and epistemological perspectives on mathematical proof, by Maria Alessandra Mariotti and Nicolas Balacheff
2. Proofs as bearers of mathematical knowledge, by Gila Hanna and Ed Barbeau
3. Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context, Man-Keung Siu
4. Theorems that admit exceptions, including a remark on Toulmin, by Hans Niels Jahnke
5. Truth versus validity in mathematical proof, by Viviane Durand-Guerrier
6. Argumentation and algebraic proof, by Bettina Pedemonte
7. Indirect proof: what is specific to this way of proving?, by Samuele Antonini and Maria Alessandra Mariotti
8. Students’ encounter with proof: the condition of transparency, by Kirsti Hemmi
9. A method for revealing structures of argumentations in classroom proving processes, by Christine Knipping
10. Strategies to foster students’ competencies in constructing multi-steps geometric proofs: teaching experiments in Taiwan and Germany, by Aiso Heinze, Ying-Hao Cheng, Stefan Ufer, Fou-Lai Lin and Kristina Reiss
11. Reasoning and proof in geometry: effects of a learning environment based on heuristic worked-out examples, by Kristina Maria Reiss, Aiso Heinze, Alexander Renkl and Christian Groß
12. When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers, by Patricio Herbst and Takeshi Miyakawa
13. DNR perspective on mathematics curriculum and instruction, Part I: focus on proving, by Guershon Harel
14. The role of the researcher’s epistemology in mathematics education: an essay on the case of proof, by Nicolas Balacheff