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

The September issue of Educational Studies in Mathematics is available. The issue contains five interesting articles:

• School mathematics and its everyday other? Revisiting Lave’s ‘Cognition in Practice’, by Christian Greiffenhagen and Wes Sharrock
• Beyond ‘blaming the victim’ and ‘standing in awe of noble savages’: a response to “Revisiting Lave’s ‘cognition in practice’”, by David W. Carraher
• The problem of the particular and its relation to the general in mathematics education, by Vicenç Font and Ángel Contreras
• Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment, by Michal Tabach, Abraham Arcavi and Rina Hershkowitz
• Centenary birth anniversary of E. W. Beth (1908–1964), by Giorgio T. Bagni

Laura Jacobsen Spielman, Radford University, has written an article called Equity in mathematics education: unions and intersections of feminist and social justice literature. The article was published online in ZDM last week, and it takes up the discussion concerning gender equity. As a theoretical background, the author integrates theoretical perspectives from feminist and social justice literature. Here is the abstract of the article:

Traditional models of gender equity incorporating deficit frameworks and creating norms based on male experiences have been challenged by models emphasizing the social construction of gender and positing that women may come to know things in different ways from men. This paper draws on the latter form of feminist theory while treating gender equity in mathematics as intimately interconnected with equity issues by social class and ethnicity. I integrate feminist and social justice literature in mathematics education and argue that to secure a transformative, sustainable impact on equity, we must treat mathematics as an integral component of a larger system producing educated citizens. I argue the need for a mathematics education with tri-fold support for mathematical literacy, critical literacy, and community literacy. Respectively, emphases are on mathematics, social critique, and community relations and actions. Currently, the integration of these three literacies is extremely limited in mathematics.

Rina Zazkis and Roza Leikin have written an article that was published online in Educational Studies in Mathematics last week. The article is entitled Exemplifying definitions: a case of a square, and here is the abstract:

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

Bharath Sriraman, editor of The Montana Mathematics Enthusiast, has written an article that was published in ZDM last week. The article is entitled Mathematical paradoxes as pathways into beliefs and polymathy: an experimental inquiry. Here is the abstract of the article:

This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russell’s paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.