The decorative impulse

Swapna Mukhopadhyay has written an article entitled The decorative impulse: ethnomathematics and Tlingit basketry. The article was published online in ZDM earlier this week. Here is the article abstract:

Pattern is a key element in both the esthetics of design and mathematics, one definition of which is “the study of all possible patterns”. Thus, the geometric patterns that adorn cultural artifacts manifest mathematical thinking in the artisans who create them, albeit their lack of “formal” mathematics learning. In describing human constructions, Franz Boas affirmed that people, regardless of their economic conditions, always have been engaged in activities that reveal their deeply held esthetic sense. The Tlingit Indians from Sitka, Alaska, are known for their artistic endeavors. Art aficionados and museum collectors revere their baskets and other artifacts. Taking the approach of ethnomathematics, I report my analysis of the complex geometrical patterns in Tlingit basketry.

Creativity and interdisciplinarity

Johathan Plucker and Dasha Zabelina have written an article in ZDM called: Creativity and interdisciplinarity: one creativity or many creativities? The article was published online on Tuesday. Here is the abstract of the article:

Psychologists and educators frequently debate whether creativity and problem solving are domain-general—applicable to all disciplines and tasks—or domain-specific—tailored to specific disciplines and tasks. In this paper, we briefly review the major arguments for both positions, identify conceptual and empirical weaknesses of both perspectives, and describe two relatively new hybrid models that attempt to address ways in which creativity and innovation are both domain-general and domain-specific.

Exploring Japanese teachers’ conception of mathematics lesson structure

Yoshinori Shimizu has written an article called Exploring Japanese teachers’ conception of mathematics lesson structure: similarities and differences between pre-service and in-service teachers’ lesson plans. The article was published online in ZDM on Saturday, and it will be one of the articles in a forthcoming issue on An Asia Pacific focus on mathematics classrooms. Japanese Lesson Study has been known in the Western world for years. It is normally recognized that the book of Jim Stigler and James Hiebert: The teaching gap, first introduced the idea of lesson study to the West.

In this article, Shimizu analyzes the teachers’ conception of structure in mathematics lessons by focusing on their lesson plans. Here is the abstract of the article:

The research reported in this paper explores teachers’ conception of what mathematics lesson structure is like by analyzing the lesson plans they wrote. Japanese in-service and pre-service teachers (n = 246) were asked to produce a lesson plan for teaching the formula for finding the area of a parallelogram. Organizations of planned lessons were analyzed in terms of the form and content of steps/phases descriptions of them. Also, the multiplicity was analyzed of anticipated students’ responses to the problem posed in the plans. The analysis revealed both similarities and differences between lesson plans produced by the two groups of teachers. In particular, it was found that in-service teachers tended to retain the description of the problem to be posed and the anticipation of student responses in their lesson plans, while they abandoned other elements that they were trained to write when they were pre-service teachers. The results suggest that these two elements constitute the “core” of Japanese teachers’ conception of lesson structure. Origins of these core elements are discussed with a focus on the role of lesson plans as vehicles for examining and improving lessons in Lesson Study.

JRME, November 2008

Using SmartBoard

Issic K.C. Leung has written an article about using SmartBoard. The article is entitled Teaching and learning of inclusive and transitive properties among quadrilaterals by deductive reasoning with the aid of SmartBoard, and it was published online in ZDM on Friday. Here is the abstract of the article:

Learning to identify Euclidean figures is an essential content of many elementary school geometry curricula. Students often learn to distinguish among quadrilaterals, for example, by categorizing their geometric properties according to two attributes, namely the length of the edges and the size of the interior angles. But knowing how to differentiate them based on their geometric properties does not necessarily help students to develop the abstract concepts of the inclusive and transitive properties among the quadrilaterals. With the aid of dynamic geometry multimedia software in SmartBoard (SB), a kind of digital whiteboard (DWB), we enhanced the teaching and learning effectiveness by the effect of “animation-on-demand” in classrooms. This is basically a dual delivery of geometric concepts by texts, narrations and words accompanied by pictures, illustrations and animations. The preliminary results of our study on 9-year-old students’ performance in tests given after three such lessons show that those students could differentiate with reasons why a square is a rhombus (inclusion) as well as a parallelogram (transitivity).

Creating optimal mathematics learning environments

Dionne I. Cross has written an article entitled Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. The article was recently published online in International Journal of Science and Mathematics Education. Here is a copy of the article’s abstract:

The issue of mathematics underachievement among students has been an increasing international concern over the last few decades. Research suggests that academic success can be achieved by focusing on both the individual and social aspects of learning. Within the area of mathematics education, the development of metacognitive skills and the incorporation of discourse in classroom instruction has resulted in students having deeper conceptual understandings of the content and increased mathematical achievement. However, studies in this field tend to focus on the effects of these practices separately, making research that seeks to harness the potential of both quite rare. This paper reports on a study that was aimed at addressing this gap in the literature by examining the effects of writing and argumentation on achievement. Two hundred and eleven students and five teachers participated in this multimethod study that investigated the effects of three treatment conditions on mathematical achievement. These conditions were writing alone, argumentation alone, and writing and argumentation combined. Analysis of covariance revealed significant differences between the groups, and tests of the contrasts showed that students who engaged in both argumentation and writing had greater knowledge gains than students who engaged in argumentation alone or neither activity.

Mathematics assessment in East Asia

Frederick K.S. Leung from The University of Hong Kong has written an article in ZDM about assessment in East Asia. The article is entitled In the books there are golden houses: mathematics assessment in East Asia, and it was published online on Tuesday. The paper is an adaption of a plenary lecture that Leung presented at the Third East Asian Regional Conference on Mathematics Education in Shanghai, August 2005. Here is the article abstract:

In this paper, some fundamental issues on mathematics assessment and how they are related to the underlying cultural values in East Asia are discussed. Features of the East Asian culture that impact on mathematics assessment include the pragmatic nature of the culture, the social orientation of East Asian people, and the lop-sided stress on the utilitarian function of education. East Asians stress the algorithmic side of mathematics, and mathematics is viewed more as a set of techniques for calculation and problem solving. The notion of fairness in assessment is of paramount importance, and there is a great trust in examination as a fair method of differentiating between the able and the less able. The selection function of education and assessment has great impact on how mathematics is taught, and assessment constitutes an extrinsic motivation which directs student learning. Finally, the strengths and weaknesses of these East Asian values are discussed.

Semi-virtual seminar in mathematics education

Matthias Ludwig, Wolfgang Müller and Binyan Xu have written an article about A Sino-German semi-virtual seminar in mathematics education. The article was recently published in ZDM. Here is the abstract of their article:

In summer 2006 the University of Education in Weingarten, Germany, and East China Normal University, Shanghai, performed a semi-virtual seminar with mathematics students on “Mathematics and Architecture”. The goal was the joint development of teaching materials for German or Chinese school, based on different buildings such as “Nanpu Bridge”, or the “Eiffel Tower”. The purpose of the seminar was to provide a learning environment for students supported by using information and communication technology (ICT) to understand how the hidden mathematics in buildings should be related to school mathematics; to experience the multicultural potential of the international language “Mathematics”; to develop “media competence” while communicating with others and using technologies in mathematics education; and to recognize the differences in teaching mathematics between the two cultures. In this paper we will present our ideas, experiences and results from the seminar.

Working with artefacts

Michela Maschietto and Maria G. Bartolini Bussi have written an article entitled Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid. The article was published online in Educational Studies in Mathematics two days ago. Here is a copy of the abstract:

This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic mediation. It describes a teaching experiment on perspective drawing at primary school (fourth to fifth grade classes), starting from a concrete experience with a Dürer’s glass to the interpretation of a new artefact. We analyse the long term process of appropriation of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech and drawings under the teacher’s guidance.

Empirical research on mathematics teachers

Sigrid Blömeke, Gabriele Kaiser, Rainer Lehmann and William H. Schmidt have written an article that has been entitled: Introduction to the issue on Empirical research on mathematics teachers and their education. The article was published in ZDM some days ago. The article is without an abstract, and it appears to be the editorial of the forthcoming issue of ZDM. This issue will have a main focus on results from the international comparative study: “Mathematics Teaching in the 21st Century (MT21)”. So, it appears as if those of us who are interested in the preparation of teachers, teacher education, teacher knowledge, etc. are up for an interesting next issue of ZDM!