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.
journal-articles
Creativity and interdisciplinarity
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
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
- Access to Upper-Level Mathematics: The Stories of Successful African American Middle School Boys, by Robert Q. Berry III
- Mapping Mathematics Classroom Discourse and Its Implications for Models of Teaching, by Mary P. Truxaw and Thomas C. DeFranco
- The Effect of Schema-Based Instruction in Solving Mathematics Word Problems: An Emphasis on Prealgebraic Conceptualization of Multiplicative Relations, by Yan Ping Xin
- Review: A Trio of Strategies for Success: A Review of Mathematics Education at Highly Effective Schools That Serve the Poor: Strategies for Change, by Joanne Rossi Becker
Using SmartBoard
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
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
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
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
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.