The February issue of Science & Education has been published. None of the articles in this issue are directly related to mathematics education, and the theme of the issue is “Politics and philosophy of science”. Still, the issue might be worth checking out, especially if you are interested in the above mentioned theme.
journal-articles
In search of an exemplary mathematics lesson in Hong Kong
Ida Ah Chee Mok has written an article that was published in ZDM on Thursday. The article is entitled In search of an exemplary mathematics lesson in Hong Kong: an algebra lesson on factorization of polynomials. The theoretical perspectives for this article are mathematical enculturation and the theory of learning through variation (variation theory). The study which is described in the article is part of the Learner’s Perspective Study (LPS). This study
(…) has engaged researchers in the investigation of mathematics classrooms of teachers in Australia, China, the Czech Republic, Germany, Israel, Japan, Korea, the Philippines, Singapore, South Africa, Sweden and the USA.
Here is the article abstract:
The author here describes an exemplary grade-8 algebra lesson in Hong Kong, taken from the data of the learners’ perspective study. The analysis presents a juxtaposition of the researcher’s analysis of the lesson with the teacher and students’ perspectives of the lesson. The researcher’s perspective applies the theory of variation for which the main concern of learning is the discernment of the key aspects of the object of learning and that the description of variations delineates the potential of the learning space. Some persistent features were illustrated, namely, the teacher talk was a major input in teaching; the technique of variation was used in the design of the mathematical problems and the dimensions of variation created in the class interaction provided a potential learning environment; the teacher taking seriously the student factor into account in his philosophy and practice. From the standpoint of enculturation, the teacher’s influence as an enculturator is intentional, significant and influential.
Problem-solving and cryptography
Tobin White has written an interesting article about cryptography and problem solving. The article is entitled Encrypted objects and decryption processes: problem-solving with functions in a learning environment based on cryptography, and the article was published online in Educational Studies in Mathematics on Thursday. Those of you who don’t have a subscription to this journal will be interested to know that the article is an Open Access article, and it is therefore available to all! (Direct link to pdf download) Here is the abstract of the article:
This paper introduces an applied problem-solving task, set in the context of cryptography and embedded in a network of computer-based tools. This designed learning environment engaged students in a series of collaborative problem-solving activities intended to introduce the topic of functions through a set of linked representations. In a classroom-based study, students were asked to imagine themselves as cryptanalysts, and to collaborate with the other members of their small group on a series of increasingly difficult problem-solving tasks over several sessions. These tasks involved decrypting text messages that had been encrypted using polynomial functions as substitution ciphers. Drawing on the distinction between viewing functions as processes and as objects, the paper presents a detailed analysis of two groups’ developing fluency with regard to these tasks, and of the aspects of the function concept underlying their problem-solving approaches. Results of this study indicated that different levels of expertise with regard to the task environment reflected and required different aspects of functions, and thus represented distinct opportunities to engage those different aspects of the function concept.
Using history in mathematics education
Uffe Thomas Jankvist has written an article about using history in mathematics education. The article was published in Educational Studies in Mathematics last week, and it is entitled: A categorization of the “whys” and “hows” of using history in mathematics education. Here is the abstract of his article:
This is a theoretical article proposing a way of organizing and structuring the discussion of why and how to use the history of mathematics in the teaching and learning of mathematics, as well as the interrelations between the arguments for using history and the approaches to doing so. The way of going about this is to propose two sets of categories in which to place the arguments for using history (the “whys”) and the different approaches to doing this (the “hows”). The arguments for using history are divided into two categories; history as a tool and history as a goal. The ways of using history are placed into three categories of approaches: the illumination, the modules, and the history-based approaches. This categorization, along with a discussion of the motivation for using history being one concerned with either the inner issues (in-issues) or the metaperspective issues (meta-issues) of mathematics, provides a means of ordering the discussion of “whys” and “hows.”
Pursuing excellence
Rongjin Huang and Yeping Li have written an article called Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China: a case study. The article was published online in ZDM on Friday. To me, this article is interesting for a few reasons:
- It has a focus on teaching mathematics
- It has a focus on how to develop exemplary lessons
- It has a focus on learning from “master teachers”
- It provides a nice insight into chinese mathematics teaching
Several aspects in this study remind me of the Lesson Study approach and theories related to Mathematical Knowledge for Teaching (MKT), both of which are among my main research interests. Here is an abstract of their article:
In this article, we aim to examine the features of mathematics classroom instruction excellence valued in China. The popular approach to pursuing mathematics classroom instruction excellence through exemplary lesson development is also investigated to demonstrate the nature of teaching culture that has been advocated and nurtured in China. Features of an exemplary lesson are analyzed in detail, and the practicing teacher’s experience through participating in the development of the exemplary lesson is examined as well. Finally, the implications of developing exemplary lessons for pursuing excellence in mathematics classroom instruction as a culturally valued approach in China are also discussed.
Re-mythologizing mathematics
David Wagner and Beth Herbel-Eisenmann have written an article entitled Re-mythologizing mathematics through attention to classroom positioning. the article was published online in Educational Studies in Mathematics on Tuesday. Here is their article abstract:
With our conceptualization of Harré and van Langenhove’s (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to change the way mathematics is done and the way it is taught.
Students’ use of technological tools
Ioannis Papadopoulosa and Vassilios Dagdilelis have written an article that was published online in the Journal of Mathematical Behavior yesterday. The article is entitled Students’ use of technological tools for verification purposes in geometry problem solving. Here is a copy of the article abstract:
Despite its importance in mathematical problem solving, verification receives rather little attention by the students in classrooms, especially at the primary school level. Under the hypotheses that (a) non-standard tasks create a feeling of uncertainty that stimulates the students to proceed to verification processes and (b) computational environments – by providing more available tools compared to the traditional environment – might offer opportunities for more frequent usage of verification techniques, we posed to 5th and 6th graders non-routine problems dealing with area of plane irregular figures. The data collected gave us evidence that computational environments allow the development of verification processes in a wider variety compared to the traditional paper-and-pencil environment and at the same time we had the chance to propose a preliminary categorization of the students’ verification processes under certain conditions.
JRME, January 2009
Journal for Research in Mathematics Education (JRME) has released the January issue of 2009 (vol. 40, issue 1). It contains the following list of articles:
- Editorial: It Takes a Community…, by M. Kathleen Heid
- RESEARCH COMMENTARY: The Effects of Spacing and Mixing Practice Problems, by Doug Rohrer
- The Slippery Road From Actions on Objects to Functions and Variables, by Tamar Paz and Uri Leron
- An Interpretive Scheme for Analyzing the Identities That Students Develop in Mathematics Classrooms, by Paul Cobb, Melissa Gresalfi and Lynn Liao Hodge
- BOOK 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
Unfortunately, only the editorial is freely available for all to read. You might also be interested in looking up the issue as listed in the ProQuest database.
Students’ perceptions
Mashooque Ali Samo has written an article called Students’ Perceptions Abouth the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Govenrment Girls’ Secondary School, Karachi. This article pays attention to misconceptions that arise in Algebra, and it has been published in International Journal for Mathematics Teaching and Learning. Here is the article abstract:
Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students‟ difficulties in understanding letters in Algebra, the overall image that emerges from the literature is that students have misconceptions of the use of letters and signs in Algebra. My empirical research done through this study has revealed that the students have many misconceptions in the use of symbols in Algebra which have bearings on their learning of Algebra. It appears that the problems encountered by the students appeared to have connection with their lack of conceptual knowledge and might have been result of teaching they experience in learning Algebra at the secondary schooling level. Some of the findings also suggest that teachers appeared to have difficulties with their own content knowledge. Here one can also see that textbooks are also not presenting content in such an elaborate way that these could have provided sufficient room for students to develop their relational knowledge and conceptual understanding of Algebra. Moreover, this study investigates students‟ difficulty in translating word problems in algebraic and symbolic form. They usually follow phrase- to- phrase strategy in translating word problem from English to Urdu. This process of translating the word problem from English to their own language appears to have hindered in the correct use of symbols in Algebra. The findings have some important implications for the teaching of Algebra that might help to develop symbol sense in both students and teachers. By the help of symbol sense, they can use symbols properly; understand the nature of symbols in different situations, like, in functions, in variables and in relationships between algebraic representations. This study will contribute to future research on similar topics.
Preservice teachers’ subject matter knowledge of mathematics
Ramakrishnan Menon has written an article entitled Preservice teachers’ subject matter knowledge of mathematics. The article has been published in International Journal for Mathematics Teaching and Learning. Here is the abstract of the article:
Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their solution, b) classify them as easy, of medium difficulty, or difficult, explaining the rationale for their classification, and c) explain how they would teach/help children to solve them. Responses were classified under three categories of subject matter knowledge, namely traditional, pedagogical, and reflective. Implications of these categories to effective math teaching are then discussed.
Reidar Mosvold 