Author: Reidar Mosvold

A comparison of curricular effect

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The new issue of Instructional Science (January, 2009) has an article related to mathematics education: A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students, by Bryan Moseley and Mary E. (“Betsy”) Brenner. Here is their article abstract:

This research examines students’ ability to integrate algebraic variables with arithmetic operations and symbols as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic to algebraic reasoning. It presents data from pre and post instruction clinical interviews administered to a sample of middle school students experiencing their first exposure to formal pre-algebra. Roughly half of the sample (n = 15) was taught with a standards-based curriculum emphasizing representation skills, while a comparable group (n = 12) of students received traditional instruction. Analysis of the pre and post interviews indicated that participants receiving a standards-based curriculum demonstrated more frequent and sophisticated usage of variables when writing equations to model word problems of varying complexity. This advantage was attenuated on problems that provided more representational support in which a diagram with a variable was presented with the request that an expression be written to represent the perimeter and area. Differences in strategies used by the two groups suggest that the traditional curriculum encouraged students to continue using arithmetic conventions, such as focusing on finding specific values, when asked to model relations with algebraic notation.

A cultural-historical approach to teaching geometry

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Stuart Rowlands has recently written an article called A Pilot Study of a Cultural-Historical Approach to Teaching Geometry, which was published in Science & Education on Wednesday. Here is the abstract of the article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.

The development of beliefs and practice

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Despina Potari  and Barbara Georgiadou–Kabouridis have written an article called A primary teacher’s mathematics teaching: the development of beliefs and practice in different “supportive” contexts. The article was recently published online in Journal of Mathematics Teacher Education. Here is the article abstract:

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher’s beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher’s reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher’s experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.

Using history of mathematics

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Charalambos Y. Charalambous, Areti Panaoura and George Philippou have written an article called Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of their article:

Scholars and teacher educators alike agree that teachers’ beliefs and attitudes toward mathematics are key informants of teachers’ instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers’ (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs’ epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs’ beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs’ beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs’ beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.

Reasons for change in enrolments

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Derek Holton, Eric Muller, Juha Oikkonen, Oscar Adolfo Sanches Valenzuela, and Ren Zizhao have written an article called Some reasons for change in undergraduate mathematics enrolments. This article article was published online in International Journal of Mathematical Education in Science and Technology yesterday. Here is the abstract of their article:

Here, we look at the enrolments of students in undergraduate mathematics courses in a number of countries. The data show various increases and decreases and we suggest some common reasons for the fluctuations. These include students’ goals of a secure and well-paid job, government actions and the state of the economy in the country concerned. We consider several ways in which departments have successfully approached downturns in numbers by their interactions with students by introducing new teaching approaches, using technology and establishing mathematics centres.

The professional education of mathematics teachers

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Springer has recently published a new book on mathematics education. The book is entitled The Professional Education and Development of Teachers of Mathematics, and it is edited by Ruhama Even and Deborah Loewenberg Ball. Here are some of the highlights of the book, as presented by the publisher:

  • Focuses specifically on mathematics teacher education development
  • Provides practical strategies for learning
  • Addresses the balance between pedagogy and mathematical content
  • Edited by the world’s leading scholars on mathematics teacher education, teacher knowledge, and teacher education

Educational Researcher, December 2008

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The December issue of Educational Researcher has been published, and it is a special issue on Foundations for Success: The Final Report of the National Mathematics Advisory Panel. The issue contains 13 interesting articles with a focus on the Math Panel Report:

TIMSS 2007

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The results from TIMSS 2007 were released today, and the media appears to be full of reports about how the students in each of our countries are doing. Overall, countries from Asia are on top as usual. If you want to learn more, there is a webcast to watch (.rm and .mov formats), international reports to read as well as a Technical Report and a very interesting set of Encyclopedias, which offer a nice overview of the mathematics (and science) teaching in each of the participating countries. That means: lots of interesting reading to do!

Terence Tao in Norway

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Terence Tao is by many said to be the best mathematician in the world today, and for two days this week (today and tomorrow) he is visiting Trondheim, Norway. Unfortunately, I don’t have the opportunity to travel to Trondheim and listen to him, but it sure would have been interesting.

Tao – born in 1975 (like myself) – is professor of mathematics at UCLA, winner of the Fields medal and lots of other prizes. He is working within many different fields of mathematics, and he frequently reports his work on his web page and his blog. Below is a small video presenting Tao: