journal-articles

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.

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:

Building intellectual infrastructure

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James Kaput wrote an article that was published online in Educational Studies in Mathematics on Friday. The article is entitled: Building intellectual infrastructure to expose and understand ever-increasing complexity. Here is the abstract of the article:

This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between “contextual” generalization of instances across context (of virtually any kind—numeric, situational, etc.) and the generalization of structured actions on symbols, (2) fundamental distinctions between the use of semiotic means to describe specific situations versus semiosis serving the process of generalization, and (3) the challenges of building generalizable research findings at such an early stage in infrastructure building.

IEJME, October issue revisited

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I have written about the October issue of International Electronic Journal of Mathematics Education in an earlier post. For some reason, the full-text version of the articles in this journal don’t appear as a new issue of the journal appears – at least for me they don’t! The articles are available now however, and you can freely download them in PDF format. This provides a nice occasion of referring to the articles again, and writing more about one of them:

In this collection, I found the article by Chamberlin, Powers and Novak particularly interesting, so I will provide you with some more details about it. The study reported in this article is related to the No Child Left Behind initiative in the U.S. In relation to this initiative, several professional development courses in the U.S. are required to assess the teachers’ content knowledge. This article reports on the evaluation of the impact of these assessments. Although the article does not provide a very thorough theoretical background, it gives a good overview of the survey that were made to investigate the teachers’ perceptions about these assessments.

One of the results of this survey was that the teachers appeared to learn more because of the assessments. They explain it like this:

We surmise that these positive effects may be due to an important aspect of theassessment process in these PD courses – the assessment and learning of mathematical topics and material was on-going and demonstrating mastery of those ideas was expected.

Many teachers appear to be reluctant to be tested, and this study apparently describes a study which had positive experiences with assessing the teachers after a course, and this might be interesting for other teacher educators or providers of in-service courses to take a closer look at.

Elementary prospective teachers’ mathematical beliefs

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Susan L. Swars, Stephanie Z. Smith, Marvin E. Smith and Lynn C. Hart have written an article called A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. The article was published online in Journal of Mathematics Teacher Education on Thursday. Here is the abstract of their article:

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.

Belief enactment

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Danish colleague Jeppe Skott has written an interesting article about research concerning teachers’ beliefs. The article is entitled Contextualising the notion of ‘belief enactment’, and it was published online in Journal of Mathematics Teacher Education on Wednesday. Skott is a prominent researcher within the field of mathematics education research in the Nordic countries, and he has a critical view on the notion of research on teachers’ beliefs, as well as the approach to this area of research. Here is the abstract of his article:

For more than 20 years, belief research has been based on the premise that teachers’ beliefs may serve as an explanatory principle for classroom practice. This is a highly individual perspective on belief–practice relationships, one that does not seem to have been influenced by the increasingly social emphases in other parts of mathematics education research. In this article, I use the notions of context and practice to develop a locally social approach to understanding the belief–practice relationships. It is a corollary of the approach taken that the high hopes for belief research with regard to its potential impact on mathematics instruction need to be modified.