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By
Goos, Merrilyn; Geiger, Vince
13 Citations
This article explores theoretical issues underpinning the design and use of online learning environments in mathematics teacher education. It considers the contribution of social theories of learning to conceptualising technologymediated interaction, focusing specifically on community of practice models and the notion of digital mathematics performance. The article begins by introducing social perspectives on collaboration. Because of the diversity of theories within this broad research paradigm, the next section outlines networking strategies that have been proposed for connecting theoretical approaches. There follows a discussion of studies that illustrate the community of practice and performancebased approaches to research into online mathematics teacher education. The main purpose of the article is to show how these approaches could be connected by examining the same teaching and learning scenarios through different theoretical lenses. The final section identifies implications of this exploration for the design of online learning environments in mathematics teacher education to capitalise on the affordances of Webbased technologies.
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By
Brunner, Esther ; Reusser, Kurt
In our study, 32 German and Swiss 8th/9thgrade classes of lowersecondary school worked with their teacher on the same proving problem. The sample belongs to the SwissGerman study “Quality of Instruction, Learning Behavior and Mathematical Understanding”. Our data analyses relate to the teachers’ approaches to generating a specific form of evidence with their classes when dealing with a particular elementary numbertheory problem. We address the question of how the different strategies can be characterized as manifestations of a certain approach to proving and try to clarify in which way the observed approach can be interpreted as adaptive teaching behavior. For this purpose, we searched for possible correlations between three main strategies or types of generating a specific form of evidence (experimental, operative, formaldeductive approach) on the one hand and (a) the teachers’ beliefs and personal characteristics and (b) the students’ prior knowledge of algebra and mathematics in general on the other hand. As our analyses show, three main approaches to proving occurred but not in equal proportions: there is a predominance of the approach that entails the highest extent of formalization and abstraction. Nevertheless, an operative way of proving is widespread too. On the whole, the findings indicate that one particular approach to proving can be interpreted as a personal preference of a specific group of teachers and, at the same time, with respect to the students’ mathematical skills as a manifestation of adaptive teaching behavior.
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By
Howson, Geoffrey
11 Citations
The paper begins with a reflective, historical overview of the role and development of textbooks and research into their use. Since much of the writing is based on personal experience, there is an obvious UK bias, although experiences there were not dissimilar to what was happening in many other countries at that time. Particular attention is then paid to comparative studies: the difficulties they pose and what can be usefully gained from them. To help in this latter aspect, an attempt is made to distinguish what would appear to be key features of textbooks (or, indeed, other educational materials) which might be assessed in such a study and, in particular, the vital role of the exercises to be found in them.
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By
Forgasz, Helen J.; Mittelberg, David
6 Citations
In Englishspeaking, Western countries, mathematics has traditionally been viewed as a “male domain”, a discipline more suited to males than to females. Recent data from Australian and American students who had been administered two instruments [Leder & Forgasz, in Two new instruments to probe attitudes about gender and mathematics. ERIC, Resources in Education (RIE), ERIC document number: ED463312, 2002] tapping their beliefs about the gendering of mathematics appeared to challenge this traditional, genderstereotyped view of the discipline. The two instruments were translated into Hebrew and Arabic and administered to large samples of grade 9 students attending Jewish and Arab schools in northern Israel. The aims of this study were to determine if the views of these two culturally different groups of students differed and whether within group gender differences were apparent. The quantitative data alone could not provide explanations for any differences found. However, in conjunction with other sociological data on the differences between the two groups in Israeli society more generally, possible explanations for any differences found were explored. The findings for the Jewish Israeli students were generally consistent with prevailing Western gendered views on mathematics; the Arab Israeli students held different views that appeared to parallel cultural beliefs and the realities of life for this cultural group.
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By
Schukajlow, S. ; Kaiser, G.; Stillman, G.
9 Citations
The teaching and learning of mathematical modelling is an important research field all over the world. In this paper we present a survey of the stateoftheart on empirical studies in this field. We analyse the development of studies focusing on cognitive aspects of the promotion of modelling, i.e. the promotion of modelling abilities resp. skills, or in newer terminology, modelling competencies. Furthermore, we provide a literature search on the role of empirical research in important mathematics education journals and point out that this topic is only seldom treated in these journals. In addition, Proceedings of the conference series on the teaching and learning of mathematical modelling and applications were analysed in order to identify the role of empirical research in this important series and the kind of topics which are examined. The literature research points out the dominance of case study approaches and cognitively oriented studies compared to studies which used quantitative research methods or focused on affectrelated issues. Finally, the papers in this special issue are described and developments and future prospects are identified.
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By
Trinick, Tony; Meaney, Tamsin; Fairhall, Uenuku
5 Citations
Many mathematics teachers around the world teach in a language different from the one in which they studied or completed their teacher education. Often these teachers must learn both the registers of mathematics and of mathematics education to teach in the additional language. This paper examines the factors that help teachers to learn these registers in Māori, the Indigenous language of New Zealand. Many of these teachers are secondlanguage learners of the Māori language and attended Englishmedium schools and teachereducation programmes. After a brief discussion about the key role of language in teaching mathematics, this paper examines data from teachers at two Māoriimmersion schools and a professional development facilitator. The analysis provides initial understanding of the factors that support or hinder their learning of the mathematics registers. Finally, a research agenda is suggested for further investigation of this issue.
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By
Takahashi, Akihiko; McDougal, Thomas
60 Citations
New common standards for mathematics were adopted by most of the states in the US by 2010. Achieving these standards, however, is a challenge, since they require significant changes in how mathematics is taught. Lesson study (jugyou kenkyuu) is a form of professional development that has been credited for supporting profound changes in teaching in Japan, but its effectiveness outside of Japan has been uneven. From research on schoolbased lesson study in Japan and from the research on and experience with lesson study in schools in the US, the authors hypothesize that certain institutional structures and practices are important for maximizing its impact, but are sometimes omitted from lesson study outside of Japan. The authors introduce a new term: collaborative lesson research (CLR), defined to include those structures and practices. A threephase model of schoolbased CLR, focused on implementation of the new learning standards for mathematics, is being piloted at 15 urban schools in three major school districts in the US. This paper provides details of the pilot program and preliminary results from some of the partner schools.
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By
Chang, YuPing; Krawitz, Janina; Schukajlow, Stanislaw; Yang, KaiLin
Show all (4)
2 Citations
Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In this study, we intentionally designed two types of assumptions in two modelling tasks, namely, one task that requires nonnumerical assumptions only and another that requires both nonnumerical and numerical assumptions. Moreover, conceptual knowledge and procedural knowledge are also two factors influencing students’ modelling performance. However, current studies comparing modelling performance between Western and nonWestern students do not consider the differences in students’ knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students’ mathematical knowledge in solving modelling tasks is differentiated. The results of our study showed that the Taiwanese students had significantly higher mathematical knowledge than did the German students with regard to either conceptual knowledge or procedural knowledge. However, if students of both countries were on the same level of mathematical knowledge, the German students were found to have higher modelling performance compared to the Taiwanese students in solving the same modelling tasks, whether such tasks required nonnumerical assumptions only, or both nonnumerical and numerical assumptions. This study provides evidence that making assumptions is a strength of German students compared to Taiwanese students. Our findings imply that Western mathematics education may be more effective in improving students’ ability to solve holistic modelling problems.
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By
Herbst, P.; Chazan, D.
25 Citations
We elaborate on the notion of the instructional triangle, to address the question of how the nature of instructional activity can help justify actions in mathematics teaching. We propose a practical rationality of mathematics teaching composed of norms for the relationships between elements of the instructional system and obligations that a person in the position of the mathematics teacher needs to satisfy. We propose such constructs as articulations of a rationality that can help explain the instructional actions a teacher takes in promoting and recognizing learning, supporting work, and making decisions.
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By
Barwell, Richard
5 Citations
Research on mathematics teacher knowledge, including work on mathematical knowledge for teaching, draws heavily on Shulman’s categories of teacher knowledge. These categories have been adopted, developed and modified by mathematics education researchers. This approach has led to some valuable insights. In this paper, I draw on discursive psychology to develop a critique of this work. This critique highlights some of the unstated assumptions of much research inspired by Shulman’s work, including, in particular, a representational view of knowledge and argues that the resulting theories do not reflect the discourses of knowledge that arise in mathematics classrooms. These ideas are illustrated with discussion of two examples, with the aim of showing how discursive psychology can offer an alternative perspective.
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