New issue of Journal of Mathematics Teacher Education

A new issue of Journal of Mathematics Teacher Education has been published (See SpringerLink - Journal Issue). The issue contains five interesting articles, all of them with a strong focus on inquiry:

The challenge in developing in mathematics teachers an inquiry stance to teaching, by Peter Sullivan.

Collaborative teacher inquiry as a tool for building theory on the development and use of rich mathematical tasks, by David Slavit and Tamara Holmlund Nelson.

The effect of video-based approach on prospective teachers' ability to analyze mathematics teaching, by Othman N. Alsawaie and Iman M. Alghazo.

Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching, by Jo Towers.

Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States, by Jinfa Cai and Tao Wang.

New issue of Journal of Mathematics Teacher Education

A new issue of Journal of Mathematics Teacher Education has been published (See SpringerLink - Journal Issue). The issue contains five interesting articles, all of them with a strong focus on inquiry:

The challenge in developing in mathematics teachers an inquiry stance to teaching, by Peter Sullivan.

Collaborative teacher inquiry as a tool for building theory on the development and use of rich mathematical tasks, by David Slavit and Tamara Holmlund Nelson.

The effect of video-based approach on prospective teachers' ability to analyze mathematics teaching, by Othman N. Alsawaie and Iman M. Alghazo.

Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching, by Jo Towers.

Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States, by Jinfa Cai and Tao Wang.

JMTE, April 2010

The April issue of Journal of Mathematics Teacher Education has recently been published. This issue contains 6 interesting articles:

• Crossing the divide: reflecting on the benefits of international collaboration, by Anne D. Cockburn
• Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching, by Keith R. Leatham and Blake E. Peterson
• Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction, by Alexander Karp
• Developing teachers’ knowledge of students as learners of mathematics through structured interviews, by Oliver F. Jenkins
• The influence of video clubs on teachers’ thinking and practice, by Elizabeth A. van Es and Miriam Gamoran Sherin
• Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment, by Salvador Llinares and Julia Valls

The article by van Es and Sherin is an Open Access article, so that one should be available even for non-subscribers!

JMTE, April 2010

The April issue of Journal of Mathematics Teacher Education has recently been published. This issue contains 6 interesting articles:

• Crossing the divide: reflecting on the benefits of international collaboration, by Anne D. Cockburn
• Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching, by Keith R. Leatham and Blake E. Peterson
• Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction, by Alexander Karp
• Developing teachers’ knowledge of students as learners of mathematics through structured interviews, by Oliver F. Jenkins
• The influence of video clubs on teachers’ thinking and practice, by Elizabeth A. van Es and Miriam Gamoran Sherin
• Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment, by Salvador Llinares and Julia Valls

The article by van Es and Sherin is an Open Access article, so that one should be available even for non-subscribers!

Appropriating geometric series as a cultural tool

A couple of new articles have been published online in Educational Studies in Mathematics lately, amongst those a very interesting one by my good colleague Martin Carlsen from the University of Agder, Norway. His article is entitled: Appropriating geometric series as a cultural tool: a study of student collaborative learning. Carlsen, along with other colleagues in Agder, have been influenced by the focus on small-group problem solving that was advocated by Neil Davidson and others some years ago. The Agder group is also strongly influenced by theories related to sociocultural perspectives of teaching and learning mathematics, and this article provides a nice overview of some of these theoretical foundations. The research reported in this article can be placed within a qualitative, naturalistic paradigm, and the data were analyzed using a dialogical approach (Carlsen here makes use of a framework developed by two other colleagues: Maria-Luiza Cestari and Raymond Bjuland). So, if you are interested in any of the perspectives referred to above, this article should be highly relevant for you! Here is the abstract of the article:

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure, four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means, i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming and by establishing shared meanings for the concept and its theoretical components.

Appropriating geometric series as a cultural tool

A couple of new articles have been published online in Educational Studies in Mathematics lately, amongst those a very interesting one by my good colleague Martin Carlsen from the University of Agder, Norway. His article is entitled: Appropriating geometric series as a cultural tool: a study of student collaborative learning. Carlsen, along with other colleagues in Agder, have been influenced by the focus on small-group problem solving that was advocated by Neil Davidson and others some years ago. The Agder group is also strongly influenced by theories related to sociocultural perspectives of teaching and learning mathematics, and this article provides a nice overview of some of these theoretical foundations. The research reported in this article can be placed within a qualitative, naturalistic paradigm, and the data were analyzed using a dialogical approach (Carlsen here makes use of a framework developed by two other colleagues: Maria-Luiza Cestari and Raymond Bjuland). So, if you are interested in any of the perspectives referred to above, this article should be highly relevant for you! Here is the abstract of the article:

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure, four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means, i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming and by establishing shared meanings for the concept and its theoretical components.

Teachers attending to students' reasoning

John M. Francisco and Carolyn A. Maher have written an article about Teachers attending to students’ mathematical reasoning: lessons from an after-school research program. This article was published online in Journal of Mathematics Teacher Education last Thursday. This article is interesting in several respects, amongst others because awareness of and knowledge about students' mathematical reasoning is something teachers need, and it should be part of every mathematics teacher's professional knowledge. Theoretically, it builds upon Shulman's classic framework, but they also make interesting links to a focus on practitioner-researcher collaboration. The article reports on a study that was made of "elementary and middle school teachers who participated as interns in the 1-year NSF-funded Informal Mathematical Learning Project (IML)". Here is a copy of the abstract of their article:

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.

Teachers attending to students' reasoning

John M. Francisco and Carolyn A. Maher have written an article about Teachers attending to students’ mathematical reasoning: lessons from an after-school research program. This article was published online in Journal of Mathematics Teacher Education last Thursday. This article is interesting in several respects, amongst others because awareness of and knowledge about students' mathematical reasoning is something teachers need, and it should be part of every mathematics teacher's professional knowledge. Theoretically, it builds upon Shulman's classic framework, but they also make interesting links to a focus on practitioner-researcher collaboration. The article reports on a study that was made of "elementary and middle school teachers who participated as interns in the 1-year NSF-funded Informal Mathematical Learning Project (IML)". Here is a copy of the abstract of their article:

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.

ZDM, February, 2010

A new issue of ZDM - The International Journal on Mathematics Education has been published. This issue has a special focus on Historical aspects of the use of technology and devices in ICMEs and ICMI, and guest editors have been Maria G. Bartolini Bussi and Marcelo C. Borba. The issue contains 15 articles which covers many aspects of the theme, from historical perspectives on the use of technology to a social perspective on technology enhanced learning. Here is an overview of the contents of this issue:

• The role of resources and technology in mathematics education, by Maria G. Bartolini Bussi and Marcelo C. Borba
• Historical comments on the use of technology and devices in ICMEs and ICMI, by Gert Schubring
• Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education, by Paulus Gerdes
• Concrete models and dynamic instruments as early technology tools in classrooms at the dawn of ICMI: from Felix Klein to present applications in mathematics classrooms in different parts of the world, by Maria G. Bartolini Bussi, Daina Taimina and Masami Isoda
• Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories, by Michela Maschietto and Luc Trouche
• Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI, by Mónica E. Villarreal and Marcelo C. Borba
• Charting the microworld territory over time: design and construction in mathematics education, by Lulu Healy and Chronis Kynigos
• Graphic calculators and connectivity software to be a community of mathematics practitioners, by Ornella Robutti
• A social perspective on technology-enhanced mathematical learning: from collaboration to performance, by George Gadanidis and Vince Geiger
• Integrating technology into mathematics teaching at the university level, by Zsolt Lavicza
• Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years, by Colette Laborde and Rudolf Sträßer
• Clarkson, P., Presmeg, N. (eds) (2008): Critical Issues in Mathematics Education: Major Contributions of Alan Bishop, Springer, New York, 257 pp., ISBN 978-0-387-09672-8, by Irit Peled
• Acknowledgements to reviewers 2009, by Gabriele Kaiser
• Acknowledgments to the members of the Editorial Board, by Gabriele Kaiser
• Advances in mathematics education: new book series connected to ZDM—The International Journal on Mathematics Education, by Gabriele Kaiser and Bharath Sriraman
  

ZDM, February, 2010

A new issue of ZDM - The International Journal on Mathematics Education has been published. This issue has a special focus on Historical aspects of the use of technology and devices in ICMEs and ICMI, and guest editors have been Maria G. Bartolini Bussi and Marcelo C. Borba. The issue contains 15 articles which covers many aspects of the theme, from historical perspectives on the use of technology to a social perspective on technology enhanced learning. Here is an overview of the contents of this issue:

• The role of resources and technology in mathematics education, by Maria G. Bartolini Bussi and Marcelo C. Borba
• Historical comments on the use of technology and devices in ICMEs and ICMI, by Gert Schubring
• Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education, by Paulus Gerdes
• Concrete models and dynamic instruments as early technology tools in classrooms at the dawn of ICMI: from Felix Klein to present applications in mathematics classrooms in different parts of the world, by Maria G. Bartolini Bussi, Daina Taimina and Masami Isoda
• Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories, by Michela Maschietto and Luc Trouche
• Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI, by Mónica E. Villarreal and Marcelo C. Borba
• Charting the microworld territory over time: design and construction in mathematics education, by Lulu Healy and Chronis Kynigos
• Graphic calculators and connectivity software to be a community of mathematics practitioners, by Ornella Robutti
• A social perspective on technology-enhanced mathematical learning: from collaboration to performance, by George Gadanidis and Vince Geiger
• Integrating technology into mathematics teaching at the university level, by Zsolt Lavicza
• Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years, by Colette Laborde and Rudolf Sträßer
• Clarkson, P., Presmeg, N. (eds) (2008): Critical Issues in Mathematics Education: Major Contributions of Alan Bishop, Springer, New York, 257 pp., ISBN 978-0-387-09672-8, by Irit Peled
• Acknowledgements to reviewers 2009, by Gabriele Kaiser
• Acknowledgments to the members of the Editorial Board, by Gabriele Kaiser
• Advances in mathematics education: new book series connected to ZDM—The International Journal on Mathematics Education, by Gabriele Kaiser and Bharath Sriraman
  

Combining constructions of knowledge

Ivy Kidron and Tommy Dreyfus have written an article entitled Justification enlightenment and combining constructions of knowledge. The article was published online in Educational Studies in Mathematics last week. Here is a copy of the abstract of their article:

This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction in context.

Combining constructions of knowledge

Ivy Kidron and Tommy Dreyfus have written an article entitled Justification enlightenment and combining constructions of knowledge. The article was published online in Educational Studies in Mathematics last week. Here is a copy of the abstract of their article:

This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction in context.

Online distance mathematics education in Brazil

Marcus Vinicius Maltempi and Ana Paula dos Santos Malheiros have written an article about Online distance mathematics education in Brazil: research, practice and policy. The article was recently published online in ZDM. Here is the abstract of their article:

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

Online distance mathematics education in Brazil

Marcus Vinicius Maltempi and Ana Paula dos Santos Malheiros have written an article about Online distance mathematics education in Brazil: research, practice and policy. The article was recently published online in ZDM. Here is the abstract of their article:

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

Mathematics education and democracy

Adriana Cesar de Mattos and Marcelo Salles Batarce have written an article that was published online in ZDM on Wednesday. This article is about Mathematics education and democracy, and here is a copy of the abstract:

In this paper, we investigate the relationship between mathematics education and the notions of education for all/democracy. In order to proceed with our analysis, we present Marx’s concept of commodity and Jean Baudrillard’s concept of sign value as a theoretical reference in the discussion of how knowledge has become a universal need in today’s society and ideology. After, we engage in showing mathematics education’s historical and epistemological grip to this ideology. We claim that mathematics education appears in the time period that English becomes an international language and the notion of international seems to be a key constructor in the constitution of that ideology. Here, we draw from Derrida’s famous saying that “there is nothing beyond the text”. We conclude that a critique to modern society and education has been developed from an idealistic concept of democracy.

Mathematics education and democracy

Adriana Cesar de Mattos and Marcelo Salles Batarce have written an article that was published online in ZDM on Wednesday. This article is about Mathematics education and democracy, and here is a copy of the abstract:

In this paper, we investigate the relationship between mathematics education and the notions of education for all/democracy. In order to proceed with our analysis, we present Marx’s concept of commodity and Jean Baudrillard’s concept of sign value as a theoretical reference in the discussion of how knowledge has become a universal need in today’s society and ideology. After, we engage in showing mathematics education’s historical and epistemological grip to this ideology. We claim that mathematics education appears in the time period that English becomes an international language and the notion of international seems to be a key constructor in the constitution of that ideology. Here, we draw from Derrida’s famous saying that “there is nothing beyond the text”. We conclude that a critique to modern society and education has been developed from an idealistic concept of democracy.

Feeling number

David Wagner and Brent Davis have written an article called Feeling number: grounding number sense in a sense of quantity. The article was published online in Educational Studies in Mathematics on Monday. In this interesting article, they draw upon different theories and ideas from psychology as well as cultural and linguistic studies. Here is the abstract of their article:¨

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.

Feeling number

David Wagner and Brent Davis have written an article called Feeling number: grounding number sense in a sense of quantity. The article was published online in Educational Studies in Mathematics on Monday. In this interesting article, they draw upon different theories and ideas from psychology as well as cultural and linguistic studies. Here is the abstract of their article:¨

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.

Engaging in problem posing activities

Ilana Lavya and Atara Shrikib have written an article that was recently published online in The Journal of Mathematical Behavior. The full title of their article is: Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. Here is the abstract of their article:

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.

Engaging in problem posing activities

Ilana Lavya and Atara Shrikib have written an article that was recently published online in The Journal of Mathematical Behavior. The full title of their article is: Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. Here is the abstract of their article:

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.