A couple of days ago, I shared with you news about the forthcoming issue of The Montana Mathematics Enthusiast. The main editor of this journal, my good friend Professor Bharath Sriraman, has been kind enough to allow me to share the editorial of this next issue with you all here on my blog. In this editorial, he brings up an interesting, important, and thought provoking discussion about scientific publishing. Enjoy reading it!
Preservice teachers’ conceptions of multidigit wholenumbers
Eva Thanheiser (Portland State University) has written an interesting article that was published online in Educational Studies in Mathematics this week. The article is entitled Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework, and in the article, Thanheiser digs into the domain of (preservice) teachers’ content knowledge of mathematics. Here is the abstract of Thanheiser’s article:
This study was designed to investigate preservice elementary school teachers’ (PSTs’) responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs’ conceptions, two correct and two incorrect. Previous findings are replicated for PSTs toward the end of their college careers, and two conceptions are further analyzed to yield three categories of incorrect views of regrouped digits: (a) consistently as 1 value (all as 1 or all as 10), (b) consistently within but not across contexts (i.e., all as 10 in addition but all as 1 in subtraction), and (c) inconsistently (depending on the task).
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.
JMTE, April 2010
- 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
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
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
- 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
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
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
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.