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.
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.
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.
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.
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.
The January issue of The Montana Mathematics Enthusiast has now been released on the journal website. The entire issue is freely available as always!
0. New Year Tidings Bharath Sriraman (USA) pp. 1-2
1. When is .999... Less Than 1? Karin Usadi Katz and Mikhail G. Katz (Israel) pp. 3-30
2. High School Teachers use of Dynamic Software to generate serendipitous mathematical relations Manuel Santos-Trigo and Hugo Espinosa-Pérez (Mexico) pp. 31-46
3. Gender and Mathematics Education in Pakistan: A situation analysis Anjum Halai (Pakistan/Tanzania) pp. 47-62
4. Early Intervention in College Mathematics Courses: A Component of the STEM RRG Program Funded by the US Department of Education Rohitha Goonatilake and Eduardo Chappa (USA) pp. 63-74
5. “What Was Really Accomplished Today?”
Mathematics Content Specialists Observe a Class for Prospective K–8 Teachers Andrew M. Tyminski, Sarah Ledford, Dennis Hembree (USA) pp. 75-92
6. Leading Learning within a PLC: Implementing New Mathematics Content Ann Heirdsfield, Janeen Lamb, Gayle Spry (Australia) pp. 93-112
7. Mathematical Reasoning in Service Courses: Why Students Need Mathematical Modeling Problems Kris H. Green & Allen Emerson (USA) pp. 113-140
8. Randomness: Developing an understanding of mathematical order. Steve Humble (UK) pp. 141-148
9. The Constructs of PhD Students about Infinity: An Application of Repertory Grids Serdar Aztekin, Ahmet Arikan (Turkey) & Bharath Sriraman (USA) pp. 149-174
The next issue of THE MONTANA MATHEMATICS ENTHUSIAST is soon to appear, and it is going to be Vol.7, No.1, January 2010. This issue is particularly exciting for me, since I am introduced as one of the new members of the editorial board! As usual, it is also going to be an interesting issue. The entire issue will be available soon on the journal website.
Here is a list of the feature articles in the forthcoming issue of TMME:
- When is .999... Less Than 1? by Karin Usadi Katz and Mikhail G. Katz (Israel)
- High School Teachers use of Dynamic Software to generate serendipitous mathematical relations, by Manuel Santos-Trigo and Hugo Espinosa-Pérez (Mexico)
- Gender and Mathematics Education in Pakistan: A situation analysis, by Anjum Halai (Pakistan/Tanzania)
- Early Intervention in College Mathematics Courses: A Component of the STEM RRG Program Funded by the US Department of Education, by Rohitha Goonatilake and Eduardo Chappa (USA)
- "What Was Really Accomplished Today?" Mathematics Content Specialists Observe a Class for Prospective K-8 Teachers, by Andrew M. Tyminski, Sarah Ledford, Dennis Hembree (USA)
- Leading Learning within a PLC: Implementing New Mathematics Content, by Ann Heirdsfield, Janeen Lamb, Gayle Spry (Australia)
- Mathematical Reasoning in Service Courses: Why Students Need Mathematical Modeling Problems, by Kris H. Green & Allen Emerson (USA)
- Randomness: Developing an understanding of mathematical order, by Steve Humble (UK)
- The Constructs of PhD Students about Infinity: An Application of Repertory Grids, by Serdar Aztekin, Ahmet Arikan (Turkey) & Bharath Sriraman (USA)
Below, you'll find Professor Bharath Sriraman's editorial, and the updated editorial board info:
TMME, vol7, no1, 2010, Editorial
The emergence of new computing technologies in the second half of the twentieth century brought about new potentials and promised the rapid transformation of the teaching and learning of mathematics. However, despite the vast investments in technology resources for schools and universities, the realities of schooling and the complexities of technology-equipped environments resulted in a much slower integration process than was predicted in the 1980s. Hence researchers, together with teachers and mathematicians, began examining and reflecting on various aspects of technology-assisted teaching and learning and on the causes of slow technology integration. Studies highlighted that as technology becomes increasingly available in schools, teachers’ beliefs and conceptions about technology use in teaching are key factors for understanding the slowness of technology integration. In this paper, I outline the shift of research focus from learning and technology environment-related issues to teachers’ beliefs and conceptions. In addition, I highlight that over the past two decades a considerable imbalance has developed in favour of school-level research against university-level research. However, several changes in universities, such as students declining mathematical preparedness and demands from other sciences and employers, necessitate closer attention to university-level research. Thus, I outline some results of my study that aimed to reflect on the paucity of research and examined the current extend of technology use, particularly Computer Algebra Systems (CAS) at universities, mathematicians’ views about the role of CAS in tertiary mathematics teaching, and the factors influencing technology integration. I argue that due to mathematicians’ extensive use of CAS in their research and teaching, documenting their teaching practices and carrying out research at this level would not only be beneficial at the university level but also contribute to our understanding of technology integration at all levels.
Uffe Thomas Jankvist has written an article called An empirical study of using history as a ‘goal’. The article was published online in Educational Studies in Mathematics two days ago. Here is the abstract of his article:
This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires, and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and reflections are analyzed using a described theoretical framework.
The January issue of Science & Education has been published. One of the articles contained in the issue is of relevance to mathematics education: A Pilot Study of a Cultural-Historical Approach to Teaching Geometry. The article is written by Stuart Rowlands from the University of Plymouth. Here is the abstract of his 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.
I want to wish all readers of the Mathematics Education Research Blog a happy new year!
2009 was a nice year in many ways, and I am certain that 2010 will be a great year too! No matter what lies ahead, I will do my best to keep you up to date on what happens in the world of mathematics education research, with a particular emphasis on journals and scientific articles. Best of wishes to all of you, and I hope that 2010 will be a productive year for each and everyone of you!