The April issue of Journal of Mathematics Teacher Education has been published. The following articles are enclosed:

Imagination as a tool in mathematics teacher education

Olive Chapman

Investigating teachers’ images of mathematics

Gladys Sterenberg

Learning to observe: using video to improve preservice mathematics teachers’ ability to notice

Jon R. Star and Sharon K. Strickland

Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills

Hari P. Koirala, Marsha Davis and Peter Johnson

The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices

Jesse L. M. Wilkins

The April issue of Mathematics Teacher has arrived, and it contains the following three articles:

• Digital Images + Interactive Software = Enjoyable, Real Mathematics Modeling by Andy Ventress
• <!– Investigating the Mathematical Process with Nonlinear Asymptotes
  Michael J. Bossé, Karen A. DeUrquidi, David L. Edwards and N. R. Nandakumar –> Investigating the Mathematical Process with Nonlinear Asymptotes by Michael J. Bossé, Karen A. DeUrquidi, David L. Edwards and N.R. Nandakumar
• Using Technology to Promote Mathematical Discourse Concerning Women in Mathematics by Lyn Phy

The last article is a free preview article, and is downloadable for everyone. The author has a focus on women in mathematics, and she discusses her use of cooperative groups, Blackboard (a course managment system) and the internet as means to facilitate meaningful mathematical discourse. The venue for examining these types of mathematical discourse is a course called “Women in Mathematics”, which the author developed in her university. They studied the following women mathematicians in the course:

• Hypatia
• Maria Agnesi
• Sophie Germain
• Sonia Kovalevsky
• Emmy Noether
• Irene Hueter

All in all, this is an interesting description of an interesting university course. At a meta-level, this article also address issues of how to use history of mathematics in your teaching. At the end of the article, the writer proposes that anecdotes and activities about women mathematicians can be used in “ordinary” mathematics courses, and this indicates a certain “direct” use of history.

Linda Pilkey-Jarvis and Orrin H. Pilkey have written an article in Public Administration Review about the use of mathematical models in environmental decision making. Mathematical models are used extensively in the context of environmental issues and natural resources, and when these methods were first used, they were thought to represent a bridge to a better and more foreseeable future. There has also been much controversy in this respect, and the authors pose the question whether the optimism about the use of these models were ever realistic. In this article, they review the two main types of such models: quantitative and qualitative.

After a review of these types of models, they provide a list of ten lessons that policy makers should learn when it comes to quantitative mathematical modeling:

1. The outcome of natural processes on the earth’s surface cannot be absolutely predicted.
2. Examine the excuses for predictive model failures with great care and skepticism.
3. Did the model really work? Examine claims of past “successes” with the same level of care and skepticism that “excuses” are given.
4. Calibration of models doesn’t work either.
5. Constants in the equations may be coefficients or fudge factors.
6. Describing nature mathematically is linking a natural flexible, dynamic system with a wooden, inflexible one.
7. Models may be used as “fig leaves” for politicians, refuges for scoundrels, and ways for consultants to find the truth according to their clients’ needs.
8. The only show in town may not be a good one.
9. The mathematically challenged need not fear models and can learn how to talk with a modeler.
10. When humans interact with the natural system, accurate predictive mathematical modeling is even more impossible.

These points are directed at policy makers, but I think several of them are also relevant for students at university level (and perhaps also upper secondary). In a simplified form, I think some of these points might even be relevant for younger pupils.
In the wrapping up of the article, they clarify their main argument:

Reference:
Pilkey-Jarvis, L. & Pilkey, O.H. (2008). Useless Arithmetic: Ten Points to Ponder When Using Mathematical Models in Environmental Decision Making. Public Administration Review 68 (3) , 470–479 doi:10.1111/j.1540-6210.2008.00883_2.x

Ferdinando Arzarello, Marianna Bosch, Josep Gascón and Cristina Sabena have written an article called “The ostensive dimension through the lenses of two didactical approaches“, that has recently been published (online first) in ZDM. Here is the abstract.

This article by Gila Hanna and Ed Barbeau was published online two days ago in ZDM. The article examines a main idea from an article by Yehuda Rav in Philosophia Mathematica, that it is “proofs rather than theorems that are the bearers of mathematical knowledge”. An interesting theme of an article, with strong implications. Here is the entire abstract:

Christer Bergsten has wrote an article called “On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions“, which was recently published (online first) by ZDM. Here is the abstract of the article:

Journal of Mathematics Teacher Education (JMTE) recently published an (online first) article by A.J. Stylianides and Deborah L. Ball entitled “Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving“. The article has a particular focus on knowledge about proof:

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof (quoted from the abstract).

M. Kaldrimidou, H. Sakonidis and M. Tzekaki have written an article that has recently been published online in ZDM. The article is entitled “Comparative readings of the nature of the mathematical knowledge under construction in the classroom“, and it makes an attempt to:

(…) empirically identify the epistemological status of mathematical knowledge interactively constituted in the classroom. To this purpose, three relevant theoretical constructs are employed in order to analyze two lessons provided by two secondary school teachers. The aim of these analyses was to enable a comparative reading of the nature of the mathematical knowledge under construction. The results show that each of these three perspectives allows access to specific features of this knowledge, which do not coincide. Moreover, when considered simultaneously, the three perspectives offer a rather informed view of the status of the knowledge at hand (from the abstract).

International Electronic Journal of Mathematics Education published their first issue this year a while ago (see my post about it). Now, the articles and abstracts are finally available as well! The abstracts are available in plain HTML format, whereas the articles can be freely downloaded in PDF format. I find one of the articles particularly interesting, as it concerns the same area of research as I am involved in myself (teacher thinking and teacher knowledge). The article was written by Donna Kotsopoulos and Susan Lavigne, and it is entitled: Examining “Mathematics For Teaching” Through An Analysis Of Teachers’ Perceptions Of Student “Learning Paths”
I enclose a copy of the abstract here: