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).