B. Pedemonte has written an article that has recently been published (online first) in ZDM. The article has a focus on a “core activity” in mathematics, and it is called: “Argumentation and algebraic proof“. Here is the abstract of the article:

This paper concerns a study analysing cognitive continuities and distances between argumentation supporting a conjecture and its algebraic proof, when solving open problems involving properties of numbers. The aim of this paper is to show that, unlike the geometrical case, the structural distance between argumentation and proof (from an abductive argumentation to a deductive proof) is not one of the possible difficulties met by students in solving such problems. On the contrary, since algebraic proof is characterized by a strong deductive structure, abductive steps in the argumentation activity can be useful in linking the meaning of the letters used in the algebraic proof with numbers used in the argumentation. The analysis of continuities and distances between argumentation and proof is based on the use of Toulmin’s model combined with ck¢ model.

Algebra is used in several different domains in mathematics, but this article has a focus on the algebra that is taught and learned in secondary school (Grade 12 and 13). After having elaborated and presented a theoretical framework for her analysis of proofs, Pedemonte presents some data that has been collected from prospective primary school teachers. These students were attending a course at the University, and their solutions to two open problems were analyzed according to the theoretical framework (the solutions of 7 students’ solutions to each of the two problems were analyzed).

The May issue of Journal for Research in Mathematics Education (JRME) has already arrived, and it contains the following articles:

ZPC and ZPD: Zones of Teaching and Learning
Anderson Norton and Beatriz S. D’Ambrosio

The Impact of Middle-Grades Mathematics Curricula and the Classroom Learning Environment on Student Achievement
James E. Tarr, Robert E. Reys, Barbara J. Reys, Óscar Chávez, Jeffrey Shih and Steven J. Osterlind

Learning to Use Fractions: Examining Middle School Students’ Emerging Fraction Literacy
Debra I. Johanning

The Linear Imperative: An Inventory and Conceptual Analysis of Students’ Overuse of Linearity
Wim Van Dooren, Dirk De Bock, Dirk Janssens and Lieven Verschaffel

Teaching With Games of Chance: A Review of The Mathematics of Games and Gambling
Laurie Rubel

The first issue of NOMAD this year has finally arrived, at least the web page has finally been updated to indicate that. Unfortunately, the articles are not available online, but you can read the abstracts (and the editorial in its entirety). The issue contains the following articles:

• The International Commission on Mathematical Instruction: a centenary of history and a future to construct by M. Blomhøj and P. Valero (editorial)
• Word problems in upper secondary algebra in Sweden over the years 1960–2000 by T. Jakobsson-Åhl
• Växelverkan mellan intuitiva idéer och formella resonemang – en fallstudie av universitetsstudenters arbete med en analysuppgift by K. Pettersson
• Classroom settings, self-regulated learning skills and grades in mathematics by J. Samuelsson
• The fifth year of the Nordic Graduate School by B. Grevholm (available in its entirety)

Stephen J. Hegedus and William R. Penuel wrote an article that was recently published online in Educational Studies in Mathematics. The article is called “Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures“, and here is the abstract of the article:

Wireless networks are fast becoming ubiquitous in all aspects of
society and the world economy. We describe a method for studying the
impacts of combining such technology with dynamic,
representationally-rich mathematics software, particularly on
participation, expression and projection of identity from a local to a
public, shared workspace. We describe the types of mathematical
activities that can utilize such unique combinations of technologies.
We outline specific discourse analytic methods for measuring
participation and methodologies for incorporating measures of identity
and participation into impact studies.

International Journal of Computers for Mathematical Learning has a column called “Computational Diversions”. Michael Eisenberg recently wrote an article/entry in this column called “Rounded Fractals“. The article is both practical and interesting, and it provides several examples concerning the generation of fractal designs. In the beginning of the article, he mentions turtle geometry (Logo), but the examples are made by making use of the method of iterated function systems. The article also contains a challenge, so anyone interested in fractals might want to take a look.

M. Pariès, A. Robert and J. Rogalski recently published an article called “Analyses de séances en classe et stabilité des pratiques d’enseignants de mathématiques expérimentés du second degré” in Educational Studies in Mathematics. The article is in French, but here is the abstract in English:

In this paper we tackle the issue of an eventual stability of teachers’
activity in the classroom. First we explain what kind of stability is
searched and how we look for the chosen characteristics: we analyse the
mathematical activity the teacher organises for students during
classroom sessions and the way he manages the relationship between
students and mathematical tasks. We analyse three one-hour sessions for
different groups of 11 year old students on the same content and with
the same teacher, and two other sessions for 14 year old and 15 year
old students, on analogous contents, with the same teacher (another
one). Actually it appears in these two examples that the main
stabilities are tied with the precise management of the tasks, at a
scale of some minutes, and with some subtle characteristic touches of
the teacher’s discourse. We present then a discussion and suggest some
inferences of these results.

David L. Farnsworth has written an article called Student presentations in the classroom. The article was published in International Journal of Mathematical Education in Science and Technology today. Here is the abstract:

For many years, the author has been involving his students in classroom
teaching of their own classes. The day-to-day practice is described,
and the advantages and disadvantages for both the instructor and the
students are discussed. Comparisons with the Moore Method of teaching
are made.

A new article has appeared in International Journal of Mathematical Education in Science and Technology. The article is written by E. Kirillova and K. Spindler, and it is entitled: Analyticity without differentiability. Her is the abstract of the article:

In this article we derive all salient properties of analytic functions,
including the analytic version of the inverse function theorem, using
only the most elementary convergence properties of series. Not even the
notion of differentiability is required to do so. Instead, analytical
arguments are replaced by combinatorial arguments exhibiting properties
of formal power series. Along the way, we show how formal power series
can be used to solve combinatorial problems and also derive some
results in calculus with a minimum of analytical machinery.