Morten Blomhøj and Tinne Hoff Kjeldsen (Roskilde University, Denmark) also wrote an article called Project organised science studies at university level: exemplarity and interdisciplinarity, that was published in ZDM. Here is the abstract of their second article:

The 2-year introductory study programme in the natural sciences (Nat-Bas) at Roskilde University is an example of a project organised, participant directed, problem oriented, and interdisciplinary science study programme. The paper gives an account of the organisational framework around the project work, and discusses in particular, the thematic organisation of project work, the notion of exemplarity, the problem orientation, the interdisciplinary nature of the problems, the assessment of the project work, and the students’ individual learning. Based on descriptions and analyses of six selected project reports from the Nat-Bas in 2005-2007, we illustrate the multiple perspectives of science and mathematics and the learning potentials found in the project work. The paper is concluded with a general discussion of the quality of the project work and its educational function in the Nat-Bas programme.

Tinne Hoff Kjeldsen and Morten Blomhøj (both Roskilde University, Denmark) have written an article that was recently published online in ZDM. The article is entitled Integrating history and philosophy in mathematics education at university level through problem-oriented project work, and here is the abstract:

Through the last three decades several hundred problem-oriented student-directed projects concerning meta-aspects of mathematics and science have been performed in the 2-year interdisciplinary introductory science programme at Roskilde University. Three selected reports from this cohort of project reports are used to investigate and present empirical evidence for learning potentials of integrating history and philosophy in mathematics education. The three projects are: (1) a history project about the use of mathematics in biology that exhibits different epistemic cultures in mathematics and biology. (2) An educational project about the difficulties of learning mathematics that connects to the philosophy of mathematics. (3) A history of mathematics project that connects to the sociology of multiple discoveries. It is analyzed and discussed in what sense students gain first hand experiences with and learn about meta-aspects of mathematics and their mathematical foundation through the problem-oriented student-directed project work.

Michael Tabach, Abraham Arcavi and rina Hershkowitz (all from the Weizmann Institute of Science, Israel) have written an article called Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment. The article was published online in Educational Studies in Mathematics on Saturday. Here is the article’s abstract:

The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students’ learning in a “computer intensive environment” designed ad hoc and implemented in two seventh grade classrooms throughout two consecutive school years. In particular, this article focuses on the description and analysis of how students initial generalizations (which relied on computerized tools that enabled different students’ to work with different strategies) shifted to recursive and explicit symbolic generalizations.

Ivy Kidron from Jerusalem College of Technology has written an article that was published online by Educational Studies in Mathematics recently. The article is entitled: Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks. Abstract:

I investigate the contributions of three theoretical frameworks to a research process and the complementary role played by each. First, I describe the essence of each theory and then follow the analysis of their specific influence on the research process. The research process is on the conceptualization of the notion of limit by means of the discrete continuous interplay. I investigate the influence of the different perspectives on the research process and realize that the different theoretical approaches intertwine. Moreover, I realize that the research study demanded the contribution of more than one theoretical approach to the research process and that the differences between the frameworks could serve as a basis for complementarities.

Alex James, Clemency Montelle and Phillipa Williams have written an article that was recently published online in International Journal of Mathematical Education in Science and Technology. The article is entitled From lessons to lectures: NCEA mathematics results and first-year mathematics performance, and here is the abstract:

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study.

Issue 4 of JRME is out, and it contains lots of interesting articles:

• RESEARCH COMMENTARY: On “Gap Gazing” in Mathematics Education: The Need for Gaps Analyses, by Sarah Theule Lubienski
• RESEARCH COMMENTARY: A “Gap-Gazing” Fetish in Mathematics Education? Problematizing Research on the Achievement Gap, by Rochelle Gutiérrez
• RESEARCH COMMENTARY: Bridging the Gaps in Perspectives on Equity in Mathematics Education, by Sarah Theule Lubienski and Rochelle Gutiérrez
• Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students, by Heather C. Hill, Deborah Loewenberg Ball and Stephen G. Schilling
• Josh’s Operational Conjectures: Abductions of a Splitting Operation and the Construction of New Fractional Schemes, by Anderson Norton
• How Mathematicians Determine if an Argument Is a Valid Proof, by Keith Weber

Pessia Tsamir, Dina Tirosh and Esther Levenson (all from Tel Aviv University, Israel) have written an article about concept formation in kindergarten children in Educational Studies in Mathematics. The article is entitled: Intuitive nonexamples: the case of triangles. Here is the abstract:

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles.

Javier Peralta from Madrid, Spain wrote an article that was recently published online in Teaching Mathematics and its Applications. The article is entitled Pythagorean approximations and continued fractions, and it relates to the Fibonacci sequence, sequences of rational numbers, etc. Here is the abstract of the article:

In this article, we will show that the Pythagorean approximations of Formula coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers converging to different algebraic irrationals. We will see how approximations to some irrational numbers, using known facts from the history of mathematics, may perhaps help to acquire a better comprehension of the real numbers and their properties at further mathematics level.

Sigrid Blömeke, Anja Felbrich, Christiane Müller, Gabriele Kaiser and Rainer Lehmann have written an article that was recently published online in ZDM. The article is entitled “Effectiveness of teacher education“, and here is the abstract:

Teacher-education research lacks a common theoretical basis, which prevents a convincing development of instruments and makes it difficult to connect studies to each other. Our paper models how to measure effective teacher education in the context of the current state of knowledge in the field. First, we conceptualize the central criterion of effective teacher education: “professional competence of future teachers”. Second, individual, institutional, and systemic factors are modeled that may influence the acquisition of this competence during teacher education. In doing this, we turn round the perspective taken by Cochran-Smith and Zeichner (Studying teacher education. The report of the AERA panel on research and teacher education. Lawrence Erlbaum, Mahwah 2005), who mainly take an educational-sociological perspective by focusing on characteristics of teacher education and looking for their effects. In contrast, we take an educational-psychological perspective by focusing on professional competence of teachers and examining influences on this. Challenges connected to an assessment of teacher-education outcomes are discussed as well.