Three new articles have been published online in ZDM lately. One of these articles is entitled The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart, and it is written by Carmel Mary Diezmann and Tom Lowrie. Here is the abstract of their article:

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

The other is written by Alan T. Graham, Maxine Pfannkuch and Michael O.J. Thomas. Their article is called Versatile thinking and the learning of statistical concepts. In the abstract you learn more about the main ideas in this article:

Statistics was for a long time a domain where calculation dominated to the detriment of statistical thinking. In recent years, the latter concept has come much more to the fore, and is now being both researched and promoted in school and tertiary courses. In this study, we consider the application of the concept of flexible or versatile thinking to statistical inference, as a key attribute of statistical thinking. Whilst this versatility comprises process/object, visuo/analytic and representational versatility, we concentrate here on the last aspect, which includes the ability to work within a representation system (or semiotic register) and to transform seamlessly between the systems for given concepts, as well as to engage in procedural and conceptual interactions with specific representations. To exemplify the theoretical ideas, we consider two examples based on the concepts of relative comparison and sampling variability as cases where representational versatility may be crucial to understanding. We outline the qualitative thinking involved in representations of relative density and sample and population distributions, including mathematical models and their precursor, diagrammatic forms.

Finally, George Gadanidis and Vince Geiger have written an article about A social perspective on technology-enhanced mathematical learning: from collaboration to performance. Here is the abstract of their article:

This paper documents both developments in the technologies used to promote learning mathematics and the influence on research of social theories of learning, through reference to the activities of the International Commission on Mathematical Instruction (ICMI), and argues that these changes provide opportunity for the reconceptualization of our understanding of mathematical learning. Firstly, changes in technology are traced from discipline-specific computer-based software through to Web 2.0-based learning tools. Secondly, the increasing influence of social theories of learning on mathematics education research is reviewed by examining the prevalence of papers and presentations, which acknowledge the role of social interaction in learning, at ICMI conferences over the past 20 years. Finally, it is argued that the confluence of these developments means that it is necessary to re-examine what it means to learn and do mathematics and proposes that it is now possible to view learning mathematics as an activity that is performed rather than passively acquired.

Kemal Altiparmak and Ece Özdogan have written an article that was recently published online in International Journal of Mathematical Education in Science and Technology. The article is entitled A study on the teaching of the concept of negative numbers. Here is the abstract of their article.

This study mainly aims to develop an effective strategy to overcome the known difficulties in teaching negative numbers. Another aim is to measure the success of this teaching strategy among a group of elementary level pupils in Idotzmir, Turkey. Learning negative concepts are supported by computer animations. The academic achievement test developed by the researchers was administered to 150 sixth-grade pupils at the beginning of and following the learning period. The teaching strategy was applied to the experiment group (n = 75) as stated above, while the traditional teaching model most frequently used in Turkey was applied to the control group (n = 75). At the end of the study, a significant difference was found in favour of the experiment group (t = 17.51, df = 148, p = 0.000 < 0.05).

To date, a number of studies have demonstrated the existence of mismatches between children’s implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children’s implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children’s eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement measurement as a potential early assessment tool of individual achievement levels in numerical processing.

Paulus Gerdes has written an article called Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education. This article was recently published online in ZDM. In this article, Gerdes provides an interesting overview of how the cultural practices of African mathematics (teacher) education has developed, and he makes a seemingly (to me) impossible connection between traditional basket weaving and exploration of technologies.

Here is the abstract of the article:

The study at teacher education institutions in Africa of mathematical ideas, from African history and cultures, may broaden the horizon of (future) mathematics teachers and increase their socio-cultural self-confidence and awareness. Exploring educationally mathematical ideas embedded in, and derived from, technologies of various African cultural practices may contribute to bridge the gap between ‘home’ and ‘school’ culture. Examples of the study and exploration of these technologies and cultural practices will be presented. The examples come from cultural practices as varied as story telling, basket making, salt production, and mat, trap and hat weaving.

The August issue (Volume 7, Number 4) of International Journal of Science and Mathematics Education has been published. This issue contains 9 articles:

• INVESTIGATING THE EFFECTIVENESS OF AN ANALOGY ACTIVITY IN IMPROVING STUDENTS’ CONCEPTUAL CHANGE FOR SOLUTION CHEMISTRY CONCEPTS, by Muammer Çalik, Alipaşa Ayas and Richard K. Coll
• INSTRUCTIONAL ACTIVITIES AND GROUP WORK IN THE US INCLUSIVE HIGH SCHOOL CO-TAUGHT SCIENCE CLASS, by Laura J. Moin, Kathleen Magiera and Naomi Zigmond
• DESIGNING AND EVALUATING RESEARCH-BASED INSTRUCTIONAL SEQUENCES FOR INTRODUCING MAGNETIC FIELDS, by Jenaro Guisasola, Jose Manuel Almudi, Mikel Ceberio and Jose Luis Zubimendi
• ENGINEERING IN CHILDREN’S FICTION – NOT A GOOD STORY? by Allyson Holbrook, Lisa Panozza and Elena Prieto
• RELATIONS BETWEEN TEACHING AND RESEARCH IN PHYSICAL GEOGRAPHY AND MATHEMATICS AT RESEARCH-INTENSIVE UNIVERSITIES, by Lene Møller Madsen and Carl Winsløw
• GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF “LIMIT” AND THE IMPACT OF THE “DIDACTIC CONTRACT”, by Iliada Elia, Athanasios Gagatsis, Areti Panaoura, Theodosis Zachariades and Fotini Zoulinaki
• IDENTIFYING SENIOR HIGH SCHOOL STUDENTS’ MISCONCEPTIONS ABOUT STATISTICAL CORRELATION, AND THEIR POSSIBLE CAUSES: AN EXPLORATORY STUDY USING CONCEPT MAPPING WITH INTERVIEWS, by Tzu-Chien Liu, Yi-Chun Lin and Chin-Chung Tsai
• PROMOTING EFFECTIVE SCIENCE TEACHER EDUCATION AND SCIENCE TEACHING: A FRAMEWORK FOR TEACHER DECISION-MAKING, by Michael P. Clough, Craig A. Berg and Joanne K. Olson
• VARIABLE RELATIONSHIPS AMONG DIFFERENT SCIENCE LEARNERS IN ELEMENTARY SCIENCE-METHODS COURSES, by Robert E. Bleicher and Joan S. Lindgren

Gwendolyn M. Lloyd has written an article that was recently published online in ZDM. The article is entitled School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States. Here is the abstract of her article:

This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbooks to which the teachers were accustomed. However, variation emerged when considering the ways in which the teachers interacted with the materials for their learning of mathematics. Whereas some teachers accepted and even embraced changes to the teaching–learning process that accompanied use of the curriculum materials, other teachers experienced discomfort and frustration at times. Nonetheless, each teacher considered that use of the curriculum materials improved her mathematical understandings in significant ways. Implications of these results for mathematics teacher education are discussed.