F.D. Rivera has written an article called Visual templates in pattern generalization activity. The article was published online in Educational Studies in Mathematics last Thursday. The study, which is described in the article, was carried out in an eighth-grade Algebra 1 class in California. Four and a half months after a teaching experiment on pattern generalization, 11 students were interviewed (clinical interviews). Clinical interviews were also made with these students directly before and after the teaching experiment. The article reports on results from the analyses of these clinical interviews.

Here is the abstract of the article:

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four and a half months after the teaching experiment using three tasks (one ambiguous, two well defined). Drawing on the clinical interviews conducted with 11 seventh- and eighth-grade students, I discuss how their visual templates have spawned at least six types of algebraic generalizations. A visual template model is also presented that illustrates the distributed and a dynamically embedded nature of pattern generalization involving the following factors: pattern goodness effect; knowledge/action effects; and the triad of stage-driven grouping, structural unit, and analogy.

Roger G. Brown from the University of Leeds (UK) has written an article entitled Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? This article was published online in Educational Studies in Mathematics earlier this week. Here is the abstract of his article:

The paper reports on the introduction of the graphics calculator into three centralised examination systems, which were located in Denmark, Victoria (Australia) and the International Baccalaureate. The introduction of the graphics calculator required those responsible for writing examination questions to consider how to assess mathematical skills within this new environment. This paper illustrates the types of mathematics skills that have been assessed within the graphics-calculator-assumed environment. The analysis of the examination questions indicated that only two out of the six mathematics examinations considered demonstrated any significant change in the types of skills assessed in conjunction with the introduction of the graphics calculator. The results suggest that it is possible to reduce the use of questions assessing routine procedures (mechanical skills) with a graphics calculator, but it is also evident that there have not been major changes in the way that examination questions are written nor the mathematics skills which the questions are intended to assess.

Richard Lissaman, Sue de Pomerai and Sharon Tripconey have written an article that was recently published online in Teaching Mathematics and its Applications. The article is entitled Using live, online tutoring to inspire post 16 students to engage with higher level mathematics, and here is a copy of the article’s abstract:

In recent years, there has been a decline in the number of students aged 16–18 studying and being able to access higher level mathematics in schools in the UK. The Further Mathematics Network (FMN) was set up to enable access to such mathematics to all students and to promote and encourage students to study at this level. The FMN has pioneered the use of Elluminate, a well established web-based package, for live mathematics tutoring. Small groups of students meet online with an experienced tutor to learn new aspects of mathematics and to look at ways to solve complex problems. There are also extensive online resources to support the students’ learning. The findings are discussed in the following article.

The Nordic Journal of Research in Mathematics Education (NOMAD) has recently released the October issue. This issue contains three research articles:

• Leif Bjørn Skorpen: Nokre spesielle trekk ved arbeidet med matematikkfaget i begynnaropplæringa (in Norwegian)
• Frode Olav Haara and Kari Smith: Practical activities in mathematics teaching – mathematics teachers’ knowledge based reasons
• Diana Stentoft and Paola Valero:  Identities-in-action. Exploring the fragility of discourse and identity in learning mathematics

Pnina S. Klein, Esther Adi-Japha and Simcha Hakak-Benizri have written an article called Mathematical thinking of kindergarten boys and girls: similar achievement, different contributing processes. This article was recently published online in Educational Studies in Mathematics. Here is the abstract of their article:

The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher–child mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children’s mathematics, spatial, and verbal skills and the teachers’ mathematical communication were assessed. No gender differences were found between the mathematical achievements of the boys and girls, or between their verbal and spatial skills. However, mathematics performance was related to boys’ spatial reasoning and to girls’ verbal skills, suggesting that they use different processes for solving mathematical problems. Furthermore, the boys’ levels of spatial and verbal skills were not found to be related, whereas they were significantly related for girls. The mathematical communication level provided in teacher–child interactions was found to be related to girls’ but not to boys’ mathematics performance, suggesting that boys may need other forms of mathematics communication and teaching.

Several studies have focused on gender differences in mathematics education, but few have focused on gender differences with small children. The study of Klein and colleagues focus on gender differences in relation to “verbal skills, variables of spatial skills, and variables related to environmental factors, including teaching methods, quality of teaching, and mathematical communication”. Four research questions are posed in the study:

1. “Do kindergarten boys and girls differ mathematically?
2. Are language and spatial skills related differently to mathematics achievements of boys and girls?
3. Do boys and girls receive different mathematical communication by their teachers?
4. Are the patterns of correlation between instructional behavior (mediation) and mathematics achievements different for boys and girls?”

A test called KeyMath was used to measure the mathematical thinking of a selection of children (n=80), half of the children were boys/girls. The test is supposed to cover an age range of 4.6-21 years. There are several subtests within this set of measures. Three tests were used to evaluate the verbal ability of the children, and two were used to evaluate their spatial skills. Observations of mathematical communications in teacher-child interactions were also made in the kindergartens. The actual testing was carried out by the authors of the paper.

The results of the study are quite interesting. They did not find any differences in mathematical achievements between the boys and girls in the study. There was, however, significant gender differences in some of the factors that were related to these results. As they state: “The boys’ mathematical achievement was significantly related to their spatial reasoning, whereas the girls’ mathematical achievement was related to their verbal skills.”

I find this study interesting in many ways, but there are a few issues that I would have liked to learn more about (and that the article does not address):

• Were the measures translated from English into Hebrew? (If so, I would like to learn more about this process)
• What are the reasons for deciding on this particular method, and using these particular measures, in the study?

The December issue of Journal of Mathematics Teacher Education has been published (volume 12, number 6). This issue is a special issue with focus on social justice perspectives in matheamtics teacher education, and it contains the following articles:

• Working with mathematics teachers and immigrant students: an empowerment perspective, by Núria Planas and Marta Civil
• ‘Gender games’: a post-structural exploration of the prospective teacher, mathematics and identity, by Anna Llewellyn
• Engaging with issues of emotionality in mathematics teacher education for social justice, by Mark Boylan
• ‘The conference was awesome’: social justice and a mathematics teacher conference, by Tamsin Meaney, Tony Trinick and Uenuku Fairhall

On Friday, a new article by Giorgio T. Bagni was released from Educational Studies in Mathematics. The article is entitled Mathematics and positive sciences: a reflection following Heidegger. Bagni takes Heidegger‘s Being and Time as a starting point in an examination of Heidegger’s ideas about sciences in general and mathematics in particular. Here is the abstract of Bagni’s article:

In this article, I make a case for the inputs that Martin Heidegger’s theoretical perspective offers to current concerns about the nature of mathematics, its teaching and learning, and the problem of subjectivity. In particular, I consider Heidegger’s notion of positive science and discuss both its applicability to mathematics and its importance to mathematics education. I argue that Heidegger’s ontological position is consonant with some sociocultural approaches in mathematics education and that Heidegger’s work can shed some light on the problem of knowing and being. Finally, I raise some questions concerning subjectivity and the link between language and mathematical objects.

The December issue of Educational Studies in Mathematics has just been published (volume 72, number 3), and it contains the following articles:

• Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks, by Kaye Stacey and Jill Vincent
• Community college students’ views on learning mathematics in terms of their epistemological beliefs: a Q method study, by Denna L. Wheeler and Diane Montgomery
• Constructing mathematics in an interactive classroom context, by Paul Ngee-Kiong Lau, Parmjit Singh and Tee-Yong Hwa
• The effects of cooperative learning on preschoolers’ mathematics problem-solving ability, by Kamuran Tarim
• Students’ perceptions of institutional practices: the case of limits of functions in college level Calculus courses, by Nadia Hardy
• Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues, by Kalifa Traoré and Nadine Bednarz
• The challenge of self-regulated learning in mathematics teachers’ professional training, by Bracha Kramarski and Tali Revach