Author: Reidar Mosvold

Activating mathematical competencies

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César Sáenz from the Autonomous University of Madrid, Spain, has written an article called The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). This article describes and analyzes the difficulties that Spanish student teachers had when attempting to solve the released items from PISA 2003. The student teachers (n=140) were first-year students, and they had not taken any mathematics courses in their teacher training at the time of the study. They didn’t have any experience with the PISA tests, and they had no more than secondary-level mathematics studies before they started their teacher education. The test they took was made from a collection of 39 released items from PISA 2003.

The article was published in Educational Studies in Mathematics on Sunday. Here is the article abstract:

This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In this way, the school knowledge variable becomes a variable associated with the PISA competence variable.


Prospective elementary teachers’ motivation

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Amanda Jansen has written an article entitled Prospective elementary teachers’ motivation to participate in whole-class discussions during mathematics content courses for teachers. This article was published on Sunday in Educational Studies in Mathematics. Here is the abstract of her article:

Prospective elementary teachers’ (N = 148) motivation to participate in whole-class discussions during mathematics content courses for teachers, as expressed in their own words on an open-ended questionnaire, were studied. Results indicated that prospective teachers were motivated by positive utility values for participating (to achieve a short-term goal of learning mathematics or a long-term goal of becoming a teacher), to demonstrate competence (to achieve performance-approach goals), or to help others (to achieve social goals). Negative utility values for participating were expressed by those who preferred to learn through actively listening. Five motivational profiles, as composed of interactions among motivational values, beliefs, goals and self-reported participation practices, were prevalent in this sample. Self-reported variations among participants’ utility values and participation practices suggested that prospective teachers engaged differentially in opportunities to learn to communicate mathematically. Results provide pedagogical learner knowledge for mathematics teacher educators.

Gestures as semiotic resources

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Ferdinando Arzarello, Domingo Paola, Ornella Robutti and Cristina Sabena have written an article called Gestures as semiotic resources in the mathematics classroom. The article was published online in Educational Studies in Mathematics a while ago. Here is the abstract of their paper:

In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching–learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.

Research fellow at University of Agder!

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University of Agder, Norway, arguably has one of the strongest research groups in mathematics education. They have a strong Master programme, a PhD programme, and five international professors in mathematics education. Now, they have announced a free position/appointment as research fellow for a period of three years. So, if you want to become a PhD student in Norway, this might be your lucky day 🙂

Some of the research areas within the field of mathematics education in Agder include:

  • Developmental research in the teaching and learning of mathematics (from day-care centres to the university level)
  • Mathematics classroom research
  • Pupils’ and students’ understanding, attitudes and motivation for mathematics
  • Problem solving and modelling in mathematics
  • History of mathematics
  • Mathematics teacher education and professional development

If you are interested, you can read the entire announcement from the link above, or you can contact Professor Simon Goodchild (simon.goodchild@uia.no).

ZDM, No 5, 2008

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For some reason, ZDM has published two December issues this year. I have already covered one of them, which is actually No 6, but I have not covered No 5 (both are December issues). ZDM, No 5 has a focus on Empirical Research on Mathematics Teachers and their Education, and it is a very interesting issue (for me at least), with 14 articles:

So, if you (like me) you are interested in research related to mathematics teachers and/or mathematics teacher education, this would certainly be an issue to take a closer look at!

A large part of the articles in this issue are related to the international comparative study: “Mathematics Teaching in the 21st Century (MT21)”. This study, according to the editorial, is the first study that has a focus on “how teachers are trained and how they perform at the end of their education”.

NOMAD, No 3, 2008

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Mathematics teachers’ observable learning objectives

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Paul Andrews has written an article entitled Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes. The article was published online in Educational Studies in Mathematics on Wednesday. Here is a copy of the article abstract:

Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

Mathematical enculturation

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Jacob Perrenet and Ruurd Taconis have written an article called Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme. The article was published online in Educational Studies in Mathematics on Tuesday, and it is an Open Access article, so it is freely available to anyone! Here is the article abstract:

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.

ZDM, December 2008

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The December issue of ZDM is out, and it contains 12 interesting articles. The theme of the issue is “An Asia Pacific focus on Mathematics Classrooms:

Embodied multi-modal communication

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Julian Williams from University of Manchester (UK) has written an article entitled Embodied multi-modal communication from the perspective of activity theory. This article was published online in Educational Studies in Mathematics last week. Here is the abstract of the article:

I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in ‘grasping’ the meaning of mathematics if the whole object-orientated ‘activity’ is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a ‘threshold’ moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning.