Approaching Professional Learning: what teachers want

Teachers do not come to professional learning opportunities as blank slates. Instead, they come to these settings with a complex collection of wants and needs. The research presented here takes a closer look at these wants across five different professional learning settings distilling form the data a taxonomy of five categories of wants that teachers may approach professional learning with. The resultant taxonomy, as well as teachers behaviours vis-à-vis this taxonomy indicate that we need to rethink our role as facilitators within these settings as well as the role that single workshops can play in the professional learning of teachers

The use of a scriptwriting task as a window into how prospective teachers envision teacher moves for supporting student reasoning

The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication and division with justification, assisting fictional students to work through their difficulties and helping them to justify their reasoning. Such tasks allow for the examination of the prospective teacher moves to support student reasoning through their imagined action and choice of words. Scripts from forty-one prospective primary teachers were examined for the study, and five clusters based on the type of teacher move for supporting student reasoning were found. Overall, the prospective teachers emphasized the elicitation and facilitation of students’ ideas. The cluster analysis, however, provided a nuanced examination of the cohort’s teacher moves. While cluster one saw the highest incident of eliciting teacher moves, albeit only in the low potential category, clusters two and three mostly used facilitating teacher moves, but varied in their use of high and low potential moves. Cluster four concentrated moves on facilitating, eliciting, and responding to student reasoning. Cluster five employed teacher moves from all main categories, with some instances of high potential moves in all categories except extending student reasoning, which can better support reasoning. The prospective mathematics teachers’ scripts and the five clusters that were found during analysis are discussed with implications for future teacher education and the support of building mathematical reasoning.Peer Reviewe

Cultural transposition of a thinking classroom: to conceive possible unthoughts in mathematical problem solving activity

This study concerns a professional development course designed and implemented for prospective teachers, centred on a teaching method regarding problem-solving activity, namely, the Thinking Classroom. The study is framed in the theory of cultural transposition, a perspective about the encounter with teaching practices from different cultural/school contexts. Cultural aspects are considered crucial and this encounter between cultures is seen as an opportunity for actors to become aware of their own unthoughts, i.e., some of the ‘invisible’ cultural beliefs about teaching and learning absorbed by their own culture. According to this framework, we present the results from a questionnaire given to all the participants, and two case studies of prospective teachers involved in the professional development, in order to discuss the kind of unthoughts on which they have focused in thinking about this training experience

Embodied experience of velocity and acceleration: a narrative

Abstract Constructing a link between what a student is learning and personal experience is an important, and sometimes difficult task. I present here a narrative of my own experience as a mathematics and physics teacher trying to create an embodied sense of motion in my students by actually putting them in motion. I use the story to present the difficulty of teaching motion in the absence of the embodiment of motion as well as the tension that is created between an embodied sense of motion and the static representations used to describe it

COMPUTER MATH SNAPSHOTS REFLECTIONS ON REFLECTIONS

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This issue's snapshot explores some generalizations of the definition of geometric reflection. Dynamic geometry tools can facilitate generalizations such as those obtained by relaxing the requirement that the reflection be through a straight line. The author compares the families of curves obtained by reflecting thru circular arcs with the curves generated in response to a physical problem proposed by Wittgenstein. He suggests that the strategy of generalizing definitions is a good avenue for bringing students quickly to the activity of doing mathematics

Understanding primes: The role of representation

In this article we investigate how preservice elementary school (K-7) teachers understand the concept of prime numbers. We describe participants' understanding of primes and attempt to detect factors that influence their understanding. Representation of number properties serves as a lens for the analysis of participants' responses. We suggest that an obstacle to the conceptual understanding of primality of numbers is the lack of a transparent representation for a prime number. Key words: Conceptual knowledge; Content knowledge; Number sense; Preservice teacher education; Representations; Teacher education; Teacher knowledge; Whole numbers Prime numbers are often described as building blocks of natural numbers. The term building blocks can be viewed as a metaphorical interpretation of the Fundamental Theorem of Arithmetic, which claims that the prime decomposition of a composite number to prime factors exists and is unique. Although the uniqueness of prime decomposition presents a challenge for many learners, its existence is the property that is usually taken for granted (Zazkis & Campbell, 1996b). However, it is the existence property that is behind the building-blocks metaphor, creating an image of composite numbers being built up multiplicatively from primes. What are the structure and the properties of these building blocks? There are two properties in particular that seem to present a mystery to the learner. One is the existence of infinitely many prime numbers, which entails very large primes. Another is the property that prime numbers are not generated by a simple polynomial function. In fact, mathematicians of different origins have struggled for centuries to discover a prime number generator. A few successes in this area have been recorded in the early 1970s (see for example Gandhi's formula in Ribenboim, 1996), but these developments present considerable mathematical complexity and are beyond the scope of our investigation. Although the understanding of elementary number theory has been the topic of a few recent studies (Campbell & Zazkis, 2002), there has not been any study focusing specifically on prime numbers. On a related matter, Zazkis and Campbell (1996b) investigated preservice teachers' understanding of prime decomposition and concluded that "if the concepts of prime and composite numbers have not been The study reported in this article was supported i

Number worlds: Visual and experimental access to elementary number theory concepts.

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called Number Worlds that was designed to support the exploration of elementary number theory concepts by making the essential relationships and patterns more accessible to learners. Based on our research with pre-service elementary school teachers, we show how both the visual representations embedded in the microworld, and the possibilities afforded for experimentation affect learners' understanding and appreciation of basic concepts in elementary number theory. We also discuss the aesthetic and affective dimensions of the research participants' engagement with the learning environment

Affect and mathematical thinking

The quantitative data about the participation to the Working Group 8 at CERME9 highlights the growing interest toward affective issues in the field of Mathematics Education. 40 manuscripts were submitted to the group, 34 were accepted for the discussion, and finally in these proceedings 29 papers and 4 posters are included. Although we have seen a general upward trend in the number of countries represented within this TWG, CERME9 set a new record in this regard with 16 countries present, representing four different continents. This meant that we had more papers both submitted and presented than ever before. 40 manuscripts were submitted to the group, 34 were accepted for the discussion, and finally in these proceedings 29 papers and 4 posters are included