Annie Savard

Developing Probabilistic Thinking: What About People’s Conceptions?

Since the important work on reasoning under uncertainty by Kahneman and Tversky in the 1970s, the description of how people think about probability by using intuitions, conceptions and misconceptions have been studied in psychology and mathematics education. Over the years, the body of the literature have identified and studied many of them. Some conceptions, such as representativeness and availability, are well known. But not all of the conceptions have been studied many times and the conceptions presented in the literature usually don’t relate them to each other. Therefore, it is now difficult to have a broader perspective on people conceptions of probability. In addition to that, some epistemological differences exist between the conceptions. Not all of them use the same kind of reasoning for addressing different aspects of probability. Thus, a broader perspective of people conceptions of probability involves not only knowing about conceptions and links them together; it also includes knowing about the mathematical aspect involved.

Using Interactive Software to Teach Foundational Mathematical Skills.

The pilot research presented here explores the classroom use of Emerging Literacy in Mathematics (ELM) software, a research-based bilingual interactive multimedia instructional tool, and its potential to develop emerging numeracy skills. At the time of the study, a central theme of early mathematics curricula, Number Concept, was fully developed. It was broken down into five mathematical concepts including counting, comparing, adding, subtracting and decomposing. Each of these was further subdivided yielding 22 online activities, each building in a level of complexity and abstraction. In total, 234 grade one students from 12 classes participated in the two-group post-test study that lasted about seven weeks and for which students in the experimental group used ELM for about 30 minutes weekly. The results for the final sample of 186 students showed that ELM students scored higher on the standardized math test (Canadian Achievement Test, 2008) and reported less boredom and lower anxiety as measured on the Academic Emotions Questionnaire than their peers in the control group. This short duration pilot study of one ELM theme holds great promise for ELM’s continued development.

Transition Between University Students to Teachers: Practice in the Middle

This article presents a study done in an elementary mathematics methods course that focused on the transition of novice teachers’ epistemological stances: former elementary student, university student, and teacher stances. In order to help them develop the teacher stance, we designed a three-phase activity, where two phases took place inside class and the last one occurred outside of class. Novice teachers were given an assignment where they had to rehearse a count in class and enact it in front of a small group of students. They had to write reflections on their rehearsal and enactment. Interviews were done 4 months after the end of the course. The results show that the reflections about mathematics in relation to the use of new teaching practices on eliciting students’ thinking allowed the novice teachers to develop the teacher stance.RésuméCet article présente une étude réalisée auprès de futurs maitres du primaire et porte sur la transition des postures épistémologiques des futurs maitres, soit: l’ancien élève du primaire, l’étudiant universitaire et l’enseignant. Dans le but de favoriser le développement de la posture de l’enseignant, nous avons développé une situation en trois phases. Deux phases ont été vécues en classe alors que la dernière a été vécue hors de la classe. Ainsi, les futurs maitres ont eu à réaliser un travail dans lequel ils devaient répéter un compte et l’enseigner à un petit groupe d’étudiants. Ils ont eu par la suite à consigner leurs réflexions sur la répétition et la réalisation par écrit. Des entrevues ont été réalisées quatre mois après la fin du cours. Les résultats montrent que la réflexion développée envers les mathématiques et l’utilisation de nouvelles pratiques enseignantes sur la sollicitation du raisonnement des élèves a favorisé le développement de la posture de l’enseignant.

Using the Relational Paradigm: effects on pupils’ reasoning in solving additive word problems

ABSTRACT Pupils’ difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils’ knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in mathematics learning to the development of relational thinking. Using this perspective, we implemented a new approach to teaching additive word problem-solving in primary school, encouraging relational thinking and modelling. We compared the overall results of additive word problems solved by Grade 2 elementary pupils in the experimental group (N = 216) and in the control group (N = 196). Our data show: (a) on average, the experimental group performed significantly better in problem-solving than the control group; and (b) in the control group, there was a considerable lack of success in solving problems that require relational thinking—there was no such effect in the experimental group.

Observing Observers: Using Video to Prompt and Record Reflections on Teachers' Pedagogies in Four Regions of Canada.

Regional differences in performance in mathematics across Canada prompted us to conduct a comparative study of middle-school mathematics pedagogy in four regions. We built on the work of Tobin, using a theoretical framework derived from the work of Maturana. In this paper, we describe the use of video as part of the methodology used. We used videos of teaching activities as prompts for discussions among teachers and the video recordings of such discussions became the data sources for our comparative research. Our use of video revealed a number of advantages and disadvantages which influenced the research.