Daniel H. Jarvis

Do mathematicians integrate computer algebra systems in university teaching? Comparing a literature review to an international survey study

We present a comparative study of a literature review of 326 selected contributions (Buteau, Marshall, Jarvis & Lavicza, 2010) to an international (US, UK, Hungary) survey of mathematicians (Lavicza, 2008) regarding the use of Computer Algebra Systems (CAS) in post-secondary mathematics education. The comparison results are organized with respect to four emerging themes: Issues in CAS integration and mathematical learning, the notion of mathematical literacy, diverse uses of CAS by practitioners, and, potential benefits of CAS integration. Our analysis suggests that the results of the literature review strongly support the findings and conclusions of Laviczas international survey. We contend that Laviczas concluding statement about the need to more holistically examine technology integration in post-secondary mathematics departments was significantly realized through both of the compared studies.

On the Integration of Computer Algebra Systems (CAS) by Canadian Mathematicians: Results of a National Survey

In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the strongest factor affecting CAS integration in teaching. Mathematicians believe thatCASis becoming an integral part of contemporary mathematics knowledge. Two main factors impeding CAS integration are the departmental culture and the time required for designing CAS-based resources. Mathematicians mostly incorporate CAS use into assignments and much less for in-class tests and final examinations. CAS integration in teaching appears to remain a predominantly individual initiative.RésuméDans cet article, nous traçons les grandes lignes des résultats d’une étude canadienne (N = 302) ayant pour objet l’utilisation des technologies fondées sur les systèmes de calcul formel en enseignement des mathématiques au niveau post-secondaire. Les résultats indiquent qu’un nombre considérable de mathématiciens canadiens utilisent les systèmes de calcul formel dans leur recherche et leur enseignement. Il ressort également que leur utilisation en recherche est le facteur le plus important pour ce qui est de l’intégration des systèmes de calcul formel en enseignement. Les mathématiciens estiment que les systèmes de calcul formel constituent désormais une partie intégrante des connaissances mathématiques contemporaines. Deux facteurs principaux en gênent cependant l’intégration: la culture générale des départements et le temps nécessaire pour créer des ressources fondées sur ces systèmes. En général, les mathématiciens se servent des systèmes de calcul formel surtout dans les tâches, et beaucoup moins dans les évaluations en classe et dans les examens de fin de session. L’intégration de ces systèmes dans l’enseignement demeure largement le fait d’initiatives personnelles.

Geogebra, Democratic Access, and Sustainability

The aim of this chapter is to highlight the international trends in GeoGebra usage since its emergence as a powerful, open-source mathematics software in 2002. GeoGebra Institutes are being formed around the globe under the auspices of the International GeoGebra Institute (IGI), and the GeoGebra Wiki and User Forum are being well used by an increasing number of academics and enthusiasts. Within this chapter, comments made by a variety of these international users will be highlighted to address the questions of democratic access and software sustainability vis-a-vis the open source context, and to offer insight into the meaningful and expanding role that the software now plays in many regions of the world.

Messy but meaningful: exploring the transition to reform-based pedagogy with teachers of mathematics and coordinators in Ontario, Canada

The RE4MUL8 Project involved the creation of an online/mobile resource for Intermediate Division (Grade 7 and 8) teachers of mathematics. This resource showcases video documentaries of seven key mathematics topic lessons (fractions, integers, proportional reasoning, composite shapes and solids, solving equations, and, patterning and algebraic thinking), as delivered by seven teachers in Ontario, Canada who were nominated by their respective District School Boards as being, or becoming, highly effective practitioners in the area of reform-based mathematics education. As part of a qualitative case study research design, these teachers, often along with their math coordinators, were then interviewed following the lesson, and shared reflections on the lesson itself and, more generally, on their ongoing journey towards reform-based mathematics teaching. This paper reports on three major themes that emerged from these discussions, namely, problem-based learning, the reality and necessity of ‘messy time’ transition to reform-based pedagogy, and, balancing instructional planning and practices.

A man left albuquerque heading east: word problems as genre in mathematics education

Gerofsky presents mathematics word problems as a specific genre, discussing and critiquing their traditional components (i.e., “set-up”, “information,” and “question”; p. 27) and their uses throughout the history of education. She further recommends strategies for analyzing and altering this genre in order to enrich the word problems developed in curriculum materials and implemented in classrooms. As a condensed version of the researcher’s doctoral thesis, the book is structured accordingly. Chapter 1 provides an introduction; chapters 2 and 3 deal with the theoretical background of genre, drawing heavily upon literary and linguistics sources and ideas; chapter 4 provides a rationale for, and description of, the methodological decisions made in the research; chapters 5 and 6 analyze the interview data from the various levels of participants; and chapter 8 explains the researcher’s own creative recommendations for educators and curriculum writers. Chapter 7, dealing with the elaborate history of the word problem genre, could have possibly been positioned directly following chapter 3, in terms of its theoretical nature. However, Gerofsky’s choice of penultimate positioning of this chapter does provide the reader with a necessary context for her major conjecture (i.e., the evolution of word problem utility), and also sets the stage for her recommendations regarding teacher practice in chapter 8.