Intelligent Partnership with Technology: Moving from a Mathematics School Curriculum to an Undergraduate Program

Abstract

Through an analysis of the Ontario secondary school mathematics curriculum and the core mathematics program at Brock University, Windsor, Ontario, Canada, the authors provide a detailed description of what constitutes a student's intelligent partnership with technology when learning or doing mathematics. While the Ontario curriculum provides many opportunities for students to develop such a partnership, there is little evidence that students are instructed in that way or that teachers are made aware of all the complexities of such a partnership. On the other hand, the core mathematics program at Brock University is specifically designed to engage undergraduate students, many of who are future teachers of mathematics, in an intelligent partnership with technology starting from the first-year transition course. This evolution culminates in an independent project that requires the design and implementation of a computer environment to study a mathematical concept or conjecture, or the exploration of an application. Such an approach may be a good model for learning and doing mathematics even in secondary school, as the new generations of students are increasingly digitally literate and drawn toward technology.

KEYWORDS:

• technology
• university mathematics education
• school mathematics curriculum
• intelligent partnership
• MICA

Notes

Hughes (2005) uses these terms to discuss pedagogies that would implement technology in transformative ways and finds that, regrettably, professional development of teachers mostly focuses on how to merely operate the technology.

LOGO computer language, for example, can act as a cognitive amplifier and is one of the “promising educational developments that have been abandoned before being fairly tested” (Maddux, 2005, p. 22); “one of the great missed educational opportunities to date” (Maddux & Johnson, 2006b, p. 3).

This notion of learning about computers (e.g., in computer science and programming courses) and with computers (e.g., using them to aid instruction in various courses) was introduced by Demb (1974). Schrader (2008) takes these notions further and writes about learning from, about, with, and in technology (e.g., in virtual, immersive environments).

Adult numeracy involves understanding and using mathematical information at school, at work, and in everyday life (e.g., handling money and budgets, using measurements for cooking, or reading a map (Human Resources and Skills Development Canada, 2011).

The titles of the curriculum statements (in the right-hand column of Table 1), that are further used in the Figure 1, are those of the authors of this article.

FIGURE 1 Relevance of technology to each of the identified steps in learning and doing mathematics according to the recent mathematics curricula.

At the time this paper was written, the MICA III core course was split into two elective, one-semester. project-based courses due to its very specific applied mathematics content (PDEs).

We encourage the reader to look at examples of student projects on the department's Web site (http://www.brocku.ca/mathematics/resources/learningtools/learningobjects/index.php).

Abramovich and Sugden (2008) provide many examples for faculty to use when mentoring their students to conjecture, to explore their conjectures using spreadsheets, and then to move to proving.

Both the object and a summary of the written report (based on the original report submitted as an assignment for the course) are accessible via a Web site ( Brock Math, n.d.).

Start with a positive integer n. The next term in the sequence is 3n + 1 if n is odd or n/2 if n is even. Repeat this process until you reach 1.