Teaching Mathematics and its Applications - current issue

Bridging the gap between mathematical conjecture and proof through computer-supported cognitive conflicts

Lee, C.-Y., Chen, M.-P. — 2008-02-18

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students’ conviction based only on empirical experience and to create a need for deductive explanations, we developed a problem-solving activity with technology support intended to cause cognitive conflict. In this article, we describe the process conducted for this activity that led students to contradictions between conjectures and findings. The teacher could create familiar problem-solving situations and use students’ naïve inductive approaches to make students think mathematically and establish the necessity for proof via computer support.

Reorganizing freshman business mathematics I: background and philosophy

Green, K., Emerson, A. — 2008-02-18

This article is the first of the two-part discussion of the development of a new Freshman Business Mathematics (FBM) course at our college. Part I of the article describes the background and history behind the course, and provides a theoretical framework for the design of the course. This design involves students in learning and applying mathematics to real world problems using common business tools, in this case spreadsheets. This new course is centered on the concept of building and interpreting models of data, but touches on many topics in statistics, pre-calculus and calculus.

Using dynamic geometry software to convey real-world situations into the classroom: the experience of student mathematics teachers with a minimum network problem

Guven, B. — 2008-02-18

As any ordinary person knows, the shortest distance between two points is a straight line. What, then, is the shortest distance between three points? Four points? The study reported in this article deals with the observed actions of Turkish student mathematics teachers as they were working with minimal network problems. Having analysed the mathematization processes of student mathematics teachers in computerized environment, I describe here how new mathematical relationships can be discovered from real-world situations. The results showed that using real world situations in computerized classrooms leaves the doors open for the students for decision making, experimental verification, conjecturing and even for construction of proofs.

Complex variables in junior high school: the role and potential impact of an outreach mathematician

Duke, B. J., Dwyer, J. F., Wilhelm, J., Moskal, B. — 2008-02-18

Outreach mathematicians are college faculty who are trained in mathematics but who undertake an active role in improving primary and secondary education. This role is examined through a study where an outreach mathematician introduced the concept of complex variables to junior high school students in the United States with the goal of stimulating their interest in mathematics and improving their algebra skills. Comparison of pre- and post-test results showed that ninth-grade students displayed a significant change in algebraic skills while the eighth-grade students made little progress. The outreach mathematician lacked some awareness of the eighth-grade students’ foundational background and motivation. This illustrates the importance of working more closely with the participating teacher, who understands better the curriculum and the students’ background knowledge, levels of maturity and levels of motivation.

Getting the best out of Excel

Heys, C. — 2008-02-18

Excel, Microsoft's spreadsheet program, offers several tools which have proven useful in solving some optimization problems that arise in operations research.

We will look at two such tools, the Excel modules called Solver and Goal Seek—this after deriving an equation, called the ‘cash accumulation equation’, to be used in conjunction with them.