Making the Black Box Transparent
Although introducing technology into our mathematics curricula allows us to tackle problems of size and complexity as never before, we face a danger of introducing tools to students before they have a sufficient understanding of how mathematics content within their reach can be used to shed light on the algorithms within the tools or on the use of the tools themselves. Fortunately, we can view mathematical theory and technology not as opponents but rather as partners that make the whole of mathematical understanding richer than the sum of its parts. Indeed, bringing technology into our classrooms can encourage new questions that technology-free mathematics must answer. This article focuses mainly on a common example in technology-rich mathematics curricula, namely, the line of best fit, followed by a discussion of two additional examples—interpolating polynomials and complete graphs. In each case, connections between theory and technology do not appear to be as widely known and used as they could be.