Computational media and “What if?”

Digital technology allows greater computational power in smaller and more portable, and affordable devices.  By “computational” I do not mean only “doing sums”. Software such as Geogebra , Geometer’s Sketchpad and Cabri are also computational media. What makes them so is their use of computation to keep track of relationships between objects. These objects can be numbers, algebraic symbols or geometric points or constructions.  Most computational media, from spreadsheets up, is dynamic. What this means is that the initial data or parameters can be updated and the medium automatically updates the established relationships between objects. Just as for spreadsheets, computational media begs us to ask the fundamental question “What if?”

• What if we add two whole numbers? How will the oddness or evenness (parity) of the answer depend on that of each number? What if we multiply?
• What if the coefficients of a quadratic function are chosen randomly? How do the roots vary?
• What if  the slopes of two straight lines are varied? How does their angle of intersection vary?
• What if we choose whole numbers randomly? What is the probability that they will be prime numbers?
• What if we change a point on a parabola? How will the slope of the tangent line vary?

Computational media practically begs us to ask “what if ?” questions and to experiment to obtain data that helps us formulate an answer. This exploration is largely missing from present-day mathematics teaching, in which “instruction” plays a dominant role. Exploration to begin to answer “what if?” questions, stimulates independent thought, creativity and higher-level mathematical thinking.  In short, it helps students be mathematicians instead of simply learning about mathematics.

For more insight into the importance of creativity in school experiences, take a look at Ken Robinson’s TED talk:

For a more detailed account of learning to be rather than learning about, take a look at  John Seely Brown’s talk on Teaching 2.0: