#
Mathematical

Salad

## Building mathematical creativity

06 July 2018

Have you ever heard of the Brick Test?

If you haven’t (or even if you have) try the following:

Sit down for five minutes or so with something to write with and try to come up with as many uses for a brick as you can. Be descriptive. Get creative. There are no wrong answers. Don’t worry about the fact that it’s called a ‘test’ – no-one will see it but you.

Now think about what this test could be measuring, and how it might be scored.

This is an example of what’s termed a ‘divergent thinking’ task, and one of the most simple and enduring. It was originally conceived of by JP Guilford et al in the 1950s and is often called Guilford’s Alternative Uses Test (Guilford suggested that both divergent thinking and convergent thinking were important in order to be creative). I originally came across this idea in Malcolm Gladwell’s book *Outliers* some ten years ago, and was captivated by the presentation of an alternative or indeed a complement to the traditional IQ and other intelligence tests for capturing that elusive quality of creativity that one often finds in the minds of highly successful people. Research by Lewis Terman – still to some extent ongoing as the oldest and longest-running longitudinal study in the field of psychology – suggests that high IQ alone does not seem to correlate with ‘success’. Gladwell asks: what, besides a ‘threshold’ of (somehow measured) intelligence makes a Nobel prize winner? His answer: creativity.

So what has this got to do with mathematics, or indeed mathematics education? Creativity often seems to have little place in the mathematics curriculum and this may be said to be driven by its omission from assessment in school mathematics. We don’t present portfolios of both successful and unsuccessful avenues of exploration in maths as we might in art; we don’t perform intensely and emotively to gain top grades in maths like we might in drama; we don’t create original melodies and harmonies in maths like we might in music. Because creativity in mathematics can’t be measured, right?

Did you think about how the Brick Test might be scored?

You may have said something about the number of answers – important but not the only thing. It’s also worth thinking about whether they are all very similar to one another or not. Guilford used four parameters: *fluency* for number of ideas, *flexibility* for how different they were, *originality* for how rare the idea was compared with the comparison group, and *elaboration* for how well the intended use was described. This I knew, but I didn’t know that there are similar ideas in mathematics education research, and that Leikin (2009) designed ‘Multiple Solution Tasks’ to test creativity in mathematics. The premise is simple: like the Brick Test, ask students to come up with as many routes through the problem as possible. It is another divergent thinking task, but a specifically mathematical one. Have a look at this example from the work of Rott & Liljedahl which I was fortunate to see presented this week, with a student’s response underneath:

So why is the maths education community investigating measuring creativity in mathematics education? Although the research is only now starting to develop in this area, some researchers suggest that creativity, along with number sense and working memory, could have an important correlative relationship with mathematics achievement as well as contributing to problem-solving:

*In education creativity is relative; a creation of a product (e.g. solution or idea) is seen as creative when it is novel and useful for a specific student (Leikin, 2009). Creative skills are thought to be beneficial for learning in general (Kaufman & Sternberg, 2010), and learning mathematics in specific (Kattou, Kontoyianni, Pitta-Pantazi, & Christou, 2013), although conclusive evidence is lacking... Experienced problem solvers show different phases in their solution process (Carlson & Bloom, 2005), in which both divergent and convergent thinking play a role. Generally, the focus in math education is on convergent thinking (giving the correct answer). However, excellent mathematics learners are characterized by the understanding that more than one approach can lead to equivalent results and the ability to solve problems in different ways, in other words, are characterized by mathematical creativity (Leikin & Lev, 2007).* (Kroesbergen & Schoevers , 2017, p.420)

Of course, measuring a concept like ‘creativity’ in mathematics is not without its significant issues. In particular, Rott & Liljedahl suggest that solutions (products) are not a good proxy for processes, and measuring solutions only is far too limited. They also suggest that what we often term as ‘creativity’ is in fact ‘imagination’, separating the two by the idea that imagination begins with and operates within the conceivable, whereas creativity is extra-logical, transcending logical boundaries. By Rott & Liljedahl’s definition, school mathematics students may often be imaginative but rarely creative.

How do you feel about creativity in mathematics teaching and learning? You can tweet us @CambridgeMaths or comment below.