Embedding divergent thinking and creativity in mathematics
To classify subjects as creative and non-creative is a contradiction. Like any other higher-order thinking skill, creativity is central to learning in any discipline (Miller 2015). The late, great Sir Ken Robinson put it best when he said, ‘creativity is as important as literacy, and we should treat it with the same status’ (Robinson 2006). As educators, we must endeavour to craft learning experiences that motivate our students to be imaginative and creative by employing divergent thinking skills, so that the classroom reflects the playground (Miller 2015).
If we consider mathematics, there is a persistent societal norm the subject is dry, dull, and black-and-white, leading many to ‘hate it’ (Li 2019). Ideas about being creative in the subject can seem foreign because of the way maths is spoken about and taught in our schools. It is particularly troubling if we consider the vast difference in opinion a positive relationship with the subject at school can have. Schools seem to dichotomise students into those who think they are bad at maths always thinking so, and those who are good at maths becoming mathematicians, engineers, teachers, or academics. This is because the latter overwhelmingly agree that the subject can be as expressive as any of the fine arts under the right conditions, implying the subject is creative, but few teachers tap into this in their pedagogy (Taylor 2020). Consequently, if we want to stop disenfranchising our students from mathematics and change the ‘image problem’ the subject has, we must reconsider the way it is taught and look for opportunities to embed creative thinking. The problem with convergent thinking
Mathematical creativity and divergent thinking
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Creativity looks different in every subject and in mathematics it is typically defined as ‘non-algorithmic decision making’ (Devlin 2019, para. 14). This implies that mathematical creativity is incompatible with convergent thinking strategies, because the latter only works when students apply a learned skill or worked example to arrive at a specific solution, like an algorithm. This is supported by the traits of mathematically creative individuals, typically characterised by ‘their understanding that more than one approach can lead to equivalent results and their ability to solve problems in different ways’ (Leikin & Lev 2007 in Kroesbergen & Schoevers 2017, p. 420). Furthermore, it is these students who embrace creativity that typically score higher on exams, because they can overcome the cognitive hurdles of the most complex and challenging problems (Kroesbergen & Schoevers 2017). It is for this reason competitions such as the Australasian Problem Solving and Mathematics Olympiads (APSMO) design their programs to ‘focus on the students’ ability to solve mathematical problems in a creative manner – as opposed
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Convergent thinking is a broad term that encourages students to use their prior knowledge and learning experiences to ‘hone-in’ on one specific solution to standard questions (Cropley 2006; Nelson-Delaney 2020). It does not require significant creativity but is a successful strategy for school exams and standardised tests when the problems are linear and logical (Cropley 2006). However, a reliance on convergent thinking alone cannot help students when they encounter a cognitive hurdle that requires them to think around the problem in unfamiliar scenarios (Nelson-Danley 2020). In these circumstances, students need to tap into their creative thinking to work the problem; however, if they have never been exposed to such thinking their predicted success is low. This is unfortunately the case in many schools where teachers and students have placed an increased importance on convergent thinking strategies to be successful in mathematics.
As an example, the breadth and pace of the Queensland senior syllabus does not lend itself to depth, and consequently teachers tend to favour pedagogical approaches that promote convergent thinking because that is the path of least resistance. Additionally, the pressures felt by students regarding short term metrics such as ATAR results emphasise the importance of this approach because convergent thinking is seen as the safer path toward success. However, the highest degree of difficulty on senior mathematics exams are called ‘Complex Unfamiliar’ questions that require students to adopt nonconvergent thinking styles. Only those students who have embraced creative thinking in mathematics are successful with them, and those who try and apply convergent strategies fail. If such students have a negative pre-existing attitude towards mathematics, this will only enhance their hatred for the subject, because they equate their failure with an inadequacy (Buckley 2013). This is a specific example, but it highlights the limitations of convergent thinking strategies and the problems educators face if they only endorse this type of linear style of thinking. This is because teaching mathematics for short-term success alone employs a finite mindset in the infinite game of education (Sinek 2020). According to Game Theory, playing an infinite game with a finite mindset will never be successful, and as such, teachers must embrace more opportunities for students to think creatively in mathematics (Sinek 2020).
