Mathematics for Dyslexics and Dyscalculics, 4th Edition

3Cognitive (Thinking) Style in Mathematics

Introduction

We use the term cognitive (or thinking) style in mathematics to refer to the way a person thinks through a problem. Allport (1937, quoted in Riding and Rayner, 1998) describes cognitive style as a person’s typical or habitual mode of problem solving, thinking, perceiving and remembering. We have the optimistic attitude of many teachers and would challenge the word ‘habitual’. Mathematically, its history can be dated back as far as Descartes (1638, cited in Krutetskii, 1976), who described two styles of problem solver. The first solves problems by a succession of logical deductions, whilst the second uses intuition and immediate perceptions of connections and relationships. These two contrasting styles are described again in later literature. Boltevskii (1908, cited in Krutetskii, 1976) and Harvey (1982) labelled the two styles geometers and algebraists, where the algebraist links most closely to the logical, sequential thinker and the geometer to the intuitive style. Kovalev and Myshishchev (in Krutetskii, 1976) used the term ‘intuitive’ to describe a person who is not conscious of every step in his thought processes, but who perceives essential connections more clearly and quickly than his complementary stylist, the ‘discursive’ thinker. Skemp (1981 and 1986, also Choat, 1982) describes relational and instrumental understanding. Marolda and Davidson (2000) describe ‘Mathematical Learning Profiles’ looking at how students ...