Mathematical thinking style is about how your mind prefers to work when you do mathematics — not how good you are at it, but the form your reasoning naturally takes. Drawing on Rita Borromeo Ferri's research and Vadim Krutetskii's classic study of mathematical minds, it describes three styles: analytic thinkers reason in symbols, formulae and logical steps and feel at home with the abstract; visual thinkers reach for pictures, diagrams and spatial relationships and grasp ideas as holistic images; and integrated thinkers move fluidly between the two, using whichever serves the problem. The styles describe a preference, not an aptitude — each is a complete and capable way of doing mathematics, and strong mathematicians are found at every pole.
Mathematical thinking styles (Borromeo Ferri, 2010) is a validated framework in mathematics-education research describing how a person prefers to imagine, represent and reason through mathematical ideas. It distinguishes an analytic style (formal, symbolic, step-by-step reasoning), a visual style (pictorial, holistic, spatial imagery), and an integrated style that draws on both. It develops Vadim Krutetskii's classic study of the mathematical mind, which identified analytic, geometric and harmonic types (1976). This is a preference, not a test of ability, and no style is better than another. (Mathematical thinking styles (Borromeo Ferri, 2010))