The author tells the story of an exploration he undertook, what he learned, and the questions he was able to answer as a result. Thinking, on the part of the learner, is complex, far from explicit, and some might say intangible. But, by recognising certain "clues" it might be possible to begin to understand how different types of thinking influence how students react when faced with a problem, or calculation. You might not recognise the term multiplicative thinking, but you will certainly know when you see it demonstrated by a learner in a mathematics classroom. (Contains 3 figures.)