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Here are some of the things that I’ve learnt about mathematical problem solving over the past few years: 1. Fluency in facts, procedures & concepts act as a foundation for problem solving, 
2. One main point of consistently asking students the same questions, in order to prompt their thinking, is that they then internalise these these questions and they become part of the students’ natural metacognitive processes whilst problem solving.
3. Heuristics like ‘solve a simpler problem first’ describe well what an expert problem solver does, but give little guidance to a novice.
Helpfully, @colinfoster77 summarises and expands upon these 3 points, and adds several more incredible insights in what is the most concise (2.5 pages) summary of the research on maths problem solving that I’ve seen. This is a must read!
This would be a perfect reading to spark discussion, or design a problem solving program, within a maths department. Link: atm.org.uk/write/MediaUpl… Thanks to @mrbartonmaths for the heads up on this one. @mic_epstein, you’ll love this for your upcoming workshop.
