Lesson Study for Enhancing the Curriculum

Problem solving features strongly in the revised National Curriculum:

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The national curriculum for mathematics aims to ensure that all pupils can … solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. (p.2; National Curriculum , 2013)

Problem solving features prominently in both the Foundation and the Higher tiers of the new GCSE specification:

“Students should be aware that mathematics can be used to develop models of real situations and that these models may be more or less effective depending on how the situation has been simplified and the assumptions that have been made.” (p.1; GCSE Specifications, 2015)

Problem solving is not sufficiently emphasised in most schools.

“While the best teaching developed pupils’ conceptual understanding alongside their fluent recall of knowledge, and confidence in problem solving, too much teaching concentrated on the acquisition of disparate skills that enabled pupils to pass tests and examinations but did not equip them for the next stage of education, work and life.” (p.9; Ofsted, 2012)
“Schools should increase the emphasis on problem solving across the mathematics curriculum” (p10; Ofsted, 2012)
“In a few good and outstanding lessons, pupils were given substantial problems to solve that required them to think hard about the problem, draw on their previous knowledge, and grapple with applying it in a new, unusual or complex context.” (p.31; Ofsted, 2012)
“In the very best schools, ‘using and applying mathematics’ was integrated into day-to-day teaching. For example, new topics were introduced by presenting a suitable problem and inviting pupils to use their existing knowledge in innovative ways. More generally, the lack of emphasis on using and applying mathematics remained a weakness that is persistent.” (para 103)

To read about the benefits of lesson study within a US perspective, see this New York Times article.