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Example use
Teachers in these clips are well aware of the important role played by examples and exemplification in learning mathematics. We see this both in their own choice of examples and in the ways in which they use students' examples to shape their lessons. In A, contrasting examples are used deliberately by the teacher to explore how 'half' might show up in different numerical situations. In T2 the idea of counter examples to a conjecture is a strong theme, as a student's conjecture appears to work in one example, but is a special case. B1 uses student-generated examples to start the class thinking about remainders. In M3 students are asked to find examples of situations in which increases in one variable are related to increases in another. In S3, we see a teacher setting a range of examples for students to work with, and the range covers the possibilities discussed at the start of the lesson. She indicates that some are harder than others. In J2, students give examples of angle relationships they have discovered and these are varied enough to provide a rich mathematical experience for all students. As well as these particular clips, in all the lessons students' ideas were used routinely in very positive ways.
