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Challenge standard methods and textbook characteristics
Not simple tasks but more complex ones that would give students a purpose to use certain mathematical methods
One group of teachers discussed the fact that if they only offered simple examples, students could use ad hoc "build up" methods and derived facts rather than powerful methods. You had to offer tricky examples to make new methods necessary. For example, students would use additive strategies for ratio unless you started with nasty numbers; students base all percentages and conversions on additions of parts of known conversions unless you start with nasty numbers.
