a) If a teacher wants to help learners to become proficient in mathematics, she must first of all be proficient herself. In the study guide, Kilpatrick’s (2001) five strands of mathematics proficiency are listed on page 39, on the left hand what proficiency in a learner means, and on the right side, what proficiency in a teacher means. A teacher is teaching problem solving to Grade 6 learners and she uses the following example:
+ + = +
but + + = + +
and the weighs 6 kg, what is the weight of the cylinder and the cube? In this problem, why is adaptive reasoning needed to solve the problem? Remember that in Grade 6 learners do not know yet how to work with
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