Class Workshop 11 - Learning Mathematics Skempification Objective: TLW review fraction operations in the light of Skemp’s framework of instrumental and relational understanding, and use questioning to move ourselves forward.. Schema Activation: Refresh your definitions of … Instrumental understanding is: Relational understanding is: Focus: Most teachers can agree that they wish to teach for relational understanding. But how can you determine if a student has relational or instrumental understanding? Using the idea of going from the known to the new, how can we move students from instrumental to relational? As with many ideas about learning, we can begin with ourselves. We generally have a storehouse of instrumental understanding from how we were taught. Starting from that, what questions do we ask to assess the type of our understanding? What questions do we pursue to advance our understanding? Work through the operations on fractions. For each operation, consider:

a) How do you think about _________ of fractions? b) What is the rule for computation? c) Do an example. Can you make sense of the answer? (Is it about right? Explain.) d) Why is the rule what it is? e) Can you do the operation in a non-symbolic model? (Picture, number line, context…)

1) Addition

2) Subtraction

Work through the operations on fractions. For each operation, consider: a) How do you think about _________ of fractions? b) What is the rule for computation? c) Do an example. Can you make sense of the answer? (Is it about right? Explain.) d) Why is the rule what it is? e) Can you do the operation in a non-symbolic model? (Picture, number line, context…)

Multiplication

3) Division Reflection: Pick one of the preceding operations of which your understanding was more instrumental. How did you know? How do you move forward or what would you do to deepen your understanding?