This video spotlights instances where students' words and actions seem to indicate understanding. On further investigation the apparent understanding was revealed to be different from or more fragile than what might have been assumed from the evidence. This is a situation in which teachers frequently find themselves.
The teacher reflects on this issue and follows up on some questions she has about students' prior knowledge.
All clips originate from the same group of students working with Bits and Pieces II and Bits and Pieces III.
As you view the video, consider the following:
- What are the goals of Bits and Pieces II, Problems 3.1, 3.2?
- How would you expect students to think about 2/3 of 3/4 and 3/4 of 2/3 after their experiences with Problems 3.1 and 3.2?
- What are the goals of Bits and Pieces II, Problem 3.3, 3.4?
- From their experience with Bits and Pieces II, 3.3 and 3.4, what strategies would you expect students to develop for multiplying mixed numbers?
- What are the goals of Bits and Pieces III, 2.1?
- What do students have to know in order to be successful with Bits and Pieces III, 2.1?
- How does Bits and Pieces III 2.1 relate to the development of an algorithm for multiplying decimals?