Now let's look at a portion of the segment in more detail. In this Observe Viewer activity, you can watch how the teacher prepared the students to understand what a conjecture is and helped them see the distinction between gathering data about their conjecture and finding proof for it.
When you've formulated an answer to each question, select "Show Answer" to see our response.
Question: How does group work help students develop reasoning and proof skills?
Students have to explain their reasoning and justify their answers to one another, rather than just convincing themselves or the teacher. Both their explanatory skills and their questioning skills are developed.
Question: Does the group organization in this activity present any challenges?
Some students do seem to be dominating the discussion, particularly in two-person groups. With this kind of setup the teacher must be sensitive to factors that may hinder mathematical exploration.
Question: How does the use of historical context help students develop an understanding of reasoning and proof?
The context helps students relate their own efforts to find a proof for the conjecture to the work of Thales centuries ago. Showing them that the reasoning and proof process they are participating in is related to this early work provides insight into how mathematics progresses and the centrality of the concept of proof to that progress.
