Very exciting day….quite a buzz as I arrived today. Looking forward to some interesting sessions in the next few days. The hard part is deciding which sessions to choose.

**Teaching Proof: Lessons From an Action Research Study. Pete Johnson, Eastern Connecticut State University**

Yesterday, I attended a research session on proof,where’s a 5-person panel each explained research they had done on encouraging justification and proof in both middle and high school math courses. From that session, there were two takeaways for me:

- When we provide a proof, for whom is the justification intended? Who is the audience for the communication? Let’s focus on the end user.
- An interesting activity is to provide a number of givens, then having students work to support the “strongest claim”. We often tailor arguments to fit our pre-determined conclusions. But what are the possibilities, given provided information?

My first session today continues my focus on proof.

“writing proofs” is not a topic or a bit of content, it is a a process, a way of thinking that evolves over time

Much of the discussion in this session focused on the following challenge:

Prove that if n is an odd positive integer, then n squared is an odd positive integer.

A few approaches emerged. Let n = 2k + 1, then simplify n-squared. Are we guaranteed that the result is odd?

Another attendee suggested letting n = m + 1, but then how do we know that m-squared is even? What is the assumed toolkit of knowns and agreed upon principle in this problem? What does it mean for a number to be odd?

Also, the group tended to focus on the oddness, but have we proven that the result is positive, or an integer?

Findings: Teaching proof as a “separate topic” does not work. Also, instruction in formal logic does not seem to transfer well to mathematical proof.

**Engaging Activites for Your Classroom: technology in Middle School Mathematics**

The main event of this session featured activities utilizing the TI Nspire CX Navigator system. A few years ago, I acquired the Navigator system for the TI84 calcs, and had used it in some of my classes. But, over time, I found the system cumbersome, and that the classroom payoff was not often worth the set up required. I was eager to try this updated system, as it is now wireless, and integrates with the new color CX calculators.

My first impression is that sending files has become more intuitive, and the entire interface is cleaner and less clunky than the 84 software. The examples demonstrated today were pulled from the TI Activity Exchange, and could easily be edited for use with TI Publish View, which mentioned in an earlier blog post.

Looking forward to more great math discussions tomorrow!