Sunday, July 26, 2015

Redefining Math (still)

I find myself thinking a lot about redefining math, and posting things on this blog about that topic. Here, again, is a quote from a brilliant mathematician that forces us to rethink our idea of what “math” means.

I must include a paragraph from this article verbatim. Terry Tao, math prodigy.

That spring day in his office, reflecting on his career so far, Tao told me that his view of mathematics has utterly changed since childhood. “When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed,” he said in a lilting Australian accent. “I sort of imagined a committee would hand me problems to solve or something.” But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. “It’s as if your only experience with music were practicing scales or learning music theory,” he said, looking into light pouring from his window. “I didn’t learn the deeper meaning of the subject until much later.” (p. 46, 7.26.15 NYTMag)

Read more here, and add this to the “How do we redefine mathematics in school?” pile.

NCSM 2015, Boston. Tuesday

NCSM Boston Tuesday Notes. Not the band, the math conference, but I liked this picture better than generic pictures of Boston.

Elham Kazemi
Developing a school-wide culture of risk.
Teaching mathematics well is both possible and difficult.

(She spoke for a bit, then asked attendees at her session to tweet questions to her. Nice use of twitter to get audience participation.)

How do we organize schools for teacher learning?
1. Fostering and developing an intellectual culture establishing a vision for working on practice together, how we get better at practice and offering opportunities for teachers to deprivatize their practice and work on it together. It takes a lot of trust. Take risks. Foster that culture.

2. Strategizing and planning for accountability and assistance.
Who will be applying pressure and support?

3. Developing and elaborating a shared set of principles and practices for teaching shared vision for math instruction. Developing tools, establishing routines.
Facilitating a common language for talking about practice among principals, teachers and coaches.

You can change teachers thinking about something without changing what those teachers do in classrooms. -Dylan William

They used something called “Math Lab” that is like lesson study. While the lesson was being taught, they would use something called Teacher Time Out. Teachers would collaboratively make a decision or confer for a moment about what to do next. Students sometimes gave their opinions also. Students see that teaching is about learning.

Talking is not teaching.

They used the term “open-source teaching”.

They shared this website:

Karen Karp
Teaching K-5 Students Who Struggle in Mathematics
I sat next to Sandi Stanhope at this one and we just laughed because Karen is so engaging and funny.
This was partly about RTI, and she was happy to see NCSM’s position paper on that topic.
Relational understanding versus instrumental understanding.
Teachers help students make connections.

There is data showing that Tier 2 Interventions aren’t helping.
Kids are getting worksheets. The kid didn't get it with a teacher, now why would they get it with a worksheet?
Kids sitting at computer with a generic program, essentially a worksheet on a computer. They are practicing what they don’t know.

Karen talked about misconceptions and rules that teachers should not teach. She wrote a great article about this in Teaching Children Mathematics called 13 Rules that Expire.

You can't think just about your year. You have to think about the future of these ideas.
What is our responsibility to the teachers that come after us?

Telling isn't teaching.

Told isn't taught.

Explicit instruction isn't telling.

At all grades, students who struggle see each problem as a separate endeavor.

They focus on steps to follow rather than the behavior of the operations.

They tend to use trial and error - disconnected thinking not relational thinking.

They need to focus on actions, representations and general properties of the operations.

Create scenarios. When do I add? What does it mean to add? Not just addition problems.