Pentagon Patterns

Facilitator(s): Ramon
Date of Meeting: December 16, 2014
Problem: pdf
Further Reading: pdf

Still looking for a name for our group, we went around introducing ourselves and each offered one word for our group vision:

Fun, Math, Community, Community, Building, Sharing, Other People’s Thoughts, Resources, Escape, Learning, Ideas, Adult/Young Adult, Inspiration

Discussing Building a Web Presence for OUr Group 

Since this was only our second meeting, we spent some time talking about the roles and the goals of our group. Our discussion focused on our vision for what role we might play in supporting math teachers in the larger adult education community, and specifically on what kind of web presence we might develop as a platform for that work. We looked at a wikipage, which may or may not be our final web platform, as a way to both share what we’ve done so far and to think about what we would want our web presence to be able to do.

The purpose of the web site would be to capture the work we do and bring it to a larger community of adult education teachers. We should try to reach a larger audience than just the folks already here. We’ll have to figure out how to reach teachers who are working in isolation. We need to come up with a name for our group and/or the site, so we can have a web presence we can invite folks to. Some sites have ways for folks to subscribe, and a feature that notifies members when there are new posts. We could do something similar to a phone tree, where each person sends an email to three teacher friends – though not until we come up with a name and an official web site address.

We should be conscious of not duplicating existing efforts – for example, there is the NCTM (National Council of Teachers of Mathematics) webpage. Other folks felt that it was important to be focused on adult ed., which NCTM is not. Also NCTM can be overwhelming, and it you are not a paying member, many resources are not available to you. Also that we are able to “talk back” to folks who reach out and build relationships.

Articles: We like the idea of having articles available – articles with problems imbedded in them that talk about the teaching of those problems as well as articles about the philosophy/pedagogy of problem solving. To make articles more accessible, we should have some kind of annotation – have folks weigh in on why they choose them, what inspired them, an evocative quote, some taste of our discussion. There is more interest in reading theory and research if it is connected to this community of people and explored in our meetings. Provides an opportunity for us to connect in a richer way.  We would post articles associated with each meeting, but would we also post other articles? Some, but not too many. Nice way of staying on top of current research.

Documentation: We should take photos of our work to post with problem and facilitator notes. It is useful for people who would like to teach the problem later to see multiple solutions and ways of thinking about the problem. We want there to be some way for people in the group to post and for everyone to be able to talk/process with peers. Also to capture and share our math work from these meetings (write-ups, audio recording, photos, videos) and potentially the math work of students for teachers who take the problems we do together into their classrooms

WordPress and Wiggio were mentioned as potential platforms to look into.

Would everyone be able to post? It shouldn’t fall on just one person.

John, Tyler and Mark volunteered to process people’s opinions and explore this question of a web platform and present something at our January meeting

Pentagon Pattern

First, Ramon distributed a single sheet with only a figure on it. He had us work individually then share with partner. The discussion prompts were “What does this make you think? What questions do you have about this? What does this information lead you to think?”

Second, he facilitated a whole group share.

Next, he told us that the figure we’d been discussing represented a specific figure in a sequence of figures. He then asked questions similar to those above, having us work individually and then share with partner

Marh, Cynthia, Daphne - Pentagonal Numbers


Tyler - Pentagonal Numbers

Teacher Thinking

Board Work on Pentagonal Numbers

Math Circles

We gave out an article that talks about math teacher circles. It has a great non-routine problem in it, called Frogs and Toads. Here’s a link to an interactive version of the same problem – Frogs. The article gives the solution, so don’t read too much of the article if you want to solve the problem on your own. The article lists several math teacher circle online resources.

Jacob (who co-authored the article) talked about his experience studying teacher circles, and the shift in his own thinking about the kinds of problems that teachers can do together that give them the experience of working on problems that are really open and  non-routine. What I took away from his comments are that he feels there are different levels of non-routine problems. There are some that are problematic, have a few possible solution methods and are somewhat unfamiliar to us, but not entirely so. For example, there were different ways we approached the pentagon problem, but we all were looking for some kind of pattern and then a generalization to describe those patterns. Then there is another kind of non-routine problem, one that is completely open, where as problem solvers, we are not sure of our first step and in fact have to give a lot of thought to deciding what the problem is. For example, what if we had all been limited in our approach to the pentagon problem, and given the instruction – “No patterns”?

This led to a brief discussion that that had several underlying questions that will continue throughout these meetings – what are our goals, what kinds of problems should we work on, and how are those two questions connected.

Some thoughts from the conversation:

  • Doing math is asking new questions.
  • For most of us, when we were students in school, we did not experience the kind of math teaching and learning we want to develop in ourselves, our classrooms and our students. For some this group is about learning math content through problem solving and learning how conceptual knowledge can be developed through inquiry.
  • Non-routine is a relative term.
  • We can engage students in conversations about the goals of math education and the problems they work on – Why do we need to know what we need to know? And do we actually need to know it?
  • We want to use these problems with students. Where is the sweet spot between what is challenging for us and them? We shouldn’t limit ourselves and our students to the same questions.
  • Pattern recognition is important.
  • We should ask ourselves why we would bring a particular problem to class. What is the purpose?

In attendance: Solange, Jacob, Tyler, Cynthia, Daphne, Usha, Eric, John, Denise, Arleyah, Ramon, Brian, Kevin, Mark

Programs represented: Fifth Avenue Committee, Literacy Assistance Center, Lehman College, The Door, Borough of Manhattan Community College, CUNY Start, Fortune Society, CUNY Adult Language & Literacy Program, CUNY Collaborative Programs

Location: Literacy Assistance Center – 39 Broadway, 12th Floor

Respectfully submitted by Mark

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