Unpacking Practice - Megan Franke - UCLA

Learning from Practice

Phase 2

Experimenting with Problem Posing

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Listen to what I have learned about unpacking practice, around problem posing, with teacher education students.


Experiment Phase 2

Taking on a Systematic Focus

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I now am moving into specifically unpacking a particular practice.

I am focusing on posing problems. There are many options for high leverage practices.

Following on my initial engagement, where teacher ed students chose a wide range of not very productive practices on their own, I decided I needed to choose the practice focus. I have chosen problem posing for a number of particular reasons.

Problem posing:

  • practice exists in every classroom
  • there are many ways to get better at problem posing
  • it is critical to the ongoing lesson development
  • it involves content, students, issues of participation and equity
  • even at the beginning teachers will see "results"
  • can see student willingness and knowledge
  • important for English language learners
  • research base for its importance to student understanding
  • There are many other practices we could focus on that can accomplish many of these same things. I wanted clear places to start.



Initial Assessment: 3 aspects of practice

Assessment

What do the students think about "practice"?

Initial Assessment

Tracking our Conversations

Each time we, as a class community, had conversations about unpacking problem posing we used the board to map our conversation. The maps from four conversations are included here. I use these maps to provide evidence about how the group was thinking about problem posing. We used them as a class to keep track of our thinking and ideas about problem posing. You can look to see for yourself and see what you think students were considering.

Day 1 - students generate a list of what they noticed about one class session - the focus was not on problem posing. The students generated quite a range, some detailed and some very general, some pertaining to mathematics and some not.

Day 2 - students use the same common video as day 1, a video they know well, and focus specifically on problem posing. We re-watch the video focusing just on problem posing. The list of what they noticed is short, uses some language that needs unpacking, and is general in nature. In re-watching they notice how the teacher focuses on a key mathematical idea in unpacking the problem.

Day 3 - students use two QUEST sites (Hurley and Lampkin). We created a list of what they noticed. They had little to say. I had to work hard to get them to talk about the problem posing they watched. I asked many questions and prompted them using specifics from what i knew was in what they had watched. this was the students first engagement with the sites and it was in pairs in the computer lab.

Day 4 - students revisited the Quest sites at home. they also began to look at problem posing in their student teaching assignments. Here students had much to say. The conversation was lively and involved multiple participants engaging with each other. The students did provide details but wanted to move to general ideas quickly. I used my prompting to push for unpacking of the details of practice. We organized the conversation after we had all of what was said all over the board.


Using Quest Materials

The QUEST materials provide opportunities to examine multiple teachers pose problems and elicit student thinking. The two practices of focus.

We specifically examined:

Mary Hurley and Sue Lampkin

Mary Hurley

Sue Lampkin


Creating a Systematic Approach

Developing Mathematical Teaching Practice Cycle

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Step 1: Examine problem posing in a common video (already watched)

Step 2: Examine problem posing together using two QUEST sites

Step 3: Fill out framework questionsfor one QUEST teacher

Step 4: Discuss framework responses in class

Step 5: Try problem posing in your student teaching

Step 7: Fill out framework for your problem posing

Step 8: Discuss with colleagues

Step 9: Try again in student teaching

Step 10: Fill out your framework

For each step build a list of details of problem posing, drawing from the classroom examples, students' attempts and our conversations

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Mathematics Teaching Practice Framework

Assessment/Teaching

Suporting students to understand and detail practice

Tracking their thinking over time

Mathematics Teaching Practice Framework

Examples of student responses to framework


Discussion Board - Day 1

See board Day1


Discussion Board Day 3

see board Day 3


Web page formathematics ed students

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Detailing the Work

For a closer look at the details of the sequence of work with the teacher education students click on the link to their page. here you can download the assignments and see the links to the QUEST sites.

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Mathematics Methods Site


Final Reflection, Math Methods

Belief

What I believe about how children learn mathematics...

Action

What I will do in my classroom...

Without specifically soliciting about problem posing, 94of the students talked about aspects of problem posing in their final reflections... For example, one student commented,

Beliefs

"They participate in different ways. They often don't wait to hear/read the whole math problem before they answer. They rush through math problems just to get it don because they think speed is all that matters."

Actions

"Pose problems that will help develop strategies. Make sure children know what the problem is asking. Provide context that gives support. Have children solve problem in more than one way. Ask specific questions about their strategies."

Assessment: Reflection on Teaching Mathematics

Examples of student responses


Discussion Board Day 2

See board Day 2


Discussion Board Day 4

See board day 4



This electronic portfolio was created using the KEEP Toolkit™, developed at the
Knowledge Media Lab of The Carnegie Foundation for the Advancement of Teaching.
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