Wednesday, November 1, 2017

After our check-in, we returned to the Patterns and Functions article by Marilyn Burns and shared some responses. Some things that stood out:

• we were impressed by the importance of incorporating writing into math class
• it’s important to start early so over time students will learn how to express themselves
• students who can do the thing, often cannot articulate what they did
• it is easier to get students to articulate their process than it is for them to write it
• When writing, students often get stuck thinking of writing as a lofty complete thing – not as a way to think or draft ideas
• questions on the HSE exam ask students to explain process or too identify true statements (as opposed to just identify calculate an answer)
• precise language is important
• writing helps students (everyone) think through things and to remember more
• in the chapter, vocabulary was incorporated and students were encouraged to use it right away
• as a model for teaching vocabulary, we can start with the informal (start with what students see, what they know, what they have) and use that to introduce more formal definitions or terms (informal–> formal)
• students use the formal vocabulary immediately as scaffolding and as assessment

Next we looked at the…

Four Parts of a Japanese Lesson

and discussed the roles of the teacher in each:

1. Posing the Problem

   • add context of something students have done earlier – use an activity or concept they are familiar with to pose a new problem
   • use a picture or a model
   • connect math to students’ experiences
   • clarify terms/words/vocabulary so everyone is on the same page
   • explicitly ask students to explore many different ways to solve (task is not just to find the answer)
   • teacher doesn’t teach students how to do it
   • give time for students to explore

• Students Individual Problem-Solving

  • go around and see what stages students are in
  • look for different ways students are approaching the problem
  • think about which students to have present
  • think about what order to have students present in
  • give hints and guidance to students who need it

• Whole Class Discussion

  • call on students in a specific order and have them explain and/or put their work on the board
  • ask students to identify connections between the solution methods/approaches
  • does not distinguish what is correct and what is incorrect
  • look for opportunities to praise perseverance
  • listen to what students discuss for ideas that integrate the goal of the lesson that can be emphasized in the summing up phase
  • Q: Does (or at what point) the correct answer get discussed? A: By students seeing and understanding the different methods, they will know

• Summing Up

  • have basic statement of this written out beforehand
  • give final and careful comment on student work/ideas in terms of mathematical sophistication
  • take ideas from students, using the words they used in class discussion, and condensing it down to one statement
  • “A lot of great ideas have come out and everyone will walk out of here with different ideas. Two takeaways I was us all to consider are…”

Eric pointed out that a certain kind of problem is necessary for this kind of lesson structure to work. It made me think of this list of criteria that Marilyn Burns came up with for Mathematical problems:

• There is a perplexing situation that the student understands.
• The student is interested in finding the solution.
• The student is unable to proceed directly toward a solution.
• The solution requires the use of mathematical ideas.

This seems like a useful list when considering which problem we will use for our research lesson.

We need a tie-breaking vote for the problem that will be at the core of our research lesson. Both A Fair Price and the Popcorn Series received 27 points in our borda count vote.

Both of those problems come from full lesson plans. We won’t use either lesson plan for our research lesson, but we make take elements from one (or both). Hopefully reading these lesson plans will help us each decide which problem (and why we prefer that problem).

• Lesson Plan for A Fair Price (Evaluating Statements about Enlargements)
• Lesson Plan for Popcorn Series

In addition to the lesson plans, the following may be helpful in choosing which problem it makes sense for us to work with.

• Our Broader Goal : This is where we want our students to be years from now. Does one of these problems seem like a step towards this?
• The lesson objectives for both problems (keeping in mind the objectives for the popcorn series refer to all three activities). Do one of these sets of objectives and goals resonate with you more than the other?
• At the time of our lesson study, the TASC was the HSE exam for NY, so we looked at the TASC Geometry standards relevant to these problems: These problems do overlap in terms of the math content, but do you see one being a better fit with these standards?

Please enter your final votes here.

As a final note, we also decided as a group to add an additional meeting so that we could dedicated two whole meetings to writing the research lesson.

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