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Chapter 8 – Option 1 (Reflection)

12/08/2020 11:38 AM | Anonymous

Comment on something from this chapter that you found thought-provoking.

If you need more specific direction, then please reflect on the questions on page 207. Are you comfortable asking them in your teaching context?

Comments

  • 01/04/2021 1:36 PM | Carrie Allen
    I LOVED when Tracy discussed the 4th grade class and the conjecture that the student had made about decomposing numbers while using multiplication. My favorite part about this was that the two teachers, took the time to DO THE MATH. It's so easy to just praise or knock down an idea a child has, but it takes a great deal of bravery to DO THE MATH with them. It is also my favorite idea to lend to teachers and parents.

    The fact that Tracy took the time to think about this for herself and share with all her math friends made it that more exciting. I also share these things with my friends and colleagues and I usually get the "Well you're a math nerd" look, but to hear that so many people found this just as interesting as me, made my day.

    There were so many interesting things in this chapter, that it was hard to observe it all. But I flagged them for later use.
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    • 01/09/2021 1:11 PM | Anonymous
      YES! The question about changing the numbers being multiplied and how that changes the product is not immediately clear. I really appreciated the teacher giving voice to the various student conjectures AND taking the time to work out the math on her own in order to best guide the class discussion the next day.

      I myself have sometimes said to HS students: your method doesn't work because xxx and here is the method that works. It takes more time/effort to find the "kernel of truth" in student errors and help them build understanding from that vantage point.
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  • 01/08/2021 8:55 AM | Cortni Muir
    What sticks with me is the importance of representations. I feel strongly that math is so much more then procedures. When students can represent problems and their thinking in a variety of ways, it helps use to see how well or not well they understand a problem. Representations often help us to identify misconceptions and can guide our way of discussing problems with students. Using different models helps students to make connections to what they are doing.
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    • 01/09/2021 1:16 PM | Anonymous
      I agree 100%, representations can be the key to making connections and consolidating learning.

      One of my refrains with my students is "How Else Can We Show This?", I'm constantly asking them to show another way: a graph, a diagram, computation, algebraic manipulation, etc. in order to deepen understanding.

      This doesn't mean that I require students to show more than one method for a given type of problem; but by explicitly discussing various methods, I'm hoping they become more flexible problem-solvers and add more tools to their mathematical toolbox.
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