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Chapter 5 – Option 1 (Reflection)

02/08/2019 10:03 PM | Anonymous

SMP 8 “Look for and express regularity in repeated reasoning” has been one of the more challenging MPs for some educators.  What ideas from chapter 5 on the Recognizing Repetition Routine helps extend your thinking or push it in a new direction?

Comments

  • 02/09/2019 8:47 AM | Marianne Springer
    The recognizing repetition routine provides a great approach to helping students identify patterns. This is a topic that we previously covered in depth in Algebra 2, but with the Common Core, I believe the focus is now in Algebra 1 instead. We don't do much with visual patterns like this in our Alg 2 curriculum at any rate. The multiplying binomials task looked like something that could be used to help students see factoring patterns using algebra tiles as manipulatives. I've only used algebra tiles for "completing the square", but I'd like to consider extending use of this manipulative for both multiplying binomials and factoring for the beginning of next year. That would go nicely with this routine.

    I was also hoping to find a task with an Exponential growth or decay pattern to use, but I didn't see one. On the "fostering math practices" page, I thought the Swimming Laps task might be a good launch to make students aware of repeated reasoning and help them articulate patterns. Then, perhaps I could use a compound interest problem right away instead of starting with a doubling problem, which is what I've typically used. Money might engage students more and make them really focus on repetition in the thinking process.
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    • 02/09/2019 6:34 PM | Cindy Noftle
      Using the compound interest problem would be a great way to start off. Trying to get the students hooked is so hard but money seems like the way to go.
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    • 02/09/2019 10:10 PM | Anonymous
      Marianne,
      Thanks for suggesting the www.FosteringMathPractices.com website. There are a lot of resources, including tasks for each routine. You will need to register to access the tasks (free).

      For Recognizing Repetition, here is the direct link to the page.
      http://www.fosteringmathpractices.com/routinesforreasoning/recognizing-repeptition/

      Karen
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    • 02/11/2019 3:02 PM | Sarah Giaquinta
      I was also thinking about how this routine lends itself to Algebra 1 so nicely, but what problems can I use for Algebra 2 & beyond? Thanks for the Fostering Math Practices reminder!
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  • 02/13/2019 8:38 AM | Dave Johnston
    As the authors describe, some middle school students tend to generate patterns by "building on" instead of recognizing the broader pattern ("each new table adds 3 blocks" vs "the number of chairs is 3 times the number of tables, plus one"). This routine aims to develop student thinking by encouraging students to search for regularity as *they construct their own models* of the problem (visual/concrete/algebraic/etc). When we work on these problems, I don't recall that I ever encouraged students to construct their own representations. Rather I provided the first few iterations and asked them to analyze them. This routine is so much stronger, providing students more opportunities to observe the repetition in multiple ways.
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    • 02/13/2019 2:57 PM | Megan Staples
      Hi Dave -
      You're pointing out something that I think is super important -- this idea of Building On vs Building. The Building On can often lead to students seeing a recursive formulation -- where they're focused on the change between two figures. This chapter definitely wants students building the full structure/figure, and then they can better see the quantities they're using each time.
      Until I read the chapter, and your comment, I hadn't thought so clearly about that distinction, but it seems like a really important one if we want students to be able to write the generalization as an explicit function.
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  • 02/13/2019 3:08 PM | Megan Staples
    First, hello everyone. This is my first post. I got behind at the beginning, and I've finally caught up on the reading so I can post on the proper week!

    From this chapter, I found I really liked the deliberateness of this routine. I've done tasks like this, but I tend to do more what's in chapter 4 with connections representations (which really focuses on the structure of the visual). So this chapter helped me see another approach to such tasks/prompts and how to focus questioning for a pattern (that then links to the structure of the visual).

    The chapter also reminded me of two questions that I really love that I believe come from Mark Driscoll's book on algebraic thinking grades 6 - 10. He suggests the questions -- What's changing? and What's staying the same? These seem really useful questions for helping students focus on what's being done again and again -- and sometimes that "again and again" is constant (e.g., you always add 2; there are always 4 'arms') and sometimes it has to be expressed as something that changes from figure to figure (the arm length changes, and goes up by 1 each time).
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  • 02/24/2019 5:38 PM | Allison Day
    I really enjoyed reading about this routine, especially since it a routine I have not taught. One of the big ideas that stood out to me is that students will use different senses to notice patterns. I think sometimes we give students a task and anticipate how they will go about understanding it but need to give them the time, space, and manipulatives to solve problems. I think we often take manipulatives away from students too quickly and don’t encourage them to use them as students get older. Using manipulatives can help students make sense of the problem, especially in problems where they are constructing/recreating and image such as the tower problem example in the book. When they are building something it can help when they are asked to describe their steps and process.

    Having students recreate the elements of the pattern will really help the teacher identify what the student is thinking. This will be helpful if students are struggling to notice the repeated reasoning and/or if they are having trouble communicating it. By partnering students carefully, I can have them ask and prompt each other with wonderings, questions instead of me leading the discussion.

    Using the Four Rs will help clarifying students’ thinking and help with the annotations. I think it is important for students to be really clear when describing their thinking so that the annotation will match exactly what they said.
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