June 22, 2016

Partial WHAT?!?!

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Recently, Kim was asked to meet with a group of math specialists wanting some advice for helping children negotiate the reading demands of multiple step word problems. During the meeting, Kim offered several suggestions and strategies, but as one might expect in a cross-disciplinary meeting such as this, the conversation bounced between math and literacy. One of the things that this particular group of teachers shared with Kim was a way of doing long division called  “Partial Quotients” that Kim had neither seen nor heard of before. (In case you’re not familiar, check out this one-and-a-half minute  tutorial video from the University of Chicago.)

As the teachers walked Kim through the process, she was skeptical.  In the back of her mind, she heard herself judging this methodology. Why bother? This isn’t any easier than the way I was taught. But as the orientation continued, she realized that her initial judgments were unfounded. The real reason she had rejected the partial quotients methodology initially was because she didn’t understand it.  It was new and unfamiliar and, like many things that are new and unfamiliar, it felt hard. By the end of the tutorial, however, Kim was eager to go home and share this with her husband and two sons.  It felt like long division had just gotten a lot easier!

Kim’s story illuminates the need for educators of all stripes to embrace a dynamic mindset. While Kim’s mind was busy resisting partial quotients, another part of her mind was busy retaliating with her deeply held belief that all ideas hold potential, so long as we allow ourselves the opportunity to see it. How much do we miss when we resort to snap judgments? Even the seemingly worst ideas deserve consideration and at least some analysis. We can never know what will spark new thinking or insight. When your initial reaction to something is negative, stop and ask yourself, these questions:

  • What is the truth in this idea?

  • Why am I offended by it?

  • What piece of this perspective can I embrace to better balance my thinking/working/living?


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  2. Teaching multiple ways to solve math problems definitely made my brain more limber in all problem-solving situations. However…I’m not sure I could bring this flexibility to accepting a reading program and “fidelity to the program,” Steve. Peace be with you as you navigate this “edge” you’ve found.

  3. What am I resisting?
    Most on my mind is our district’s move toward a reading program. I’m resisting the call for “fidelity to the program.” So, I’m going to try the questions you pose and see where I end up.

    What is the truth in this idea?
    As Michael Fullan and Pasi Sahlberg have noted, really big changes happen when systems change, not just teachers. This decision represents a real attempt to change a system. A lot of thought and effort have gone into choosing the “right” reading program. The call for “fidelity” is a recognition that islands aren’t the way to go.

    Why am I offended by it?
    My fidelity is to learning and learners. I believe that I know them better than a reading program; if I don’t, then my #1 job is to make sure I know them well and figure out the next steps they might need to take. I resist any attempt to relieve me of my responsibility to think for myself. Fidelity to a program points me toward a kind of teaching that I think is counter-productive.

    What piece of this perspective can I embrace to better balance my thinking/working/living?
    I definitely need to keep my focus on de-islandification — some might call it building bridges .:) But, I’ll also need to keep my focus on the needs of the learners in my classroom and what I know they want. I suspect that walking this edge is probably only possible if I realize the good intent that lies behind what I’m skeptical about, and try to encourage the overall goal of conversation about practice.

    And about that partial quotients algorithm. Love it! When I figured out how to do that and partial products (I’d been taught the One-True-Algorithm as a kid) I found I could do some pretty impressive mental math!

    • Janet F. says:

      You are absolutely right about that mental math and the other algorithms! I taught gr. 5 for 25 years and gr. 3 for 13 plus 1 each of K and 1st……and tutored a lot. I can get third graders to do 3 X 3 digit multiplication correctly using lattice, they love it AND it gives them a reason to want to learn their facts so they can use it on something “impressive”…..now…..number sense and making predictions has to be part of it, so they are not just little robots…..but that is another long story. Yeah…fidelity to the program….sorry……..fidelity to the learner and his/her needs and place at that moment in time. The flip side? Differentiation. Can’t have it both ways. NOT to mention truly creative teaching which can integrate needs spontaneously after much prior thought and planning. I could go on.

      • Yes to all these, Janet.

        My challenge will be to figure out my best role as we make the changes we are making in our district, to keep my eyes on the prize, while keeping close contact with colleagues who are excited about the changes. B&Y’s questions might help me walk this line better than I would without them.

  4. Janet F. says:

    Oh bless you, Kim. (And Jan!) Now on to Lattice Multiplication. All three of these methods are dismissed outright by so many: partial quotients, partial products and lattice. They ALL have merit and have much useful potential for all kinds of learners. Just because something is traditional doesn’t make it better. Yes, it is familiar and yes it may appear to be faster, but before you dismiss it, you need to give it some time and thought.

    Your post has great merit. Thank you.

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