Flexibility and adaptability: partial-quotients algorithm

How do we teach flexibility, adaptability, and multiple paths to success? How do we teach collaboration and taking the path of another?

Last Friday, I had an opportunity to teach my school’s 5th graders.  The lesson was on long division and the partial-quotients algorithm.  I took a 3-pronged approach. At the end of the lesson, I wanted these young learners to be able to say

    • I can take organized notes that will be useful when I study.
    • I can divide using more than one method.
    • I can show connections between the traditional algorithm and the partial-quotients algorithm.

I know that exceptional math students can show their understanding more than one way.  Most of these young learners prefer one method over the other.  I asked them to work in their bright spot strength first and then challenge themselves to work the same problem with the other algorithm.

I know that working with more than one method is a struggle for many learners.  Once I’ve found success, why would I try another method?  Sigh…why do some resist trying new things?

In Algebra I, we want learners to use the point-slope form of a line, the slope-intercept form of a line, and the standard form of a line.  We meet quite a bit of resistance to any method other than the slope-intercept form of a line.

What if we work on flexibility and adaptability ? How might we challenge ourselves to embed this expectation? It is not enough to find an answer. How many ways can I show what I know? What if I listen to a different point of view and try another path?

One comment

  1. Jill,
    I am so pleased that you were working with the 5th graders on the partial quotients algorithm, not only for its wonderful ability to tie division back to place value, but also for the students to “see” mathematics from many different perspectives. When I taught math, the students knew first that they could never respond to a question with just the answer; we worked hard together for them to give the answer and why this was their answer (thus explaining either their process or their conceptual knowledge in the argument). They knew second that we were going to work on multiple methods to achieve a solution. Eventually, they could focus on the one most comfortable to them. But, the process of learning multiple methods strengthened their mathematical acumen, allowed them to appreciate their peers’ understanding and confidences differently, and also opened them up to being uncomfortable in some methods and persevering through. Unfortunately, I think there are too many teachers of mathematics who don’t model this process themselves. So, thank you for being the model and the guide!


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