NYABS Part 4: An Average Algorithm Leads to Deep Thinking

Algorithms typically route us completely around opportunities for deeper thinking.  However, in this post, we see that using icons to represent a variety of strategies produces an opportunity to richly compare and contrast strategies, including an algorithm, to see what we can learn.  This post features 10 questions that can be used in this scenario to promote deep thinking.  And it all begins with a very average algorithm.

Other Posts in “This is Not Your Average Blog Series” (NYABS)

NYABS Part 1:  Leveling Off

NYABS Part 2:  Passing Out

NYABS Part 3:  Number Trading

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4 Comments

  1. Aaron on December 22, 2015 at 12:28 pm

    Thank you for sharing your blog. This is a great series and good to think about getting beyond standard algorithms and helping students build meaning. The more students can get at the “why” the stronger their math ability will be.

    • stevewyborney@gmail.com on December 24, 2015 at 8:32 am

      Great point, Aaron. Reaching the “why” is very important and it also takes us into the territory of truly important understanding. Spending time in the “how” doesn’t lead us into that territory very often. Focusing on meaningful connections leads us to places where we can investigate and explore deeper understandings. That’s where the richness and wonder of math lies. The “why” is the place of investigation, questioning, and building perspectives. It’s an important place to be.

  2. Lauren Giordano on December 14, 2015 at 10:24 am

    Hi Steve,

    Thank you so much for sharing this blog with me. It really touched upon some of the questions I was wrestling with when planning a lesson last week to introduce mean to grade 4 students. I’m curious to know how this played out with students and how much time was spent on this? Since I am pushing into this grade 4 classroom twice as week, many decisions are out of my control. I can, however, guide decisions during weekly planning meetings and I want to be armed with this information for the next time around.

    Again, thank you for sharing.

    Cordially,
    Lauren

    • stevewyborney@gmail.com on December 14, 2015 at 4:33 pm

      Hi Lauren,
      I appreciate your note, and thank you for taking time to view the blog. The concepts in the videos do not take very long to experience separately. I recommend introducing them in the same order as they appear in the blog series: leveling off, passing out, number trading, and then the algorithm. The students will likely enjoy the leveling off, especially if you try it as a whole class. I sometimes use piles of dictionaries, or other uniformly thick books. Then students can use blocks or cubes (or anything) to level off at their desks. You can even have then begin with an already leveled off set of numbers and have them work backward to find a variety of sets of numbers that all share the same mean. The passing out activity, also will not take long, especially if you are working with whole numbers. The variations generally will come in the ways the numbers are passed out (by 2’s, 5’s etc.) Number trading typically moves away from manipulatives, so it works nicely next. Then after you teach the algorithm, you might actually want to ask students how it compares to number trading. They may find some interesting connections. None of the individual parts take very long, but when you decide to dig deep and explore the depth and richness of the connections, you should likely plan on that taking longer as students seek and discover (and possibly debate) some of the connections along the way. I hope that helps!

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