Recursion: Smaller Sibling Pyramids

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Lesson synopsis

humanRecursion, Iteration (Looping), and Concurrency. In the first of two sessions (at most an hour each), students are asked to calculate a simple summation by themselves, based on a procedure they are given. Then, through a guided role-playing procedure, students are asked to do the same problem by pushing a sub-problem off onto a ‘little sibling’. In the second session, they use a divide-and-conquer approach to understand a simple formula for summation. During this session they also talk about the big ideas behind these three problem solving methods.

Age Levels

8 - 13 years


Introduce students to:
how arithmetic sequences solve real world problems
tail-end recursive algorithms for arithmetic series
a divide and conquer approach that leads to a simple formula
informal ideas about time complexity.

Anticipated learner outcomes

Students will be able to describe how to solve an arithmetic sequence summation problem:
by doing it again and again (non-concurrent iteration)
with a smaller sibling (tail-end recursively)
articulate that both methods take the same number of steps, but recursion is less work for the individual
divide and conquer has a surprising outcome – namely a formula that can be calculated in only a few steps.

Optional Writing Activity

This activity introduced the idea of how to efficiently calculate an arithmetic series, such as 1+2+3+4. This could be used to calculate the simple human pyramid where one person is added as support for each layer. Invent your own problem that produces a different arithmetic pattern such as 1,5,9,13,17. Ask someone in your class to solve it by simple addition, by recursion, and to see if they can come up with a formula based on divide and conquer.

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Douglas Engelbart
Douglas Engelbart

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Liz Gerber - Image credit Lisa Beth Anderson
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Liz Gerber - Image credit Lisa Beth Anderson

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Gerber's work funded by the US National Science Foundation and the National Collegiate Inventors and Innovators Alliance has appeared in peer-reviewed journals, including Transactions on Computer Human Interactions, Design Studies, and Organization Science.
As an award-winning teacher and researcher, Liz has touched the lives of more than 6,000 students through her teaching at Northwestern's Segal Design Institute and Stanford University's Hasso Plattner's Institute of Design and through her paradigm-shifting creation, Design for America, a national network of students using design to tackle social challenges.

Image credit - Lisa Beth Anderson

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