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

Objectives

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.
Bletchley Park
Dr. Sue Black
Dr. Sue Black

Dr. Sue Black has demonstrated the power of social networking. She used Web 2.0 technologies to help raise awareness of, and critical funding for, Bletchley Park, the UK World War II center for decrypting enemy messages. She has also been an active campaigner for equality and support for women in technology fields, founding a number of online networking platforms for women technology professionals. A keen researcher, Dr. Black completed a PhD in software measurement in 2001. Her research interests focus on software quality improvements. She has recently won the PepsiCo Women's Inspiration Network award, been named Tech Hero by ITPRO magazine and was awarded the first John Ivinson Award from the British Computer Society. In 2011 Dr. Black set up The goto Foundation, a nonprofit organization which aims to make computer science more meaningful to the public, generate public excitement in the creation of software, and build a tech savvy workforce. Read Sue's blog about The goto Foundation: http://gotofdn.org

@ symbol
Ray Tomlinson
Ray Tomlinson

Have you ever considered that someone, at some point, was in a position to choose what symbol would be used separate the user from their location in an email address? That person, it turns out, was Ray Tomlinson, and in 1971 he chose "@". Tomlinson is credited with demonstrating the first email sent between computers on a network, and when asked what inspired him to make this selection he said, “Mostly because it seemed like a neat idea.”

After completing his Master’s degree at MIT in 1965, Ray joined the Information Sciences Division of Bolt Beranek and Newman Inc. of Cambridge, Massachusetts. Since then he has made many notable contributions to the world of network computing. He was a co-developer of the TENEX computer system that was popular in the earliest days of the Internet; he developed the packet radio protocols used in the earliest internetworking experiments; he created the first implementation of TCP; and he was the principle designer of the first workstation attached to the Internet.

Gordon and SenseCam QUT
Gordon Bell
Gordon and SenseCam QUT

Gordon Bell is a pioneering computer designer with an influential career in industry, academia and government. He graduated from MIT with a degree in electrical engineering. From 1960, at Digital Equipment Corporation (DEC), he designed the first mini- and time-sharing computers and was responsible for DEC's VAX as Vice President of R&D, with a 6 year sabbatical at Carnegie Mellon University. In 1987, as NSF’s first, Ass't Director for Computing (CISE), he led the National Research Network panel that became the Internet. Bell maintains three interests: computing, lifelogging, and startup companies—advising over 100 companies. He is a Fellow of the, Association of Computing Machinery, Institute of Electrical and Electronic Engineers, and four academies. He received The 1991 National Medal of Technology. He is a founding trustee of the Computer History Museum, Mountain View, CA. and is an Researcher Emeritus at Microsoft. His 3 word descriptor: Computing my life; computing, my life.

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

Liz Gerber earned her MS and PhD in Product Design and Management Science and Engineering at Stanford. She specializes in design and human-computer interaction, particularly how social computing supports the innovation process. Her current research investigates crowd-funding as a mechanism for reducing disparities in entrepreneurship.
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

Cursor
James Dammann

If you have used a word processor today, moved your mouse on your laptop, dragged an object around on your smartphone, or highlighted a section of text on your tablet, you can thank Jim Dammann. In 1961 during his second year at IBM and just one year after completing his PhD, Jim created the concept of what today we all take for granted -- the cursor. This idea he documented in utilizing the cursor within word processing operations.

After retiring from IBM, Jim went on to inspire future generations of software engineers at Florida Atlantic University. His work there too demonstrated his creativity for he spent considerable effort enhancing their software engineering program by integrating ideas and feedback from local industries into the University curricular. Today, Jim lives in the Westlake Hills west of Austin Texas and spends most of his time in his art studio. He wrote and published The Opaque Decanter, a collection of poems about art, which provided a new view at part of art history.

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