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.
RISC processor
John Hennessy
John Hennessy

Have you ever wondered how computers can execute complex commands in mere seconds? John Hennessy is a pioneer of reduced instruction set computing (RISC) architecture which employs small, highly-optimized sets of instructions to greatly enhance computer performance. He was instrumental in transferring the technology, specifically MIPS RISC architecture, to industry. He co-founded MIPS Technologies and co-authored the classic textbook with David A. Patterson, on Computer Architecture.

As Stanford faculty he rose to be the Chairman of the Computer Science Department, Dean of the School of Engineering, then Provost and finally the President of Stanford in 2000 (and till date). Hennessy holds a Master’s and Ph.D. in Computer Science from SUNY Stony Brook. He is an IEEE Fellow and was selected to receive the IEEE Medal of Honor in 2012. Hennessey also launched significant activities that helped to foster interdisciplinary research in the biosciences and bioengineering at Stanford.

Router
Sandra Lerner

It is difficult to imagine a time when computers were not capable of sharing information and resources with great ease. Sandra Lerner pushed the boundaries of network computing as one of the co-founders of Cisco Systems, which introduced one of the first commercially viable routers. The router was born while Sandra was working at Stanford University in the 1980’s after earning her Master’s degree there in Computer Science. To avoid the tedious task of transferring information between computers using floppy disks, she and co-founder of Cisco, Leonard Bosack, created a local area network, or LAN, between their campus offices using a multiprotocol router that Bosack developed. Shortly thereafter the pair started Cisco Systems, and began selling the router which was a success, because it could work with so many different types of computers. After Leaving Cisco in 1990, Lerner started the trendy cosmetics company Urban Decay and became a philanthropist and avid activist for animal rights.

CGA palette
Mark Dean

If you have ever used a PC with a color display you have been acquainted with the work of Mark Dean. After achieving a Bachelor’s degree in electrical engineering from the University of Tennessee, Dean began his career at IBM. Dean served as the chief engineer on the team that developed the first IBM PC, for which he currently holds one third of the patents. With colleague Dennis Moeller, he developed the Industry Standard Architecture (ISA) systems bus, which enabled peripheral devices such as printers, keyboards, and modems to be directly connected to computers, making them both affordable and practical. He also developed the Color Graphics Adapter which allowed for color display on the PC. Most recently, Dean spearheaded the team that developed the one-gigahertz processor chip. Dean went on to obtain a MSEE from Florida Atlantic University and a Ph.D. in electrical engineering from Stanford University. He is a member of the National Academy of Engineering, has been inducted into the National Inventors Hall of Fame, and is the first African-American IBM Fellow.

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

Punch card from a COBOL program
Jean Sammet

Jean E. Sammet was one of the first developers and researchers in programming languages. During the 1950’s - 1960’s she supervised the first scientific programming group for Sperry Gyroscope Co. and served as a key member of the original COBOL (COmmon Business-Oriented Language) committee at Sylvania Electric Products. She also taught one of the first graduate programming courses in the country at Adelphi College. After joining IBM in 1961, she developed and directed the first FORMAC (FORmula MAnipulation Compiler). This was the first widely used general language and system for manipulating nonnumeric algebraic expressions. In 1979 she began handling Ada activities for IBM’s Federal Systems Division. Ada is a structured, object-oriented high-level computer programming language, designed for large, long-lived applications, where reliability and efficiency are paramount. Jean has a B.A. from Mount Holyoke College and an M.A. from the University of Illinois, both in Mathematics. She received an honorary D.Sc. from Mount Holyoke (1978).

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