MaMaMu

MaMaMu: Non-Mathematical Themes

Most people envisage the Magical Mathematics Museum being organized like a math textbook or a university department of mathematics.

... but let's organize at least part of the museum whimsically along non-mathematical themes ...

Mathematics in War
(Vauban fortifications, Ballistics, Cryptography)

Math Magic
(this image is the same if rotated upside down)
(c) Scott Kim - used with permission

Mathematics in Biology
(Osteoporosis, Viral Architecture)

Mathematics in Literature
(Jorge Luis Borges wrote mathematically witty stories like "The Lottery of Babylon".)

Mathematics in Crime
(Fingerprint uniqueness was recognized in 1788 and was
followed by development of competing classification systems.)

Mathematics in Industry
(Tire treads will be at the hub of our exploration of patterns)

Mathematics in Art

Snakes
by M.C. Escher 1969

All M.C. Escher works (c) 2008 The M.C. Escher Company - the Netherlands.
All rights reserved. Used by permission. www.mcescher.com

MaMaMu: Board Games?

Do board games have a central or peripheral place in mathematics education? Both involve problem solving, but are the problems similar enough so that proficiency in one translates to proficiency in the other?

Research in education has started to adopt the powerful scientific methodologies used in medicine. Ramani and Siegler used one of these (the Randomized Controlled Trial) to investigate the effect of a board game on the mathematical competency of pre-schoolers.

They randomly allocated pre-school children to play for one hour on either a "number board" or a "colour board". The result: mathematical competency of the children playing on the "number board" was significantly better nine weeks later.

This is a phenomenal result: cheap to implement; far reaching in its positive effects. You can read more about it in Child Development, March/April 2008, Volume 79, Number 2, Pages 375-394

There is anecdotal evidence that games are pedagogically useful well beyond pre-school and well-beyond "number boards", but quality scientific studies are lacking.

On balance it is probable that encouraging strong problem solving through games will have a positive influence on problem solving ability in mathematics. Hence, MaMaMu will strongly support and showcase board games in the expectation that quality scientific evidence will be forthcoming.

The same positive effects are also likely to be associated with computer games and puzzles. For example, Bloxorz (click on the graphic below) has rich game play that children and adults adore. The Magical Mathematics Museum will aim to add a social dimension to some of these computer games and puzzles by projecting them on large monitors and designing the space to encourage multiple children to sit together to play.

MaMaMu: A Celebration of Struggling

Struggling with tough problems is at the heart of mathematics education so the Magical Mathematics Museum will be a celebration of struggling.

SNAP Math Fairs (www.mathfair.com) have students create their own version of a quality puzzle. The students solve their puzzle, and then present the problems en masse to their parents. Few parents survive a math fair unscathed.

Game Club (www.thinkfungameclub.com) lets students loose on quality puzzles most of which have gradated levels of difficulty. Look at the amazing concentration of the grade 1 boy in the above video. If one had to choose between a child successfully memorizing mathematical facts and being able to defeat a puzzle like this - the puzzle wins hands down.

MaMaMu: Full Spectrum of Problems

Too often mathematics is presented in an unending staccato sequence:

problem -> solution
problem -> solution
problem -> solution
problem -> solution

One correct solution for every problem.

This is bogus!

Mathematics education is kept vibrant by adding authentic diversity. Some problems ...

are impossible.
have a unique solution.
have multiple solutions. The student needs to find ALL of them.
have an infinite number of solutions.
are unsolved.

One of these mini-sudokus is impossible; one has a unique
solution; one has more than one solution. Which is which?

The full spectrum of problems belong in every elementary school curriculum. That includes unsolved problems in mathematics. By junior high, students should expect that some problems that they struggle to solve will actually be impossible. That's real life!

Do numbers thrown into these rivers always end up at "1"?

This question is unsolved for one of the rivers.
For the other river, the question is regularly solved by grade 4 students.

MaMaMu: Inspired Input

The following inspirational people will be solicited for input to the Magical Mathematics Museum, but everyone who is interested is welcome to change, argue or add to the ideas presented here.

Architects:
Matt Taylor (student of Frank Lloyd Wright; designer of Davos Workspace, World Economic Forum; MG Taylor Corporation), Kazuya Morita (Kazuya Morita Architecture Studio, Kyoto)

Sculptors:
Nat Friedman (The International Society of the Arts, Mathematics, and Architecture), Bathsheba Grossman (Mathematically inspired artist)

Retailers:
Bill Richie & Tanya Thompson (ThinkFun), Carlos Neumann (Zometool Inc.), Kate Kadon (Kadon Enterprises)

Board Game Designers:
Kris Burm (top pure strategy game designer)
Reiner Knizia (top game designer)

Board Game Educators:
Scott Nicholson (games pod cast), Scott Alden (creator of www.boardgamegeek.com)

Board Game Researchers:
Geetha Ramani and Robert Siegler (demonstrated long term benefits of pre-preschoolers playing a number game. Child Development, 79(2), 375-394)

Puzzle Designers
Jerry Slocum, Scott Kim, Erich Friedman, Ivan Moscovich, Dennis Shasha

Mathemagicians
Arthur Benjamin, Persi Diaconis, Jim Totten (see comments below)

Mathemugglers
Ronald Graham

Institutional Innovators
Albrecht Beutelspacher (Mathematikum), George Thomas (MathCamp, Math Path), Andy Liu & Ted Lewis (SNAP Math Fair), Tom Rudmik (Master's Academy), Ilan Chabay (The New Curiosity Shop), Tom Rodgers (Gathering

4 Gardner)

Bill Richie (CEO of ThinkFun) suggested David Eggers as an institutional innovator. His "826 Valencia" hooks school aged students onto the literary arts by giving them 1 to 1 authentic feedback. Each expression of "826 Valencia" uses a cool storefront to advertise its presence. The original sells pirate supplies - another sells costumes for superheroes. You can see David Eggers give an inspirational talk on www.ted.com

Popularizers and Educators of Mathematics
Ian Stewart (University of Warwick), Peggy Kaye (author of "Games for Math"), Antonio Gutierrez (web site "Geometry from the Land of the Incas"), David Leeming (Editor "Pi in the Sky" published by the Pacific Institute of Mathematical Sciences), Jean Springer (Alberta Women's Network), Indy Lagu (Mount Royal College), Malgorzata Dubiel (Simon Fraser University), Richard Guy & Robert Woodrow & Bill Sands (University of Calgary).

Inspirations from the past
Júlio César de Mello e Souza (1895-1974) was a mathematician and educator who argued against classroom instruction and for mathematical laboratories and games. He achieved worldwide fame under the pen name Malba Tahan. His book "The Man who Counted" is still a best seller. His native Brazil never took his ideas on mathematics education seriously.

A second MaMaMu, located in Brazil, is to be dedicated to Júlio César de Mello e Souza.

Leo Moser (1921-1970) was a first rate mathematician at the University of Alberta. He believed children should be exposed to the unsolved problems of mathematics.

MaMaMu: Publicity Stunts

The museum should aim to grab headlines by doing unusual things.

School children roll dice to determine how the modular rooms will be snapped together (see "MaMaMu: Architectural Chaos" below) .

To repaint the external facade every few years, school children roll dice to choose the red, yellow, blue and black contribution to the final paint colour. What will it be: Hideously bilious yellow? Embarrassingly radiant pink?

Student spelunkers are hired to rescue people who get lost. This lends the museum an edge of danger and intrigue.

There is no admission price, but adult visitors must play a lottery game.

MaMaMu: Engage, Educate, Inspire - and Make Money

The Magical Mathematics Museum aims to

Engage students, teachers and the public in problem solving.

Educate students and the public in mathematics, and teachers in classroom-practical evidence-based education.

Inspire students, teachers and academics.

These educational objectives need to be realized within a sustainable business model. The key is to attract three groups of people: K-9 teachers, the public, and donors.

K-9 Teachers are attracted - First, by ensuring that a classroom trip to MaMaMu is curricularly linked (not a luxury that takes time away from curriculum.) Second, by giving their students a rich experience, and third by interacting one-on-one with the teachers - perhaps teaching them a mathematical magic trick, perhaps brainstorming a solution to an issue they've encountered in their mathematics classroom.

The Public are attracted - First, by a public persona that is mathematical, charismatic and fun (maybe a juggler or mathemagician). Second, by the desire to improve their children, and third because they have heard that MaMaMu offers something a bit different from the daily grind.

Donors are attracted - not only with attendance statistics, but by the transparent proof of success provided by continuous web-cam broadcasts. We will celebrate with our donors in a way that highlights them as innovative community leaders.

MaMaMu: Computer Programming

Introductory computer programming using the language Scratch (http://scratch.mit.edu/) will be encouraged at the Magical Mathematics Museum.

More advanced programming languages may be available in special sessions, but likely will not be a regular feature of the museum.

Other programs that allow fast access and have high motivation will also be highlighted in the Magical Mathematics Museum.

Conway's game of life is essential both because of Martin Gardner's contribution to it, and because it is so interesting for students to see the complex results of simple rules.

The editor for the game "N-ball"(www.ragdollsoft.com/nball/) which requires students to work on a Cartesian grid to design their own puzzles for each other to solve might also be a possibility.

MAMaMu: Architectural Physical Engagement

The content of the Magical Mathematics Museum will engage children mentally, but the architecture should engage them physically:

Playgrounds for the child-like adult ...

Tantalizing peepholes for mathematical voyeurs ...

Labyrinths & mazes for GPS savvy children...

Squeeze passageways for the escape artist ...

Gallery climbways to show-off proofs, mathematical objects, mathematics history, and highlight talent from local schools ...

MaMaMu: Architectural Exposure & Intimacy

The architecture for the Magical Mathematics Museum should include both exposed and intimate spaces.

Exposed macro-spaces for

Public problem solving
Hands-on workshops
Spying with spy ware
Broadcasting of International gaming events

Photograph on the right shows Spassky (U.S.S.R.) and Fischer (U.S.A.) under the International Spotlight.

Secluded bunk-bed micro-spaces for

Intimate problem solving
Student pod casts presenting problems and hints

Photograph on the right shows grade 1 engineers spanning the micro-space beneath their desks with a magnetic spider web.

Let's play with degrees of intimacy like Kazuyu Morita.
This pod is from his architecture studio in Kyoto. It is both exposed and intimate at the same time.

Kazuya Morita's web site is: http://morita-arch.com/work/c-pod.html

MaMaMu: Architectural Furniture

The architecture of the Magical Mathematics Museum should be ambiguous - right at the

intersection of architecture and furniture.

The cat-house should be an inspiration. Children like this tactile architecture so let us concentrate on relatively inexpensive, internal, tactile architectural experiences - foregoing stunning, but expensive external facades.

Verner Panton (1926-1998) was an adept at exploiting the intersection of architecture and furniture. I encourage you to check out Verner Panton's web site pictured below: www.panton.ch/design

MaMaMu: Architectural Disorientation

One of the purposes of the Magical Mathematics Museum architecture is to disorient visitors.

Let's add the following:

Awkwardly shaped rooms
Sloping floors
Irregular steps
Skylights that lack external reference points
Movable walls so repeat visitors remain disoriented
Shadow walls that also allow children to explore 3D projections
Mirrors that also allow children to explore symmetry

Here today - gone tomorrow. That would disorient visitors too much, but let's fit MaMaMu into an 18-wheeler just as a 3D mathematical packing exercise.

MaMaMu: Architectural Chaos

When you ask people to think of a Mathematical Museum, most envisage a highly symmetric and ordered architecture.

Instead, MaMaMu explores chaotic architecture.

One example of chaotic architecture would be to design two rhombus-shaped rooms which can be snapped randomly together…

These rooms would be difficult for people to navigate through. This is desirable. We want to disorient our visitors.

This chaotic pattern was discovered by Roger Penrose.
You can find more about it here: http://en.wikipedia.org/wiki/Penrose_tiling

The Magical Mathematics Museum is intended as a tribute to the great popularizer of mathematics, Martin Gardner. These blog entries are a first iteration... Change them, argue with them, add to them.

If you would like to learn more about Martin Gardner, please read the excellent interview by Colm Mulcahy which can be found here: www.maa.org/columns/colm/cardcolm200610.html and watch David Suzuki's program on Martin Gardner: http://concise.britannica.com/new-multimedia/mp4/newdim025.mp4

Martin Gardner

Email: gamesbygord@gmail.com