Making a
Math in the Mall Display

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by

Malgorzata Dubiel & Katherine Heinrich

Department of Mathematics and Statistics
Simon Fraser University
Burnaby, British Columbia, V5A 1S6

Email: dubiel@sfu.ca

Fax: (604) 291-4947

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Introduction: How did it start?

Our work in popularizing mathematics through displays with hands-on activities began with the teaching of our course Mathematics for Elementary School Teachers (MATH 190). Our goal was and is to change the attitudes of student-teachers to mathematics. Our strategy is to prepare (and later let students prepare) various projects which would allow them to see a glimpse of what we see in mathematics: the beauty of it; the excitement and amazement upon seeing something unexpected; the mathematics around us; and the people of mathematics.

The projects proved very succesful and we started to think about reaching younger children. Our first opportunity was the Homecoming event organized for the 25th anniversary of Simon Fraser University in September 1990. We put up a display which we called Is this Math?, using some of our Math 190 projects; puzzles, games, geometrical models, videotape with a week's worth of Square One TV (with permission of PBS), and a display of our choice of books. The display was even more succesful than we expected. When colleagues from computing science complained that our display was diverting traffic from their exhibits, we knew we were on the right track. The president of SFU visited the display and was sufficiently impressed to promise funding a shopping mall version.

For our first foray outside the university we chose Lougheed Mall - a large mall in Burnaby, close to SFU and to several elementary schools. While preparing the event, we were contacted by organizers of the Science and Technology Week 91 and, at their request, agreed to repeat the display three weeks later in another Burnaby mall, Metrotown. Since then, our mall appearances have been restricted to Science and Technology Weeks and similar events, as this makes the organization much easier. We also take some of the activities to schools or occasionally have groups of children visit the Department.

Suggested activities for a Math in the Mall display

Listed below are some activities we found succesful:

1. Kaleidocycles and hexaflexagons

   We discovered them through Martin Gardner and Doris Schattschneider books. You can copy our designs, which are ready to cut, glue and decorate, or you can construct your own. Decorating is an important part of the process as it allows the child to discover the symmetries of the object, and is the main part of the magic. The instructions are given on a separate page, but here is some additional advice:

   • Construction paper is not a suitable material: it is too soft and falls apart quickly - too much effort wasted. Manilla tag is a reasonably inexpensive alternative. Ours is called cover stock. Glue: for hexaflexagons, any glue stick or school glue will do. For kaleidocycles, we foud only rubber cement acceptable, since this model requires some elasticity to turn well. Smaller children need to be supervised or helped when working with this glue.

   • Hexaflexagons are the easier of the two, and quicker to make. However, before gluing you have to make sure that you have three pairs of triangles, separated by folds, on each side - otherwise it will not work. Do not start colouring before constructing your hexaflexagon: cut, fold and glue first, then decorate. If a design on a hexagonal face is a picture, or something which makes a distinction between the centre and the outside of the face, the result will be more surprising and magical.

   • Kaleidocycles: Here, you can colour first and then cut and glue. The form creates a three-dimensional object, which has four faces. Like with hexaflexagons, some designs will make a more interesting model than others, but you need to see first which triangles will show on each face - you need to make one model to understand it. When you cut the form, score all the lines and fold according to the instructions, unfold and try to observe what is happening.

   • Necessary tools:
     • scissors (have a pair of left-handed ones)
     • knitting needles and rulers - for scoring the edges
     • glue: rubber cement for kaleidocycles, to allow for flexibility, and glue sticks hexaflexagons
     • coloured markers for decorating

2. Platonic solids

   Forms to make them, tools as above, and lots of models.

3. Drinking straw models

   
   Flexible plastic drinking straws are used to make geometrical models - the icosahedron being the most popular choice. You need several bags of straws (Safeway sells great straws in four solid neon colours under its own brand, if you can find them), and masking tape - scotch tape does not work well on some types of straws, apart from being much more expensive. You cut through the shorter end of a straw, squash it to make it narrower and insert it into the longer half of another. When you join three straws together, you make a triangle, four - a square. The polygons made in this way can be assembled using masking tape to make three - dimensional models. This activity is very popular with small children, but everybody loves it, including our helpers, who always manage to build a strange object during slower moments.

4. Pentagonal stars

   A Math 190 student from Singapore taught us how to make these. The basic idea is that if you tie a knot on a rectangular strip of paper and flatten it, you get a regular pentagon. When you fold the strip of paper around itself several times and then push the edges in to pop it out you get a pentagonal star. We use gift wrapping paper cut into long strips of various widths. You have to make sure the strip is very even, and discover by trial and error how many times to fold so your star pops out well - this depends from the type of paper used, and the width of the strip. The folds need to be tight. Notice also, that if you fold the paper tightly and carefully, it knows where to go. Common mistake is to force the paper to fold along a wrong side.

5. Mobius bands

6. Puzzles and games

   You can find them in the Science Word gift store, some toy stores, Moyers' Teacher Store and Kids are Worth it!, Science and Nature and many others, but it may take time to build your collection. There are different ones for every age. Mathematicians love them: they teach strategies, problem solving, geometric intuitions and much more! Erick Wong, who last year, at 17, got a degree in math and computing science at SFU, told a Vancouver Sun reporter who intervieved him afterwards that his love of mathematics started with puzzles his mother was giving him in elementary school. The card game described on another page teaches an important concept in mathematics: pattern recognition. It is really addictive! You can also buy a similar one, called SET, in Moyers' Teacher Store and Kids are Worth it!, and possibly other places.

7. Posters

   Have lots of poster boards and posters on geometry, Escher, math careers, your department, math humour, activities one does not usually associate with mathematics (eg. knitting, design, architecture) etc. There are many good posters available. Start collecting now.

8. Books and mathematical toys

   A display of your favourites (be careful - you may lose them). Or prepare a list of books, resources and places to get them, to give to teachers and parents. See the list of some of our favourites at the end.

9. Computers with interesting software

   Examples are tetris, fractals, Lifelab, Geometer's Sketchpad etc.

10. Videos

    Many interesting math videos are available from various sources, including videos about platonic solids and others from Key Curriculum Press (toll-free number 1-800-338-7638). You can also get permission from PBS to show recordings of Square 1 TV or other programs - they had an interesting Nova program about Fractals. Malls often will let you VCR for the day.

Help with the display

We recruit colleagues and graduate and undergraduate students. Students from Math 190 often like to help, partially because they have to demonstrate volunteer work for the admission to professional programs in education. Talk to the mathematics specialists in the Faculty of Education. You will not have difficulties in finding help when repeating your display: people who help once usually come back - they have fun participating.

Various work-study programs for undergraduate students have been used by us to pay student assistant for work done in preparing displays and presenting them to the public. We also get Science and Technology Week T-shirts to give to volunteers.

Financing

Approach anybody you can think of: your department/university/college; professional organizations (CMS has a special fund for this activity during Science and Technology Week - see references 10 and 12), provincial (state) ministries of education, advanced education, science and technology; the mall (go to Promotions Director or similarperson), or other facility in which the display is to be held. In Lougheed Mall we got a 40% discount in a stationery store (Willsons). If there is a science store in your mall, approach them for cooperation.

In Canada, Science and Technology Week provides easier access to help with organizing, financing and advertising, as well as attractive T-shirts for volunteers and as prizes.

Another possibility is Science Fairs: we've been invited to a few of them recently.

Advertising

Local community papers and school boards are the most effective instruments, but try everything available. Most community papers are very enthusiastic, as are some local radio stations. Your college/university Media office will help with advice and press releases.

Do not neglect word of mouth!

Math in the Malls across Canada

Kathy Heinrich described our displays in the article Science Awareness Week Project, in the May - June 1992 issue of CMS Notes. As the then chair of the CMS Education Committee, she invited mathematics departments from other universities across Canada to organize such activities duringScience and Technology Week, suggesting that some funding might be available from CMS.

The first response was from the Department of Mathematics and Statistics at Memorial University. In October 1992, as a part of Science and Technology Week, Ed Williams and Bruce Shawyer organized an event in the Village Shopping Mall in St. John's. The display included several fun activities aimed primarily at children aged 10 to 15: How to get to second base, a Mall Math Trail, a Math Challenge with a prize for the best solution, and many others. The exhibit was extremely well received and became an annual event. In 1994 it was expanded to a Math and Science in the Mall multi-display, with twelve different group participating, and attracted between four and five thousand people.

The Department of Mathematics, Statistics and Computing Science at Dalhousie organized a Math in the Mall display in October 1993, in the Halifax Shopping Centre. It included computer and video displays, and exhibits borrowed from a local science museum: a giant Tower of Hanoi, and other games and puzzles. There was no display in 1994, but there are plans for 1995. For information contact R.P. Gupta or Richard Nowakowski.

Simon Fraser's Mathematics and Statistics Department visits at least two malls yearly. In 1994 we were joined by the Physics Department with a very popular holography display, and by the School of Engineering. The activity is also spreading to smaller communities. Salmon Arm had a mall display in 1994. Prince George is interested - there it will possibly be a cooperative effort between Prince George Children's Festival, the Fort George Museum, and the University of Northern BC.

Final suggestions

Don't try to be too ambitious at first. Select 2 - 3 activities and have lots of models. Increase the activities with the experience and/or the number of helpers. Make sure you test all the activities yourself first!

Be visible - have a big sign, one or two big models, and posters - make your own, especially about geometry, design, mathematical people, jokes etc. Also, make sure you choose the location well. Be in the centre of the mall or near a major entrance! Some malls, though, have restrictions on the height of signs and poster boards.

• Have several long tables and chairs, so there is a lot of working space.

• Have lots of handouts for parents and teachers.

• Discuss the local mall requirements and rules - for example, they usually require that you carry sufficient insurance. Your university usually provides for such events. If you want to bring computers or VCR monitors, make sure there is a power outlet nearby; bring your own power bar, ask the mall for an extension cord or bring your own if required.

• If you are ambitious and have enough help, consider organizing a Mathematics Trail through the Mall. (see references 12, 13) and the list of our favourite trails.

Suggested readings

The list below includes both articles about math displays and trails, and a selection of our favourite books:

1. B. Bolt, Mathematical Cavalcade, Cambridge University Press.

2. B. Bolt, Mathematical Funfair, Cambridge University Press.

3. B. Bolt, More Mathematical Activities, Cambridge University Press.

4. B. Bolt, The Amazing Mathematics Amusement Arcade, Cambridge University Press.

5. M. Gardner, Mathematical Carnival, MAA.

6. M. Gardner, Mathematical Magic Show, MAA.

7. M. Gardner, Mathematical Circus, MAA.

8. M. Gardner, The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, 1959.

9. M. Gardner, The Second Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, 1961.

10. M. Gardner, Perplexing Puzzles and Tantalizing Teasers, MAA. (The easiest book for younger children.)

11. M. Gardner, Riddles of the Sphinx, MAA. (For older children, grade 7 and up.)

12. D. Schattschneider, W. Walker, M.C.Escher Kaleidocycles, Pomegranate Artbooks, 1987. (A book with several very ineresting ideas and wonderful models of kaleidocycles and solids to make, decorated with Escher pictures - definitely worth buying! We buy a new one every two years.)

13. M. Burns, The I Hate Mathematics! Book, Little, Brown and Company.

14. M. Burns, Math for Smartypants, Little, Brown and Company.

15. K. Heinrich, Science Awareness Week Project CMS Notes, Vol.24 #4, May-June 1992.

16. E. Muller, Math Trails, CMS Notes, Vol.25 #2, March 1993.

17. E.R. Williams, Math in the Mall, CMS Notes, Vol.25 #1, January-February 1993.

Some interesting mathematics trails:

1. A Mathematics Trail around the City of Melbourne, by Dudley Blane and Doug Clarke, The Mathematics Education Centre, Monash University, Melbourne.

2. Niagara Falls Math Trail, by Eric Muller, Department of Mathematics, Brock University, St. Catherines, Ontario.

3. The Village Mall Mathematics Trail, by Ed Williams, Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, Newfoundland.

4. Loon Lake Mathematics Trail, by Malgorzata Dubiel and Katherine Heinrich, Department of Mathematics and Statistics, Simon Fraser University.