Making a
Math in the Mall Display
by
Malgorzata Dubiel & Katherine Heinrich
Department of Mathematics and Statistics
Simon Fraser University
Burnaby, British Columbia, V5A 1S6
Fax: (604) 2914947
Introduction: How did it start?
Our work in popularizing mathematics through displays with handson
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 studentteachers 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:
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 threedimensional 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 lefthanded 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
Platonic solids
Forms to make them, tools as above, and lots of models.
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.
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.
Mobius bands
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.
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.
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.
Computers with interesting software
Examples are tetris, fractals, Lifelab,
Geometer's Sketchpad etc.
Videos
Many interesting math videos are available from various
sources, including videos about platonic solids and others from Key
Curriculum Press (tollfree number 18003387638). 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 workstudy 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 Tshirts 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
Tshirts 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 multidisplay,
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:
 B. Bolt, Mathematical Cavalcade, Cambridge University Press.
 B. Bolt, Mathematical Funfair, Cambridge University Press.
 B. Bolt, More Mathematical Activities, Cambridge University Press.
 B. Bolt, The Amazing Mathematics Amusement Arcade, Cambridge
University Press.
 M. Gardner, Mathematical Carnival, MAA.
 M. Gardner, Mathematical Magic Show, MAA.
 M. Gardner, Mathematical Circus, MAA.
 M. Gardner, The Scientific American Book of Mathematical Puzzles
and Diversions, Simon and Schuster, 1959.
 M. Gardner, The Second Scientific American Book of Mathematical
Puzzles and Diversions, Simon and Schuster, 1961.
 M. Gardner, Perplexing Puzzles and Tantalizing Teasers, MAA.
(The easiest book for younger children.)
 M. Gardner, Riddles of the Sphinx, MAA.
(For older children, grade 7 and up.)
 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.)
 M. Burns, The I Hate Mathematics! Book, Little, Brown and Company.
 M. Burns, Math for Smartypants, Little, Brown and Company.
 K. Heinrich, Science Awareness Week Project CMS Notes, Vol.24
#4, MayJune 1992.
 E. Muller, Math Trails, CMS Notes, Vol.25 #2, March 1993.
 E.R. Williams, Math in the Mall, CMS Notes, Vol.25 #1, JanuaryFebruary 1993.
Some interesting mathematics trails:
 A Mathematics Trail around the City of Melbourne, by Dudley Blane
and Doug Clarke, The Mathematics Education Centre, Monash
University, Melbourne.
 Niagara Falls Math Trail, by Eric Muller, Department of
Mathematics, Brock University, St. Catherines, Ontario.
 The Village Mall Mathematics Trail, by Ed Williams, Department of
Mathematics and Statistics, Memorial University of Newfoundland,
St. Johns, Newfoundland.
 Loon Lake Mathematics Trail, by Malgorzata Dubiel and Katherine
Heinrich, Department of Mathematics and Statistics, Simon Fraser
University.