The mandate of the SNAP Mathematics Foundation is to encourage the development of mathematics learning resources at the classroom level with very little retraining of the teaching staff, with very flexible budgets, and by utilizing the energy and natural curiosity of the students themselves.
The SNAP Mathematics Foundation is a non-profit organization whose members are educators from all levels and from a variety of occupations.
Our name is an acronym for our guidelines for an unconventional type of math fair. However, the SNAP foundation is not just about math fairs. It is based on the idea that learning mathematics is accomplished by solving meaningful, interesting problems.
Our supporters
SNAP received its initial funding from the Canadian Mathematical Society and from private donations. PIMS, the Pacific Institute for the Mathematical Sciences, has been a long time financial supporter of our math fairs. BIRS, the Banff International Research Station, has provided funding for the BIRS math fair workshops that have been held in Banff on a regular basis. Currently, our major supporter is Thinkfun -- a company that provides excellent a varietry of excellent puzzles.
Who are we?
The members of the SNAP foundation are educators from all levels and from a variety of occupations. At present, our board members include:
- Mike Dumanski, Edmonton Catholic Schools, (DumanskiM@ecsd.ca).
- Tiina Hohn, Grant MacEwan College, Edmonton, (hohnt@macewan.ca).
- Indy Lagu, Mount Royal College, Calgary, (ILagu@mtroyal.ca).
- Ted Lewis, Prof. emeritus, U of A, (tlewis@math.ualberta.ca).
- Andy Liu, University of Alberta, Edmonton (aliu@math.ualberta.ca).
- Bill Ritchie, CEO, Thinkfun, (BillR@thinkfun.com).
- Wen-Hsien Sun, CEO, Chiu Chang Publishers, Teipei.
- Tanya Thompson (tcthompson@hotmail.com), Collingwood, Ontario.
- Jim Timourian, Prof. emeritus, U of A, (jgt@sassoun.com).
- Paul Vaderlind, Stockholm University, (paul@math.su.se).
Curriculum connections
The mathematics curriculum may vary from one jurisdiction to another, so we want to avoid tying the SNAP math fair to any particular curriculum. However there are certain aspects of a SNAP math fair that are common to every curriculum.
Problem solving
A SNAP math fair is problem based, and a key component of a SNAP math fair is the problem solving that takes place in preparation for the math fair. The focus is on good, challenging, age-appropriate and engaging puzzle problems.
Our teachers are organizing their students into math problem solving teams to dicuss how to solve a math problem and to explore the different ways in which a problem can be solved. As an addititonal challenge we provide more math problem exploration through preparation for a school math fair. Nicole Beaudoin
Assistant Principal from Edmonton, Canada
Math fair puzzles should require a variety of reasoning skills: recognition of patterns, use of a simple mathematical principal. The puzzles may require exploration and conjectures.
There may often be occasions when trial and error will lead a student to a solution even 'though there is a deeper underlying mathematical fact that would have led more efficiently to the solution. In this case, once the student has already solved the puzzle, it is difficult to think of a more compelling motivation to explain the concept, or to show why it is useful.
As a particular example, consider the following problem from our puzzle pages, which is considered to be a puzzle suitable for the lower grades:
Place the numbers from 1 to 6 in the circles below so that every three numbers in a straight line have the same sum.
Most children will solve this by trial and error and you should praise their solution even if you didn't expect this approach. In the process of solving it, many will discover that the 7 is unimportant — that they really only have to work with the numbers from 1 to 6, and that they need to partition these six numbers into three pairs each of whose sum is the same.
This will afford them practice in addition. However, they may not recognize that there is another approach: the sum of the numbers from 1 to 6 is 21, and so the sum of the three pairs must be 7, that is, 21 divided by 3. Even if they used a trial and error approach, there is an opportunity to bring in mathematics in a meaningful way when discussing their solution with them.
Communication
Mathematics is not an isolated activity. Students need to learn how to communicate mathematical ideas, questions, and solutions. They should learn how to do this in written form and in conversation, using their own language. When the math fair is presented to the public, the students have an opportunity to practice their communication skills with the visitors.
SNAP math fairs include a hands-on component as an integral part of the investigative strategy and explanation of the problems presented. Most of the time this is done with manipulatives that students build themselves. This helps the students gain ownership of the problem far beyond anything commercially available in the market, and it helps them understand that models, diagrams, and manipulatives can help them communicate.
Their presentations must be attractive, informative, and flexible to accommodate different levels of difficulty.
Other connections
Parts of the above are sometimes stated as separate curriculum objectives. For example, a SNAP math fair is not specifically intended to enhance computational skills. There are, however, certain puzzles that encourage this, but not all of them do. Also, the communication component of the SNAP math fair frequently involves what is commonly thought of as "representation": the students usually have to present the problem in a different setting than it was when they solved it.
In preparing their presentations, students will make connections between mathematics and other disciplines. They helps them understand that mathematics is a useful part of everyday life. One teacher put it this way:
"I like to think of the math fair as providing students with an opportunity to do the problem-based mathematics for a particular purpose and to a specific audience, like the language arts. The students understand this line of thinking, and eventually begin to understand that mathematics is no different than any other discipline."
Suhana Kadoura
Teacher from Ottawa, Canada
The SNAP approach and "inquiry-based learning"
The SNAP approach to problem solving encourages students to develop the solution on their own rather than following a set template. It is clearly an "inquiry-based learning" strategy, but the intent and scope is limited. We do not advocate that all mathematics be taught this way, but we believe it can become an invaluable part of the problem-solving component of the math curriculum.
In preparing for the math fair, the student's activity is focussed on a specific problem. The purpose is to have the student involved in problem solving in a meaningful way. That alone is sufficient. The problem may encompass only a very narrow part of mathematics, it need not reveal a broad concept or fundamental mathematical principle.
During the problem solving phase in preparing for the math fair, there will be times when the teacher helps the student. However, after the student has solved the problem, there is a significant role reversal: at the math fair itself, the students become the teachers, and they help passers-by with the problem.
Although each student in the math fair is primarily interested in a single problem, experience suggests that success at the math fair translates into success in the rest of the math curriculum. Teachers have reported that participation in a math fair reverses a negative attitude and starts the student on a successful road. In some cases, the reversal is dramatic.
Some history
The first SNAP type math fair was designed by Mike Dumanski and Andy Liu in 1997-1998. Mike was vice-principal of Our Lady of Victories Elementary School, and Andy was a professor in the Math Department at the University of Alberta. Andy has won many national and international teaching awards, and is well-known for making mathematics exciting for children. The staff at Our Lady of Victories found that the typical science fair was too competitive and that parents were the ones who did most of the project. They approached Mike about doing another activity, and Mike thought they could do something with math. "I really didn't know where to go, so I called the University of Alberta and they put me in touch with Andy." Andy and Mike then worked out a set of guidelines for the math fair, and these are essentially the ones that we have been using ever since.
At the same time, Jim Timourian was the undergraduate chair in the mathematics department at the University of Alberta, and he was worried about the state of Math 160, a math course that was offered to preservice Elementary teachers. Ted Lewis was slated to teach the course in the second term. At a meeting with Andy and Ted, it was suggested that the students in Math 160 could do a math fair for themselves.
By coincidence, Ted had contact with a teacher at Parkallen Elementary School. A deal was struck that the Math 160 students would bring their math fair to Parkallen school, and that in return, the Parkallen students would hold their own math fair and invite their parents. The math fairs at Our Lady of Victories and Parkallen were unbelievably successful, and since then a large number of schools in the Edmonton region have adapted the SNAP math fair to their needs. The SNAP program has been spread through workshops and conferences, and mainly by teachers themselves.