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Mathematical Association of America -- American Mathematics Competitions

Math Club

Organizaton

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Academic Guidelines

The math club should have a balanced focus between mathematical enrichment topics and mathematical problem-solving, with the balance determined by both the interests of the participants and the club sponsor.
In both cases, the students must be actively involved in the problem-solving and topic presentations. This guideline means that students have to be able to explain their problem and to demonstrate the solution or topic to the others in the club.

Selecting problems and solutions may depend on the goals of the math club sponsor and the problem-solving ability of the club members. Some sponsors will specifically select topics and problems of an appropriate difficulty and assign them. Other may elect to use a cookie-jar approach where students select at random from a larger collection.

All students should be encouraged to participate and benefit.

Even if a math club is officially noncompetitive, informal competition among students will occur. The participants will quickly recognize who among them are good problem solvers, who are quick problem solvers, who are deep thinkers about mathematical problems, and who can explain things well. But this sort of competition is healthy, friendly and constructive, and even leads to cooperative efforts among the participants.

Administrative Guidelines

  1. All club members should be participants.
  2. It is ideal for students to work together in small groups.
  3. Providing snacks is an excellent incentive for students to attend.
  4. Change the location of your sessions to allow for a less regimented, more relaxing atmosphere.
  5. Schedule the meetings weekly, even if you dont have a special event planned. The first few meetings should be informal. Hold icebreakers that allow students to get to know each other.

One way that Sliffe Award winning teachers have encouraged a high level of participation is to have students work in groups of (for instance) 5 on a group of 5 problems. (Use an array of AMC problems of varying difficulties, for example.) Each of the 5 students in the group should be able to present and explain any one of the 5 problems assigned to the group. This way the students learn that part of doing mathematics is sharing insights, ideas, and experiences solving similar problems. Teamwork develops as the students work on topics and problems. Students who have difficulty in solving a problem may have other skills that result in a clearer explanation or effective presentation of a topic.

Informal surveys of Sliffe Award winning teachers show that they are about evenly divided among having Math Club or AMC contest practice sessions before and after class. Much depends on the specific school schedule and other extra-curricular activities. These teachers suggested having doughnuts at before-school gatherings and pizza as an incentive for after-school gatherings.

Club Advisor:

  • Keep a short journal:
    • Make notations each week for what worked well, and what didn’t in the practice sessions.
    • The format and rules of any meets and contests your students participate in.
    • If you can, keep a copy of the questions posed at each event, to use to prepare your students the next year.
    Next year you can look this over, and give guidance to your students. before an event, going over the rules, and any tricks you thought up which might help this year.
  • Find alternate means of transportation for students who normally need to take the bus, or ride in car pools - this may mean helping parents organize a math carpool for the mornings or evenings they have meetings
  • Get help by having other teachers assist when you need an extra hand at the practice sessions, and get a parent volunteer list which you can call on to get help with arrangements or other details (like a scrapbook, awards program, handle press/newsletter articles, etc.)
  • If there is a Math Department at a local College or University, you can see if they sponsor a student MAA chapter, which could take on your club as a community service project. A listing of these is at <http://www.maa.org/students/chapter_index.html>.
  • Check on AMC’s Math Club website for math events and meets in your area

Publicity and the Math Club:

To encourage new students and continue participation once they have become regulars, strong local support is needed. The rewards of participation should be visible and enumerated upon to invigorate the program.

  • Set up a display when school opens in the fall with T-shirts, photos of last years activities, posters or banner names of events you will be participating in this year, and any trophys you have.
  • Design posters for your first meeting with interesting math questions and post them all over school. Refer students to the first meeting for the answers.
  • Have afew of your returning students design a skit for a beginning of the year school assembly or pep rally.
  • Give a presentation to the school parents organization, outlining how participation in a math club will help their children. You can also request funds for event registrations from PTO’s/PTA’s.
  • Keep parents up-to-date on the schedule for all the clubs travel plans: meets, field trips, social gatherings, etc. and arrange for a sign up if you will need help with transportation.
  • Send regular parent emails or update fliers, have regular team reports at PTO/PTA, openhouses and the school newsletter.
  • Use the local and school newspapers to hilight club events and contests they attend. Use individual students to communicate their success stories.
  • Organize a pep rally for your math team, or have them included in another pep rally.
  • Be sure to recognize the students a school award programs.
  • Encourage teachers of lower grades to look for students who seem to like, or are good in math, to encourage them to participate in the club’s activities.
  • Take plenty of pictures during practice sessions and at meets/contests. Keep these photos and any articles and make a scrapbook. Then when local press would like a picture, you would have a variety to choose from.

Problem-solving:

Mathematical problems from the (book and web) resources suggested elsewhere in this manual are not always immediately solvable by all clubs, or all club members. Even the sample problems included in this package are not always immediately solvable. Here are some problem solving coaching tips:

  • Replace large numbers with smaller ones. Use numbers that have fewer factors, or are easily divisible.
  • Replace continuous variables with discrete variables. For example: “If a problem involves time or distance which are continuous variables, can they substituted by variables that vary in discrete steps?”
  • Reduce the number of pieces in play. Does the problem change significantly, for example: “If ten individuals are replaced with five?”
  • Make a smaller playing-field. For instance, if the problem is on an 8x8 checkerboard, is the problem easier on a 4x4 checkerboard?
  • Make a manipulative to illustrate the problem, for instance use beans or chips for counting problems, make cardboard constructions or wire sculptures for space geometry problem
  • Use an interactive computer program (such as Geometer’s Sketchpad) to illustrate the problem dynamically.
  • Use a calculator or computer to simulate, especially with probability problems.
  • Remove time or step restrictions, for instance if a problem asks for solutions with a specific number of steps.

Ideas to consider when preparing for the AMC contests:

  1. How will you choose your participants for the AMC (8, 10, 12)? Some teachers involve whole grade levels, some teachers involve specific classes, some teachers pick their schools most talented students, etc.
  2. What resources do you use to train your student participants for the AMC (8, 10, 12)?
    • Prior years’ tests in booklet form
    • Contest Problem Books I-VI from MAA Publications
    • Other problem and contest books (which ones?)
    • Text books and curricular resources
    • Materials available on the Web.
  3. Will you prepare your own solutions and training materials for training your student participants? Will you provide the AMC Solution Pamphlets or have the students create their own solutions?
  4. How will you integrate your current textbooks and curricular materials with your contest training, if at all?
  5. When will you and your participants prepare?
    • Before school?
    • After school?
    • During school – (e.g. Lunchtime, study period, special class)
    • Math Club or similar extracurricular group?
  6. Will you use the AMC (8, 10, 12) to prepare your students for other contests and activities or vice versa?
  7. Will you train students in cooperative groups or other collaborative strategies for an individually based competition such as the AMC (8, 10, 12)?
  8. Do your students cooperatively help each other with training, or do students compete independently, or a mix of the two strategies?
  9. Will you have timed “practice contests” to prepare your students for the actual competition? Will you use previous copies of AMC contests to provide these practice contests?