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Think Math Contests!

By Howard and Susan Richman
Printed in Practical Homeschooling #37, 2000.

Contests that add pizzazz to math study.
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Howard and Susan Richman

Picture this. A group of six junior-high homeschoolers are bent over my large dining room table, pencils flying on scratch paper, working away at a sample set of math problems. In a few minutes time is called, and they burst out talking excitedly about how they solved many of these very tough problems - or groaning about the ones they couldn't quite get yet. Homemade cookies are interspersed with discussion of the Pythagorean Theorem and exponents and factoring and fractions and how many handshakes would be given if everyone in a group of 10 people shook hands with everyone else. The kids don't even want to leave when the time is up for the day, and they all talk about the next meeting in two weeks.

What's going on? The kids are involved in a challenging math competition called Mathcounts with homeschool friends, enjoying learning together and really working hard to stretch themselves to be ready for the upcoming team competition at a regional college. The competition includes a full-year coaching program and encourages group discussion, active hands work, and non-routine problems. It's energizing, it's lots of work, and it's worth it.

More and more homeschoolers are starting to realize that the many math competitions available nationwide are a real boost to their home programs, jumping them into types of problem solving they wouldn't have thought possible before. Just as in the Geography Bee and the Spelling Bee, homeschoolers are making their mark in these programs. Eighth-grade homeschooler Alison Miller, who won third place in this past year's Spelling Bee, was one of four homeschoolers chosen as one of the top 30 high-school-level math students from all across the country who will take part in the USA Math Olympiad Summer Program. Six of these students will be chosen to compete internationally in Seoul in the International Math Olympiad.

But most homeschoolers won't be aiming for a national top spot in math competitions. Is there still a point to taking part? Definitely! See if these plusses sound important: more motivation and less yawns and grumblings among your kids, continuing support and encouragement for hard work and perseverance, and the new idea that they don't always have to learn about new math alone. Another perk is getting a chance to try out their wings against other kids from all across the country. Let's remember that homeschoolers don't have the monopoly on good learning, and that there are bright kids and dedicated parents out there working for quality programs within the schools. The whole experience broadens our perspective on what we're doing.

To top it off, all math competitions give you excellent learning materials to use. You can use contest materials as the main focus of your math program in many ways, if you choose to. I've done this with all of my four kids at times, and they are all very sharp in math and seem to have thrived with this approach. Texts then become tools to help us solve particular problems or gain more background on a new topic brought out in a contest exercise. With contests you also don't have to do all the planning. Most are very well organized, giving you and your kids a firm framework to follow, with clearly stated goals.

You might even want to be like my daughter Molly and create your own math competition specifically for homeschool kids. Last year, during Molly's senior year of high school at home, she created and led an online math competition for homeschooled girls ages 9-12, called Talk It Out, complete with a snazzy interactive website and t-shirts for all students who completed the program (and the kids had a little contest to design the shirts, too!). She felt girls especially can benefit from talking about math together, so her competition required the girls to write out full paragraph descriptions of how they went about solving the tricky problem sets each month of the competition. Then they all were encouraged to read one another's solutions and comment on them. There was also a discussion board, where students could help each other through tough concepts by sharing and explaining, along with extra-credit activities like experimenting with Moebius strips. The girls loved it! See www.pahomeschoolers.com/math (Ed Note: No longer working) for more info on the coming year's program.

I know other homeschooling families that do something as simple as hosting regular Math Games Days at their homes during the year, where kids are invited over to play the many great math games that can get so ignored as we struggle to "cover" a math curriculum. No difficult planning here, but lots of good fun competition and thinking and doing math. Some math games, such as the popular Twenty-Four Game even have their own regional and statewide competitions sponsored by congressional representatives. In the Twenty-Four Challenge, kids from grades 4 through 8 vie to see who can gain the most cards in this fast-paced computation game where flexible and creative thinking is a must. See www.math24.com for more info on this, see if your region hosts a competition, and to find out more about this terrific game. Then get practicing and playing!

Math Olympiad for Elementary and Middle Schools (MOEMS) www.moems.org Our family's first foray into math competitions came 12 years ago with this program; we were the very first homeschoolers to take part. I'll never forget the year when my now-20-year-old son Jacob (a dean's list computer science major at Carnegie Mellon University) was a 6th grader and won the top award for having a perfect score all year in the Math Olympiad, something only about 30 kids out of the over 80,000 taking part worldwide achieved that year. The program also was my children's first time meeting with others to work at math together, learning to talk with their friends about math thinking and approaches. Taking part encouraged me to be more active in math learning and teaching too - I was now planning special activities related to these problems, getting out many more of our many math manipulatives and games, and in general doing more of what I knew really worked well to develop sound math thinking. The Math Olympiad program costs $75 to register a team, and you can have up to 35 students per team. There are now two different levels; one for 7th and 8th graders and one for elementary students. This is a school-based competition - that is, you do not advance to a regional or state competition, but do the whole thing right where your homeschool group meets. To help kids be ready to enjoy the competition you can use founder George Lenchner's excellent book Math Olympiad Contest Problems for Elementary and Middle Schools (available from PA Homeschoolers, www.pahomeschoolers.com), which contains all problem sets from the first 16 years of the program, along with many teaching suggestions and full explanations for every one of the 400 problems. Calculators are not allowed during the competition. Certificates, pins, medals, and trophies are awarded to students, and there are even team awards.

MATHCOUNTS www.mathcounts.org. Our next step up in math contests was the middle school program Mathcounts, which is expanding the program to include 6th graders and individuals as well as teams. I worked with Mathcounts 10 years ago to encourage them to change their former policy of excluding homeschoolers, and ever since then there have been homeschool teams in almost every state. This program encourages regular team coaching sessions to help kids prepare for a regional chapter meet in February to select students to compete at the state level competition in March. From there it's on to the nationals in April - and many homeschoolers have found their way there. Check out the website for full info, and also to take part in the online problem solving game and to see the help for coaches and students. They even have a fun contest where kids can send in their original math problems for possible inclusion in the upcoming year's Mathcounts handbook. Cost to register a team of 4 students is $50 per year, and you'll receive a copy of the school handbook with practice problems ("warmups" and "workouts") to last the whole year, and lots of ideas for organizing practices. Calculators are allowed during some parts of the competition, and during one section the team works cooperatively to solve ten really tough problems. A regular newsletter goes out to coaches and another free newsletter goes to students who made it to the state level of Mathcounts. Many stay in touch with the competition for years and years.

American Mathematics Contests www.unl.edu/amc Another math competition my Mathcounts team takes part in each year in mid-November is the American Mathematics Contest, the lead-up competition to a whole group of high-school competitions. This is a one-time school-level group event set in mid-November, with 25 multiple-choice problems covering a wide range of math topics. There are now special guidelines for homeschool teams to follow. The website has full details and sample problems from previous years. The best part of this competition for us always comes right after the kids have completed the set of problems and the answers sheets are off in the mail - then we get to discuss problem solving strategies and compare answers . . . a real challenge, since the correct answers aren't sent out for several days after the official competition date. Costs are very reasonable (around $25 for a group of ten or under), and you'll get full and detailed results back on how all your students did, along with more comparative statistics than you ever expected could be developed based on one math contest! Special award pins and certificates add to the fun. Calculators allowed.

We've continued with the American Mathematics Contests (AMC) for the high school level, taking part in their new division for students in grade 10 and below (AMC-10), as well as the more challenging division for grades 12 and under (AMC-12), set every year in mid-February. Students who earn at least 100 out of a possible 150 points in this competition are invited to take part in the next level of the competition, called the American Invitational Mathematics Exam (AIME), with only 15 problems, but no multiple choices this time. From there a select group of students take part in the 5-question exam called the USAMO, USA Math Olympiad, where fully-developed written proofs are required. This helps in choosing the students for the 4-week summer program where the top students are chosen to represent the US in international competition. As with all math competitions, practicing with actual back problem sets is a real help, and can become part of your high school program - and you can order back sets inexpensively.

USA Math Talent Search www.nsa.gov/usamts/index.cfm. Tired of multiple-choice exams or speed tests? Want to take your time to really think and ponder and develop your mathematical ideas carefully? Then the USAMTS may be for you. This unique program was started by a professor at Rose Hulman Institute of Technology, based on the math competitions he'd remembered from his younger days in Hungary where speed was not the main goal, but rather well-reasoned and thoughtful work. This is an individual distance competition, where students have 4 weeks to solve a very challenging set of five math problems, developing full written solutions, proofs, or explanations, not just an answer. You are even allowed to research any topics to gain more background and information - you just can't discuss the problems with other people. Top students receive special recognition for each of the four sets of problems, and many prizes are awarded at the end of the year (my son Jacob received a set of great math books one year). This program is free to students, and problems and full info are now up on the Internet. Although there is not a team or social aspect to this competition, all the students keep in touch through a newsletter. Excellent student solutions are published to help others see ways to develop their proofs. The emphasis is on encouraging students to only compete against themselves, learning to set high goals, work hard at very difficult tasks, and learn to achieve a higher level of competence than at the start of the program. Taking part and doing very well is another route to being chosen for the AIME mentioned above.

Casio Online Classroom education.casio.com/contests.htm This is a really neat contest with six divisions for elementary- through high-school levels. And guess what the prize is! A super Casio calculator . . . each week! Kids email in answers to fascinating problems developed by various university math departments, and a random drawing from all correct entries chooses the winner. All students with correct answers are listed right on the website each week. It's fun to see that kids from all over the world take part in this contest. A great perk - they have archives of back problems, giving you lots of practice and fun challenges.

The Math Forum Problem of the Week forum.swarthmore.edu This site has been going for about five years, and includes weekly math challenges for all levels. What's unique here? Students are expected to write out full solutions to problems, describing their solution strategy and thinking process. Recognition for correct solutions, and special notice for outstanding written explanations. The Math Forum also takes suggestions for original math problems to use on the site, and welcomes new people (even students!) to serve as mentors and readers of student solutions. There's also a full archive of past problems, along with many other resources for both students and teachers. Many students from all around the world take part in this competition. The Math Forum is for all levels, elementary on up - and it's free! (Ed Note: Not any more, looks like.)

The Mandelbrot Competition www.mandelbrot.org Started by several friends who all enjoyed various math competitions while growing up, this is both an individual and team competition, with three or four rounds of problems. Costs are very reasonable - $40 to $50 a year per team of four students (and more students can take part as individuals). There are two high-school divisions, plus a middle-school competition, and there are both individual and team components. It's billed as "the competition that teaches as much as it tests" - and I can see it does just that. No calculators.

Solve-It www.udel.edu/educ/solveit/ Want to try a summer distance math contest with a big emphasis on fun and parent involvement? Try Solve-It, sponsored by the University of Delaware, for a great program for 4th- to 8th-graders. The cost is $50 per student, and you can choose between two difficulty levels (you get to choose whichever would better match your child's current abilities - grade level is not crucial here). You'll receive problem sets in the mail, along with follow-up mailings and solutions, and prizes and awards for completing the program. Involves students writing out full solutions and telling how they went about working on the problem, rather than just giving the correct answer.

American Statistical Association's Poster or Project Competitions www.amstat.org/Education/index.cfm?fuseaction=poster1 And finally . . . how about a competition where you develop an original statistics project? Try the website for full details, registration info, sample winning posters, and much more. Also, if you live in Pennsylvania, check out the special webpage for the PA Statistics Poster Competition at renoir.vill.edu/~short/posters/ (Ed Note: No longer working.) You'll get to see lots of fun samples of winning posters from recent years (even some really cute ones by kindergartners!), helping you get your ideas together for your own project. You'll realize here that doing work with math does indeed involve the real world. No fee to enter.

Are you starting to think "beyond the box" about your math program yet? Now, I wonder what the probability is that your math program at home will improve with math contests this year . . . just ask that homeschooler who's starting to perk up about his math work, and you'll have your answer.

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