Understanding mathematics competitions in North America
There are a few internationally known assessments that evaluate students’ competencies in various subjects: Programme for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS). PISA is a project within the Organisation for Economic Co-operation and Development (OECD)designed to provide policy-oriented, international indicators of the skills and knowledge of 15-year-old students around the world (http://www.pisa.gc.ca/eng/home.shtml). Within the project, three main domains are assessed including reading, mathematics and science. As for the TIMSS, fourth graders and eighth graders are evaluated based upon their level of mathematics and science. From these two assessments we can see that math and science appear to be common domains of interest in student evaluations. Therefore, for the purpose of this article, I will look specifically at the mathematics aspect and give an overview of the math contests available in North America.
Many kinds of math contests exist around the world with participants from all walks of life. However, in general, there are two kinds of students that will participate in math competitions. The first kind of students is those that do not know how good their math is and want to find out where they would rank nationally. The second kind of students is those that are gifted in math. Participating in various contests allow them to meet their esteem needs as seen in the Maslow’s hierarchy of needs because if they receive good results in the contests, their name would be accredited in the school record which in part would help build their profile in their application to cegeps and universities.
Over the past few decades, the types of questions found on these contests were mainly word problems that were either multiple choice or fill-in-the-blank questions. However, recently, we have seen the trend shifting from word problems to situational problems. Instead of a simple A, B, C or D answer for instance, one is now tested on concepts of integration and must write reasoning statements to solve a problem ranging from one to five pages. The Quebec Ministry of Education has also picked up on this trend by reforming the whole math curriculum.
So, what is a situational problem in math and how is it different from a word problem? The Quebec Educational Program describes a situational problem as “characterized by the need to attain a goal. This objective cannot be instantly achieved, since it is not an exercise involving applications”. It is a situation in which a person is seeking to attain some goal for which a suitable course of action is not immediately apparent (Burns, 2000). In these problems, there are usually multiple ways to receive the correct answer. Furthermore, there is in some cases more than one correct answer available.
On the other hand, a word problem requires children to focus on the meaning of arithmetic operations. The problem is translated into a mathematical sentence, and children do the computation called for in that sentence. There is usually one right way to get the answer; there is always one right answer (Burns, 2000). http://www.swlauriersb.qc.ca/english/edservices/pedresources/workshops/pbl.htm
From the following picture, you can get a glimpse of the math contests found locally to those found internationally.
In Canada, the Waterloo University Center for Education in Mathematics and Computing (CEMC)
has set up many different kinds of contest (http://www.cemc.uwaterloo.ca/). The most popular ones are the following: Gauss I (G7), II (G8), Pascal (G9 or less), Cayley (G10 or less) and Fermat (G11 or less). These contests encourage students to work at their problem solving abilities. They consist of solving 25 multiple choice questions within 60 minutes with a total of 150 points. The second group of contests are Fryer (G9 or less), Galois (G10 or less) and Hypatia (G11 or less). Only the top 25% of students in the class are recommended by teachers. These contests consist of solving four problems within 75 minutes, requiring full written solutions for a total of 40 points. The last group is Euclid (G12, cegep or less) which consists of answering 10 questions within 2.5 hours for a total of 100 points. All the past contests can be downloaded on their website for students to get some practice(http://www.cemc.uwaterloo.ca/contests/past_contests.html).
Amongst the Caley and Fermat participants, the top 25% are invited to attend TheMathematical Olympiad Summer Program(MOSP) which is a 3-4 week, intensive training program in the summer. The most gifted students will then be selected to attend theCanadian mathematical Olympia (CMO).
Another way to participate in math competitions is through Sunlife Financial and many Canadian universities which hold a yearly Canadian Open Math Challenge (COMC) for full time students aged 19 or less. The challenge consists of 12 total questions to be solved within 2.5 hours for a total of 100 points (http://cms.math.ca/Competitions/COMC/2012/).The top 50 students in this contest are then invited to attend the Canadian Mathematics Olympiad (CMO).
In the states, the Mathematical Association of America (http://amc.maa.org/) holds three kinds of math contests under American Mathematics Competitions (AMC). AMC 8 (G8) consists of 25 questions to be solved within 40 minutes while AMC 10 (G10 or less) and AMC 12 (G12 or less) consist of 25 multiple choice questions to be solved within 75 minutes. The participants that are within the top 1% of AMC 10 and top 5% of AMC 12 are then invited to attend the American Invitational Mathematics Examination (AIME) which consists of 15 extremely difficult questions to be answered within 3 hours. The participants that rank near the top are then chosen to attend the United States of America Mathematical Olympiad (USAMO). This contest is much more intense, consisting of six questions and 9 hours of essay writing and proof examination, lasting two days.
From this analysis, you can see that the preliminary contests are mainly all multiple choice, word problems and the more global the competitions become, the questions become more situational problems.You may notice also of the lack of contests for elementary students. Fortunately, Quebec Foundation for Academic Achievement (QFAA, a federal registered non for profit organization) holds yearly contests for students from grade two up to secondary five.
So, what are the cons about attending competitions like these? A famous Harvard educator, Dr. Tony Wager, once pointed out that many countries push and force their students to practice for and compete in these contests. This, unfortunately, is leading to these contest-driven countries to losing their worldwide competition edge because these contests can only cultivate a few survival skills, warned by Dr. Wager (http://www.tonywagner.com/7-survival-skills). Skills such as critical thinking and problem solving, accessing and analyzing information may improve in students but curiosity and imagination may be lacking. Contests can only serve as a tool for the talented and gifted students or for those that are above average in class, to help them know their level and to plan for their future career. With this said, these contests are not meant for everybody and if not taken with care, the results may cause more harm than good. Conversely, by knowing their real level compared to their peers, they may know whether or not they are suited to study particular fields such as business, science or engineering.
If the preliminary contest have more situational problem would the candidates of the more global contest be different and in what way?
What are differences between problems solving and situational problems?
As parents, how can you help your kids to solve or improve their situational problems ?