Competition in the Math Classroom

From WikEd

Definition of Competition

com·pe·ti·tion n.

- The act of competing, as for profit or a prize; rivalry.

- A test of skill or ability; a contest: a skating competition.

- Rivalry between two or more businesses striving for the same customer or market.

Using Competition in the Classroom

Many of us have had very positive experiences with competition as students,as athletes, as students in the classroom, or as participants in academic contests. Others have had feelings that weren't so positive, perhaps distressing or even painful. What are the effects of competition or competitive events in the academic community, especially in the classroom and in competition? We will also take a look at the pros and cons of math contests?

The world that we live in is competitive, sometimes very competitive. Competition is all around us and very difficult to escape. But much of the competition that we encounter is inherent to our own personality. Sometimes we create a feeling of competition to inspire or encourage ourselves to do better. So, sometimes the competition that we experience is strictly in our own mind. Parents and teachers have a wide influence on how our students and children view the world and the idea of competition. Whether we stress being competitive or being cooperative, we have the opportunity to shape our students views.

What competition does:

Competition creates a sense of urgency and pressure. It many times shifts the focus of a task to the destination and not the journey. If the task was to finish a homework assignment, we could make it a competition by seeing who could finish the assignment first. Consider how making it a competition changes the task. The sense of urgency (for those who cares about winning)goes up to some extent. The purpose of the activity shifts away from learning and attempting to understand the material and becomes a opportunity to do what it takes to finish first and win. The process becomes less important than the product.

Does the dynamic change when groups are asked to work together competitively? Suppose we asked groups to work in teams to learn a difficult concept and finish a collection of problems. The incentive will be that the first group that finishes with the correct answers will receive extra credit points. Normally in a cooperative group learning setting, ideas are exchanged, some right and some wrong, discussions take place and groups come to an agreement on the results. Introducing the concept of competition reduces the groups' willingness to exchange ideas or consider any ideas that won't lead to a final solution. Any ideas or information that is deemed extraneous will be dismissed even if it increases the learning process. These discussions sometimes cause the more competitive group members to become disjointed from the less competant group members. So no matter the good will or good intentions that are present at the beginning of the process, the structural incentive will promote both a shift in the focus of the task and the nature of the team dynamics.

Likely Consequences of Competition:

-Promotes a shift from means/process to ends/products

-Brings an external dimension into the equation

-Heightens the level of anxiety/threat

-Promotes a tendency to take on a mentality defined by “fear of failure” (and consequently winning becomes the way to relieve the anxious condition).

In groups:

-Shifts the emphasis from quality relationships to effective relationships

-Decreases incentive to think reflectively or divergently

-Reinforces the qualities of dominance and ability

-Decreases the sense of bond generally among groups and temporarily increases the bond within the winning group.

Likely Benefits of Competition:

-Increases the level of anxiety/threat for a performance (pressure may help refine skill).

-Can be structured to help refine and reinforce team skills

-Can be fun

While it seems that the consequences outnumber the benefits, it is still a very powerful and attractive tool to implement in the classroom. Can anyone argue that introducing a competition to an otherwise mundane activity is a sure fire way to get kids excited and keyed up? Introducing competition in an educational setting however requires touch and a bit of understanding of your class to reap the most benefits.

Use of Competition in the classroom

All uses of competition will not have the same effect. If we are to attempt to incorporate some degree of competition with our students, we need to be clear about what kinds of outcomes we might produce as a result. Care must be shown, as there are many undesirable effects as a result of the use of competition in the classroom.

Fewer and fewer teachers subscribe to the use of normative grading (i.e., grading on a curve). This was somewhat common in many schools in the past, however it is difficult to find any support that it was motivational or necessary. Pitting one student against another for grades has consistently been shown to have serious ill-effects. Questions arose, "What does any student’s grade have to do with any other student’s learning?” The answer is “nothing educational.” The only benefit is as a mechanism of selection and separation. Unless one sees that as their job, they might think twice before grading on a curve, along with sharing grades publicly.

Teachers playing favorites is another subtle form of competition. In a sense, the teacher is saying that there is some criteria that he/she uses to decide whom to show more affection and admiration. Showing different levels of fondness will have a negative effect on the students. Only the winners will be happy or motivated by it.

There are a few simple rules of thumb when deciding on competition in a classroom setting. In almost every case, if your competition is for a valuable outcome then the possibility that the results will have a lasting negative effect is greater than if the competition is for something more trivial. Outcomes for competition in the classroom can be broken down into three categories. The first category is that the competition is for material things of value. The second is for the teacher's affection and third is for grades.

One way to determine whether competition is healthy or unhealty is to decide based upon the following criteria:

Healthy Competition is for fun. Healthy Competition's reward is something that is not valuable, not real. Healthy Competition has no long-term bad effects. Competitors in a Healthy Competition see a reasonable chance of winning.

Unhealthy Competition feels real. The winners and losers will be affected, the reward is valuable. Winners have the ability to use their win as an opportunity to brag. Students develop a competitive frame of mind.

For some teachers, using games that result in group points can be a useful tool to bring a heightened level of attention and importance to certain group skills. This practice can fall in the healthy column, if it is done thoughtfully and deliberately. Above all, it is important to make a clear distinction among – that which is graded academically, that which is rewarded/graded for investment in the process/participation, and that which is given points.

Students need to know if the reward structure for a particular activity is about something real or is it just to make a point or have fun. For example, if we give group points and make it part of a group grade for a project, we need to keep those points separate from any points that we give for a group competitive game. We can do both, we just need to keep them separate. Let’s say, at the start of the year, we may play a game where teams get points for various tasks as well as for displaying high functioning teamwork/collaboration. This game can help build a positive classroom climate or teach cooperative group skills. It is very important to make a distinction between points for grades and points for part of a game. If these are not kept separately, we can destroy the sense of trust in the grading system and our game will be a lot less fun as students will be confused about the purpose and impact.

The same logic needs to be applied to academic outcomes. If we are playing a game with academic content, it can be fun and help reinforce certain skills and content. For example, teachers who use a jeopardy-like game, or a team knowledge bowl competition, to review for tests, raise the level of interest and excitement while accomplishing essentially the same degree of content processing. But if the outcome of the game becomes part of what is formally graded, the competition goes from the healthy to the unhealthy column. The other members of the class are seen less as participants in the activity and become obstacles to achieving a meaningful outcome. And students begin to associate the teacher less with fun and more with the cause of their dissatisfaction. If you want to test this principle, you might find 2 classes, one where competitions are graded, and one where grade outcomes and game outcomes are kept separate. Observe what happens over time. At first they will look very similar, up until the end where one team will display a lot of bitterness and the other great relief. Over time you will see the condition where the outcome is graded become more and more aggressive, more students will contest answers, the shift away from process to product discussed above will increase, and students will have less and less fun. In the condition where grades and points are kept separate (and the principles of healthy competition are maintained) the degree of fun will stay high, with the only change being the increased sophistication of the strategies incorporated in the game.

If is evident that competition in the classroom needs to be carefully decided on how and when to implement. We will now take a look at formal competitions and their effect on students.

Math Competitions - Benefits

Math competitions can be one of the most enjoyable and valuable experiences in mathematics for many students.

Athletic competetions have long been credited with providing participants with many benefits. The benefits of athletic competition are learning to work as a team player, discipline of preparation for a game, and providing an outlet for the competitive person. These same benefits occur in math competitions. Well, I have seen these same benefits show up in math competition.

Team Player

Math contests are very similar to baseball games. Each contest takes individual moments and combines them in the concept of a team game. In baseball, a batter is all alone when he faces the pitcher. However, moving a runner to the next base or sacrificing your turn at bat for the good of the team is essential to the game. Most math contests and competitions work the same way. A competitor is usually by himself for a good part of the contest, but his individual score is combined with his teammates' score to determine a team score. Yes, there is a strong emphasis on how an individual performs, however, just as important is the performance of the school. When a school is recognized with a team trophy, we are in effect recognizing all the team players. While preparing for a math meet, a real sense of camaraderie develops - a desire for students to help each other understand the material. In addition to the individual portion of the contest, many competitions include a team test. A test in which 4 or 5 teammates work on problems together in a timed test. Knowing your teammate's abilities, strengths, and weaknesses is essential to performing well.

Discipline

Just as in athletics, a student who is going to perform well at a math meet must be disciplined in their preparation. One would not expect a coach to choose his starting lineup for the basketball game tonight from the students in a Phys. Ed. class, without any additional preparation. Likewise, for a student to do well in a math meet requires significant additional preparation. Sometimes that preparation can be frustrating. Many times students will find themselves struggling for hours with one set of problems. Some students want to give up after 5 minutes and be shown the solution. However, the real value comes for those students who spend the time struggling with a problem. For them, when they finally crack the problem 2 days later, there is an incredible sense of accomplishment, as well as a renewed commitment to solving the next problem more quickly.

A student who works consistently at solving these problems, year after year, will find that they are able to solve harder and more complex problems. They also develop a habit of sticking to a problem until they solve it - one of those qualities that we all like to see in students, and one we find that we don't see as often as we would like.

The Competitive Person

Many people have a competitive streak of some type running through them. Unfortunately, not all of these people are particularly athletic in nature. Math Team provides an easy outlet for that competitive edge. For those who say there is not real competition in a math meet, I would invite you to attend the Maine State Math Meet. Imagine having an ice arena full of 900 plus students, who are all working in absolute silence for a 12-minute round. Then, when the answers are read, you will hear and see both the elation of students who solved the problem correctly, and the disappointment of those who missed it. And, as often as not, those who missed the problem will be asking their neighbor how to do it, so that they will not miss it again.

Other Benefits of Math Competitions

College Entrance Exam preparation

There are other additional benefits to math competition. One of the most obvious, in my mind, is the experience one gains in taking a timed test. Although the emphasis on college entrance exams has shifted in recent years, there is still no doubt that for many students this is an important exam. However, many students do not have experience working through a set of problems in a limited amount of time. Math competition gives students that experience. When I started coaching a math team as a teacher, a coach from another school told me that in his opinion, based on his observations after years of coaching, a student who worked diligently at math competition throughout their high school career, would typically score about 100 points higher on the SAT than a student who did not compete in math competition. Although this is not a statistical study of any type, it does seem to make sense - students who are used to working under timed conditions would be expected to do better on the SAT than a student who is not used to working under that time limit.

Confidence

Another benefit is the obvious improvement in a student's confidence level within his or her math class. I have had freshmen and sophomores who have worked at some Pre-Calculus level topics while preparing for a math meet. Obviously, these students, when they see these topics when they finally reach Pre-Calculus, will have a much greater confidence in the material. They will be ahead of their classmates who have not been in competition. Additionally, they will also be continually reviewing these topics, even after they have left the material in their math class. This preparation is going to insure that they reach a far higher level of understanding of the material than their classmates. This certainly has far reaching value, far beyond their high school careers.

Finally, there is no reason to limit math competition to the "math geeks." I tell my students that ANYONE can join the math team and prepare for and attend meets. One year, I even had a Special Ed. student, who as a senior was struggling through Algebra 1, on my math team. It was one of the most exciting things for her when she scored some points at one of the math meets. Now, she didn't turn out to be the next Newton or Pythagoras, but she was able to look at mathematics with a completely different perspective because of her experiences. She could actually say that she LIKED mathematics. Isn't that something that we would like to see for all of our students?

There is no doubt that athletics provide many benefits to students. There is also no doubt that math competition provides as many benefits, if not more, than these sports do. If you do not currently engage in math competition, I encourage you to give it a try - both for your sake, and for the sake of your students. I am confident that you will not regret your decision.

Students Teaching Students

While many educators debate the benefits of math competitions in exciting top students and introducing them to new concepts and problem types, my purpose is to write a social aspect of math competitions that is not as often discussed. Students advance academically most quickly when they are interested in the subject matter enough to discuss it amongst their peer groups. Socially, students communicate more with other students than teachers. Excitement over a topic generates discussion, igniting a greater learning process.

Students teach students more quickly because teaching is a social process. Students are more interested in communicating with each other because they are more similar to each other than they are to us teachers. Students love to talk, play games, teach, and learn from each other. This happens for topics that are valued within their peers group so long as the topics are fresh and exciting. When such topics take hold of a peer group, the excitement builds like the power of a tornado, and when the subject is educational, the only thing we can do as educators is get out of the way, let it happen, and count our blessings.

Unfortunately mathematics is not currently valued in Western culture as highly as purely recreational subjects like sports, television, music, or video games. Even the students who already recognize the value of their education (and mathematics in particular) are often unable to find large enough peer groups that foster their interests. The result is that students rarely get to the point of discussing mathematics amongst themselves unless they are told to do so, which only inhibits the excitement of the process.

Math competitions bring students together not only under the banner of mathematics, but also as a game, which appeals to young people, particularly on a social level. Students at math competitions often anticipate what kinds of problems will be thrown at them next. The top students count on finding fresh and exciting material that is not likely to be presented in even their advanced math classes at school. In this way math competitions successfully generate the kinds of social reinforcement students might otherwise only find in purely recreational activities.

Extra-curricular math activities are a great way to generate these kinds of peer groups. Currently, at least in most of the Western Hemisphere, they are one of the only ways. I teach advanced math classes online, and most of the students I teach participate in math competitions. As the number of students participating in online forums and class chatrooms has increased, the pace at which the students are learning the material has quickened dramatically. The results are not simply noticeable, but dramatic. Even without much change to the curriculum, students are moving faster through middle and high school level math into advanced college level mathematics.

Schools that are interested in building up their math programs should strongly consider creating or expanding their math competition programs. The benefits are enormous. Not only will test scores increase and students will gain admittance to more advanced universities (ask a student at MIT how many of their classmates were on math team), but the social benefits to a culture of math and science education will be enormous.

Signed life experiences, testimonies and stories

I am a math team coach and our school has a very successful math team. In a high school with only 170 students, I have 31 on my math team. We practice several hours a week, before school or in the evenings, over a three month period. Despite, the time commitment, students enjoy being on math team and learn a tremendous amount by doing it. I will say that the math competitions have increased the interest level of the students in my math classes. It has increased their problem solving skills and their calculator skills. It has also increased their social skills. The students on my math team range from the captain of the football team and the lead in the school play to the student who has no other activity or group that they belong to. These students come from very different social circles and come together to work toward a common goal, a state trophy. They have a lot of fun together and learn a lot along the way. If your school doesn't have a math team, get one. Our students love it!!! RGrunloh