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# Senior Project Research Paper

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### Senior Project Research Paper

1. 1. Kayleigh LaneMrs. CorbettAP Literature18 November 2011 The Main Problem Facing Math Tournaments The relaying problem with Math tournaments is what information to include in them.Math tournaments reflect a student’s understanding of mathematics. In general, they are used asa source of research on just how well one can put mathematical concepts together to solve aproblem. In order to fully test this, organizers of math tournaments need to verify whatinformation is to be used. The issue of what information to include in math tournaments is highlighted in the typeof Mathematics given in schools. Because some schools are said to focus on certain subjects inMath more than others, this is a primary issue suggested to occur. Researchers reveal that"Elementary concepts of number theory, despite their importance to the field of mathematics,have received scant attention in mathematics education research” (Unal). Topics, like simplenumber theorythat are significant to the foundation of mathematics, are being neglected. Thisraises the question of what information to include in a math tournament. At what level ofunderstanding are students? What material should be included? According to recent studies,some students may not even have a full understanding of even Elementary School basics. Inorder to create a tournament based on fairness and difficulty, these factors have to be taken intoaccount. Deeper knowledge of what a student can analyze is needed to create a challenging yetfair competition. Students need to be able to build upon what they already know. In correlationwith this, research has found “Only 12 of the 52 sets of standards require quick recall of themultiplication tables” (Wilson). Math standards are cheating arithmetic. Students are not all on
2. 2. Lane 2the same level of mathematics in each grade level. Some schools, or the other 40 sets, do notconsider arithmetic a high priority. Because of this, a basic concept, continuously used in theproblem solving process, is not learned. Therefore, a gap emerges in a student’s problem solvingcapability.Stephen Wilson has also noted that “school standards are full of flips, slides, and turns... as well as lots of statistics and probability” (Wilson). Students are not being taught the sameterminology in each classroom. As a result, the curriculum is altered by the way it is taught. Eachschool can change the information that a student is given. As a result, students in a mathtournament are not all on the same level of understanding on particular subtopics ofmathematics. This not only relates to Elementary school concepts. The same dilemma is found tooccur with high school and even college curriculum. Math tournaments everywhere are affected.The problem of curriculum relates to schools themselves, and this sub-problem could be solvedif all school curriculums were standardized. By this, each school would have the samecurriculum and each student would learn the same concepts. In addition to schools affecting curriculum, the way teachers develop math and explainconcepts affect student math levels as well. Math teachers relate directly to the overall problemof what information to include in math tournaments. What the participant knows is based onwhat teachers are actually teaching them.“Methods for teaching mathematics in the United Stateshave changed in style repeatedly, often with controversial results” (Lerner). Teachers emphasizewhat they think is important in the curriculum and do not contribute other details. Because everystudent does not have the same teacher, each student would be unique in his line of thinking. Atfirst glance, this may seem good in accordance with differentiation in the mathematical minds ofAmerica, but in reality, it is not. For example, one teacher could solely think that geometry ismore important than algebra while another thinks the opposite. Both teachers would put more
3. 3. Lane 3effort into the subject they preferred. The overall result would be students that are either morealgebraically based or geometric. The balance of math would be thrown off and, as a result, allmath concepts would not be utilized. Teachers need to focus on every aspect of math. In addition to this, teaching methods make students develop different habits toward math.Researchers reveal that“The value judgments of an individual who believes that mathematics is aset of rules to be memorized…and about the extent to which one can do mathematics can resultin an inability to cope with certain conceptual problems due to reliance solely on memorization”(Erteken, Dilmac, and Yazici). Problems arise because teachers make students instinctivelymemorize the material and, as a result, the students end up not grasping the overall concepts. In atournament, this would present a problem because the student must apply all concepts they havelearned instead of basing it on one particular subject. The student needs to understand thematerial in order to apply it to a different situation later on.If teachers perceive math as onlymemorization, the students under that teacher’s guidance will do far worse in a mathematicstournament. This problem could be resolved with a “shift in emphasis on mathematicalunderstanding (as compared to memorization facts) mean[ing] that teachers must learn moreabout mathematics as well as how students learn this mathematics” (Unal). Students canunderstand the material better because the teacher would understand it as well. Simplememorization would be thrown aside and the students learning ability would be taken intoaccount. The problem with memorizationthat would soon leave the mind would be resolvedbecause the overall concepts would be grasped. Therefore, students could then apply them toMath tournaments. This simple problem would be resolved, andthen there is one less problem toworry about within tournaments.
4. 4. Lane 4 The student perception of math proves to be a debated problem for math tournaments.How students see math makes a difference in what information to include in tournaments.Philosophers often note: “Adaptation is key to open education” ("The Joy of Learning—In").Ifevery child changed to one way of learning, education would seem easier. Each student couldconform to a certain method of learning. From an outside standpoint this seems to be beneficial,but in reality, this does not exactly change how a student perceives the concept. The studentswould be under one set of curriculum, but the ways of learning it are diverse.Students perceivemath in multiple ways. “Different representations support different ways of thinking about andmanipulating mathematical objects. An object can be better understood when viewed throughmultiple lenses” (Unal). A subject (in this case math) can be viewed differently by each person.The view of math that a student develops mainly depends on the effort teachers put forth towardsthe subject. Different people learn in different ways. Many people even take a stand to changemath in order for them to view it with ease as well. For example, word problems have helpedwith the so called “Number overload” dilemma (“Word Problems”). In general, people like tosee school topics applied to real life situations, so they created an easier way to handlemath.Because numerous mathematical concepts are used for explaining complex real lifesituations (“Scientific Math”),people, who can only understand math through the connection toreal life, can understand what they are learning. This overall would help with student perception. Within education, students are known to learn in a variety of ways. Whether they learnbest hands on or working by themselves, each student is different. Consequently, a problemoccurs with how best to test the student in a math tournament.“Advocates of whole-classteaching say that students benefit from an active learning approach” (Paradise, Koth, andAtkins). Students could learn better from taking part in an event that involved activity instead of
5. 5. Lane 5just a test. In order to help in this dilemma, an activity, such as a game, could be put forth as partof the tournament. This may prove to be beneficial to fairness. On the other hand, “Test scorescommonly measure one form of success, which is academic achievement” (Paradise, Koth, andAtkins). Another student, one who does not prefer active games, would benefit from just a test.They would perform higher if a test of knowledge was put before them rather than a game of witand precision. This predicament may be solved with the enacting of a testing portion of thetournament with proctors and a time limit. Finally, in regards to the active learner who enjoysworking with others but likes testing as well, a third portion of the tournament could be made.Because some students in this area place an “emphasis on abstract mathematical principles inplace of rote learning of mathematical facts,”they would benefit from working problems thatinvolve “outside the box” thinking (Franceschetti). As a result, they would work better with otherpeople in contemplating the answer to a problem andsolve it as a group. Because certain studentswork efficiently with this method, a group portion of the tournament would be beneficial to putin. According to research, organizers of tournaments could produce fairness with creation of athree part tournament that uses the same curriculum but in three different ways. Math tournaments are globally used to test the knowledge of an individual inmathematics. They“measure a students scholastic ability and achievement” in the field ofmathematics("Scholastic Assessment Test"). The main problem with these tournaments is whatinformation to use. This issue could be thoroughly resolved through standardization ofcurriculum in schools, better learning and planning by teachers, knowledge of studentperception, and finally the information on what type of ways students are best at using to analyzemath. Overall, tournaments can base the knowledge of math on grade levels and label suchtournaments accordingly. A high school math tournament could then be labeled under Varsity
6. 6. Lane 6and Junior Varsity and would then solve the dilemma of what information to include. This wouldensure fairness with the competition, and each student would have the opportunity to succeed. Asa result, this problem would besolved, and math tournaments would continue to benefit mathscholars nationwide.