The document discusses the challenges in determining what information to include in math tournaments. It notes that students have varying levels of understanding due to differences in school curriculums, teaching styles, and how students perceive math. This makes it difficult to create tournaments that are both challenging and fair. The document suggests standardizing curriculums, focusing more on conceptual understanding than memorization, and including individual, group, and testing components in tournaments to accommodate different learning preferences.

1. Kayleigh Lane
Mrs. Corbett
AP Literature
18 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 as
a source of research on just how well one can put mathematical concepts together to solve a
problem. In order to fully test this, organizers of math tournaments need to verify what
information is to be used.
The issue of what information to include in math tournaments is highlighted in the type
of Mathematics given in schools. Because some schools are said to focus on certain subjects in
Math 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 simple
number theorythat are significant to the foundation of mathematics, are being neglected. This
raises the question of what information to include in a math tournament. At what level of
understanding 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. In
order to create a tournament based on fairness and difficulty, these factors have to be taken into
account. Deeper knowledge of what a student can analyze is needed to create a challenging yet
fair competition. Students need to be able to build upon what they already know. In correlation
with this, research has found “Only 12 of the 52 sets of standards require quick recall of the
multiplication tables” (Wilson). Math standards are cheating arithmetic. Students are not all on

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the same level of mathematics in each grade level. Some schools, or the other 40 sets, do not
consider arithmetic a high priority. Because of this, a basic concept, continuously used in the
problem solving process, is not learned. Therefore, a gap emerges in a student’s problem solving
capability.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 same
terminology in each classroom. As a result, the curriculum is altered by the way it is taught. Each
school can change the information that a student is given. As a result, students in a math
tournament are not all on the same level of understanding on particular subtopics of
mathematics. This not only relates to Elementary school concepts. The same dilemma is found to
occur 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 solved
if all school curriculums were standardized. By this, each school would have the same
curriculum and each student would learn the same concepts.
In addition to schools affecting curriculum, the way teachers develop math and explain
concepts affect student math levels as well. Math teachers relate directly to the overall problem
of what information to include in math tournaments. What the participant knows is based on
what teachers are actually teaching them.“Methods for teaching mathematics in the United States
have changed in style repeatedly, often with controversial results” (Lerner). Teachers emphasize
what they think is important in the curriculum and do not contribute other details. Because every
student does not have the same teacher, each student would be unique in his line of thinking. At
first glance, this may seem good in accordance with differentiation in the mathematical minds of
America, but in reality, it is not. For example, one teacher could solely think that geometry is
more important than algebra while another thinks the opposite. Both teachers would put more

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effort into the subject they preferred. The overall result would be students that are either more
algebraically based or geometric. The balance of math would be thrown off and, as a result, all
math 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 a
set of rules to be memorized…and about the extent to which one can do mathematics can result
in an inability to cope with certain conceptual problems due to reliance solely on memorization”
(Erteken, Dilmac, and Yazici). Problems arise because teachers make students instinctively
memorize the material and, as a result, the students end up not grasping the overall concepts. In a
tournament, this would present a problem because the student must apply all concepts they have
learned instead of basing it on one particular subject. The student needs to understand the
material in order to apply it to a different situation later on.If teachers perceive math as only
memorization, the students under that teacher’s guidance will do far worse in a mathematics
tournament. This problem could be resolved with a “shift in emphasis on mathematical
understanding (as compared to memorization facts) mean[ing] that teachers must learn more
about mathematics as well as how students learn this mathematics” (Unal). Students can
understand the material better because the teacher would understand it as well. Simple
memorization would be thrown aside and the students learning ability would be taken into
account. The problem with memorizationthat would soon leave the mind would be resolved
because the overall concepts would be grasped. Therefore, students could then apply them to
Math tournaments. This simple problem would be resolved, andthen there is one less problem to
worry about within tournaments.

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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").If
every child changed to one way of learning, education would seem easier. Each student could
conform 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 students
would be under one set of curriculum, but the ways of learning it are diverse.Students perceive
math in multiple ways. “Different representations support different ways of thinking about and
manipulating mathematical objects. An object can be better understood when viewed through
multiple 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 towards
the subject. Different people learn in different ways. Many people even take a stand to change
math in order for them to view it with ease as well. For example, word problems have helped
with the so called “Number overload” dilemma (“Word Problems”). In general, people like to
see school topics applied to real life situations, so they created an easier way to handle
math.Because numerous mathematical concepts are used for explaining complex real life
situations (“Scientific Math”),people, who can only understand math through the connection to
real 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 learn
best hands on or working by themselves, each student is different. Consequently, a problem
occurs with how best to test the student in a math tournament.“Advocates of whole-class
teaching say that students benefit from an active learning approach” (Paradise, Koth, and
Atkins). Students could learn better from taking part in an event that involved activity instead of

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just a test. In order to help in this dilemma, an activity, such as a game, could be put forth as part
of the tournament. This may prove to be beneficial to fairness. On the other hand, “Test scores
commonly measure one form of success, which is academic achievement” (Paradise, Koth, and
Atkins). 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 wit
and precision. This predicament may be solved with the enacting of a testing portion of the
tournament with proctors and a time limit. Finally, in regards to the active learner who enjoys
working 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 in
place of rote learning of mathematical facts,”they would benefit from working problems that
involve “outside the box” thinking (Franceschetti). As a result, they would work better with other
people in contemplating the answer to a problem andsolve it as a group. Because certain students
work efficiently with this method, a group portion of the tournament would be beneficial to put
in. According to research, organizers of tournaments could produce fairness with creation of a
three part tournament that uses the same curriculum but in three different ways.
Math tournaments are globally used to test the knowledge of an individual in
mathematics. They“measure a student's scholastic ability and achievement” in the field of
mathematics("Scholastic Assessment Test"). The main problem with these tournaments is what
information to use. This issue could be thoroughly resolved through standardization of
curriculum in schools, better learning and planning by teachers, knowledge of student
perception, and finally the information on what type of ways students are best at using to analyze
math. Overall, tournaments can base the knowledge of math on grade levels and label such
tournaments accordingly. A high school math tournament could then be labeled under Varsity

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and Junior Varsity and would then solve the dilemma of what information to include. This would
ensure fairness with the competition, and each student would have the opportunity to succeed. As
a result, this problem would besolved, and math tournaments would continue to benefit math
scholars nationwide.