Sunday, April 12, 2015

NNV Math Club Revisiting Mathematical Proofs



Song:  Tao

Artist:  Kitaro



This week at Alex's Math Circle...
they spent the whole of their time going over mathematical proofs.

As there are many new members to the math club...
and in preparation for the ARML Nationals...
the class was separated into two groups:

beginners / advanced. 

(The ARML local competition is next week at UNR.
The result will determine who will be on the team going to the ARML Nationals.)



Sherry Griffin (founder of the NNV Math Club)...
is welcoming the new members and explaining the structure
of the day's lessons.


For the first half of the class...
Alex went with the advanced members to work on their 
mathematical proofs in the hallway just outside of the class.



The young man teaching the class on mathematical proofs often teaches at the math circle.

He is a junior at high school
and he is not only the most experienced...
he is one of the strongest members in math.

I just learned today that...
just like Alex...
he also wishes to one day teach math...
almost certainly, as a university math professor.

He led the class as he always does...
through easy to understand logical explanations...
through small thorough steps delivered in logical sequence...
and with much patience and maturity. 

Although the relatively new members all have strong basic math skills...
many are new to mathematical proofs.



The young man started at the basics of mathematical proofs for the beginner group.

Mathematical proofs are an exercise in logic.
Logic is the basis for all scientific methods.

The young instructor went on to explain the use of:

the setting or understanding of the problem parameters...
the definition of the terms...
the hypothesis...
showing the inductive and deductive reasoning used to reach a conclusion...
which, thereby, proves the answer.

These are the types of problems that are used in ARML.

It is not enough to merely arrive at the correct answer...
they must show how they had arrived at the answer
by writing a mathematical proof.







Halfway through the day's lesson...
the advanced group returned to the classroom...
and they all worked on the problems the young instructor had printed out for them.










Alex has come a long way since he first started at the NNV Math Club
(Sherry Griffin had just started the club).

He was in the seventh grade.

This was where Alex was first introduced into the world of mathematical proofs.

The same young man teaching today's class had also taught mathematical proofs back then.



At the conclusion of the day's lesson...
Alex was discussing some of the details of his plan
to start his own local math competition for middle schoolers.

Alex wants to design the tests used in the competition.

The questions would involve:

Algebra
Counting and Probabilities
Number Theory

These are the same types of problems used in Mathcounts...
but Alex would stage his competition during the off season of Mathcounts
so the competitors of his competition could get more practical experience...
and therefore, stay sharp for Mathcounts.

He wanted to line up a university math professor to check his test answers.


Alex wants to reach out to the youth...
to get them interested in math while they are still young...
to give them a competitive atmosphere so they may feel the excitement...
and importance, of math.

Sherry Griffin often expresses the need to do well in the application of math 
to the math circle.

Her reasoning is that as the world becomes more and more technologically advanced...
there will be a greater divergence between the higher paying professions...
and the lower ones...
and that math is the key to many of the higher paying ones.


I don't know if Alex's competition will eventually come to the point of fruition...
but he is excited at the prospect of leading more children 
on to the path of a better life...through math.



















2 comments:

  1. Very cool that Alex wants to start his own competition. What a great experience, for him and for the participants, that would be.

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  2. Alex is looking forward to putting on his competition. He is working with Sherry Griffin in order to learn how to structure such an endeavor. He will then also have to visit the many middle schools in the county to spread the word about the contest and, hopefully, recruit many competitors.

    ReplyDelete

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