Experiences of a Beginning
MATHCOUNTS® Coach
Dr. Kevin W. Hopkins
Southwest Baptist University
Why did I start?
• Familiar with other contests, even organized some (http://www.sbuniv.edu/~khopkins/tourney.htm for information on Jan. 29, 2005 contest).
• Saw MATHCOUNTS® National Finals on ESPN in 2003.
• Had vested interest—both at BMS and at Summerscape.
•
Decided
I had the God given skills and interest to get involved.
• Read MATHCOUNTS® site (http://www.mathcounts.org) to see what can be accomplished.
How MATHCOUNTS®
Works
•
After
several months of coaching, participating schools select students to
compete
individually or as part of a team in one of more than 500 written and
oral
competitions held nationwide and in U.S. schools overseas.
•
The first
competitions are held at the local level in February with winners
progressing
to state competitions in March.
•
Results at
the state level determine the top four individuals and top coach who
earn the
honor of representing their state or overseas team at the national
finals.
•
At all
levels, MATHCOUNTS® challenges
students' math skills, develops their
self-confidence and rewards them for their achievements.
Why Participate in MATHCOUNTS®
•
Each
year, more than 500,000 students participate in MATHCOUNTS®
at the
school level.
•
Those
who do tell us that their experience as a Mathlete is often one of the
most
memorable and fun experiences of their middle school years.
•
MATHCOUNTS®
provides students with the following benefits:
•
A
challenging and fun activity that helps them in their math classes.
•
A
chance to share common interests with new and often long-lasting
friends.
•
An
opportunity to meet students from other schools.
•
The
experience of developing teamwork skills.
•
A
chance to vie for scholarships and prizes.
•
A
sense of accomplishment that comes from setting and achieving goals.
•
An
opportunity to explore mathematics and mathematics-related careers.
•
A
chance to explore cool mathematics that isn't always taught in middle
school
classrooms.
Why MATHCOUNTS®
Works
•
MATHCOUNTS®
motivates and
rewards students by fostering teamwork and a competitive spirit.
•
MATHCOUNTS®
is more than
a competition. It involves students and teachers in year-long coaching
sessions
and helps students at all levels improve their problem-solving skills.
•
MATHCOUNTS®
builds math
skills, promotes logical thinking and sharpens students' analytical
abilities.
•
MATHCOUNTS®
provides America's
middle school teachers with creative, state-of-the-art curriculum
materials,
free of charge.
•
MATHCOUNTS®
introduces
students to math-related careers through contacts with engineers and
other
professionals who serve as volunteers.
•
MATHCOUNTS®
is
educator-driven. Materials and activities are structured to meet
student needs,
as identified by educators.
How did I start?
•
MATHCOUNTS®
sends a Handbook to every middle school across the country. It is also available online at
www.mathcounts.org.
•
MATHCOUNTS®
has old contests available, some online, some for purchase from the
website—can
use for classroom (allowed in their copyright information).
•
For a
beginning coach
this is enough to get started.
•
Found a
connection at Bolivar Middle School in 2003-04.
•
Found
opportunity at
Summerscape, June 2004.
I did more
research
•
Searched
web for other contest and problem archives (more on this later).
•
Located
books (and am still looking—more later).
What did I do?
•
Met
twice a month with Math Contest Club.
•
Had
a summer class at Summerscape,
a
program at Drury University for gifted 6th-9th
graders.
•
Had
the students look at problems and then tried to generalize the results
as we
went over them.
How does this fit into the context of Standards and Grade Level Expectations?
•
Goal 1-
Students in
Missouri public schools will acquire the knowledge and skills to
gather,
analyze and apply information and ideas.
•
1.6-
Students will
demonstrate within and integrate across all content areas the ability
to
discover and evaluate patterns and relationships in information, ideas
and
structures.
•
Goal 3-
Students in
Missouri public schools will acquire the knowledge and skills to
recognize and
solve problems.
•
3.3-
Students will
demonstrate within and integrate across all content areas the ability
to
develop and apply strategies based on one’s own experience in
preventing or
solving problems.
•
3.6-
Students will
demonstrate within and integrate across all content areas the ability
to
examine problems and proposed solutions from multiple perspectives.
•
Problem
solving-a
valuable life skill (especially problem solving under pressure) (see
Art of
Problem Solving-Volume 2-preface).
•
Develop
creativity-needed for solving problems (see Art of Problem
Solving-Volume
2-preface).
Grade Level Expectations
•
I.1, Grades
5-8--By the end of grade 8, all students should know a variety of
problem-solving strategies (such as organizing data, drawing a picture,
looking
for a pattern, writing an expression using a variable).
•
I.2, Grades
5-8--By the end of grade 8, all students should know computational
strategies
with whole numbers, decimals, fractions, and integers.
• IV.1, Grades 5-8-- By the end of grade 8, all students should know problems may be looked at in more than one way.
How does this fit into the context of Professional Development Event Strand Matrix?
•
Strand 1
Curriculum
–
1.1.
Demonstrating Knowledge of Content and Pedagogy
•
A. Knowledge
of content
• B. Knowledge of prerequisite relationships
•
Strand 2
Instructional Practices
–
2.3.
Establishing a Culture for Learning
•
A.
Importance of the
content
•
B. Student
pride in work
•
C.
Expectations for
learning and achievement
•
D. Teacher
interaction
with students
•
E. Student
interaction
•
Strand 4
Leadership
–
4.4. Growing
and Developing Professionally
•
A.
Enhancement of
content knowledge and pedagogical skill
•
B. Service
to the
profession
–
4.5. Showing
Professionalism
•
A. Service to students
More on resources
•
Other
Contests, many of which have archived tests.
•
See
http://www.sbuniv.edu/~khopkins/tournoth.html
for those I have discovered.
• Other resources-books (given at website as well).
• Could do a search at Amazon.com (or a similar site) for any of the following books.
• See what else people have been buying in the same vein.
• The more serious you want to coach, the more resources you might want to get.
• Can only coach as seriously as the kids want to compete.
• NCTM book-Children are Mathematical Problem Solvers, other NCTM books on math teaching and journals (see http://www.nctm.org for catalog).
•
Art
of Problem Solving, Vol 1 and Vol 2
•
See
http://www.artofproblemsolving.com/
for more info.
•
This
website offers on-line classes to serious MATHCOUNTS®
students.
•
Creative
Problem Solving in School Mathematics
•
Math
Olympiad Contest Problems
• http://www.moems.org/orders.htm
• Math Contest Preparation
• http://www.mathandchess.citymaker.com/page/page/1234603.htm
•
A
book written by a coach arranged topically (may no longer be available
at his website?)
•
Has
many specialized formulas.
• Math League-Math Contests
• http://www.mathleague.com/books.htm
• CountDown, by Steve Olson-reviewed in August 2004 Notices of the AMS.
• Available at Amazon.com (and other places I’m sure).
• Mathematics and Informatics Quarterly
How did it go?
•
Started
with about 15 (about half boys, half girls) at BMS—ended up with 6
going to
MATHCOUNTS®.
•
Had
problems with funding and students who were involved with other things.
•
Placement
at regional contests-had one student nearly place to go to State
MATHCOUNTS®.
Summerscape
•
Had
16 students.
• Evaluation results follow.
11. What are some suggestions
for other activities?
•
Do more on
computer.
•
Learn the
math in
gambling.
•
More songs.
•
Have more
math puzzles.
•
More games.
•
Activities
including
probability.
•
Longer
activities.
•
Play Set
more. More with the buzzer.
•
Show how
math relates to
some other card games (like probability).
•
More with
buzzer.
•
More with
buzzer.
•
Fun ones! Like math games (board games, card games)
•
More math
games,
perhaps.
12. What are some suggestions for
improvements in the course?
•
No 45 minute
test on day
1
•
Work on
gambling in math
•
Explain the
answers to
questions in more detail or slower.
•
More songs.
•
More
practices more like
the real competition.
•
Less
discussion on
calculators.
•
More songs
•
Finishing
the
explanations for how to do problems.
•
More games.
•
More times
when we did
the buzzer and kept count.
13. What should I be sure to do the
same in
future years?
•
The Jeopardy
game.
•
Sing songs,
do team
contests, and occasionally bring snacks.
•
Keep doing
the countdown
round and math games.
•
Songs
•
Going into
teams and
competing together.
•
Team Tests
•
Keep it fun.
•
Show how to
use a
graphing calculator.
•
Math games
online.
•
Math games
online.
•
Keep doing
activities
and songs! Especially the songs!
•
Games!
•
Pretty much
everything. Good class.
I had fun.
Learned some, too.
How did I see
students benefiting?
•
Attributes
of Successful Contest Students (from CountDown, by Steve Olson-reviewed
in
August 2004 Notices of the American Mathematical Society).
–
Insight
–
Competitiveness
–
Talent
–
Creativity
–
Breadth
–
A sense of
wonder
–
All
developed by
presence of a mentor in their life
•
Challenges
students to really read the problem--not just answer quickly. Will help
as they
write for the MAP.
•
Challenges
students to think through the process--can't just get the answer like
they do in
a regular class. Will help as they
write for the MAP (especially stronger students).
•
Students
see there is more to math than the skills they see in regular classroom
•
Problem
solving-a valuable life skill (especially problem solving under
pressure) (see
Art of Problem Solving-Volume 2-preface).
This skill is valuable in most any job.
•
Math
Skills-valuable as job skills.
Marketable Math Skills
• The SIAM Report on Mathematics in Industry (http://www.siam.org/mii/) found that the most important traits of nonacademic mathematicians are
–
Problem
solving:
Skill in
formulating, modeling, and solving problems from diverse and changing
areas.
–
Flexibility: Interest in,
knowledge of, and flexibility across applications.
–
Computation: Knowledge of
and experience with computation.
–
Communication:
Communication skills, spoken and written.
– Teamwork: Adeptness at working with colleagues.
•
All of these
skills are
developed by preparing for and participating in MATHCOUNTS® or other
Math
Contests.
•
Self
confidence as they learned new things (and realized they could learn
new,
difficult things).
•
Develop
creativity-needed for solving problems (see Art of Problem
Solving-Volume
2-preface).
•
Discipline-practice
makes perfect (hard for someone used to perfect on first attempt)-need
to see
rewards of hard work (see Art of Problem Solving-Volume 2-preface).
•
Students
get to compete academically.
•
Caution
here-students react differently to competitions, so don’t get there too
quickly
and scare off any students.
• Team aspect encourages cooperation—they see all can benefit and all have something to offer.
•
Teamwork-all
work together for common good—all prepare to do well at contest as
there may be
a team component.
•
Discipline
and Teamwork often associated with sports or music, but students with gifts in math
may be lacking in these areas-gives them another area where they can
develop
these skills.
• “One problem that makes students think mathematically is worth a hundred standards that just tell students what they should think.”
– Lynn Steen
– P. 869-Notices of the American Mathematical Society, September 2004
• “Too often we give children answers to remember rather than problems to solve.”
– Roger Lewin
– P. 5, GAMbit, Fall 2004
Problems Stretch Students
–
Carol Ann
Tomlinson
–
P. 10-11,
GAMbit, Fall
2004
•
“Is there
routinely work for the student to do that is a bit beyond that
learner’s
reach?”
•
“Is work
more complex and engaging rather than just “more” of a time-filler?”
•
“Is there
regular attention to ensure that the student experiences, tolerates,
and
ultimately embraces challenge?”
•
“Is the
goal of the teacher to help the student succeed at a new level of
challenge?”
•
“Does the
student experience failure as a necessary part of discovery?”
How did I benefit?
•
Saw
enthusiasm of the students and that encouraged me.
•
Got to do
“new” math-doesn’t always happen in my regular teaching load even at a
University.
•
Had to look at new ways to
explain problems (try to avoid algebra or be aware are just introducing
it).
•
Got me
involved in the school and cooperating with a teacher there.
•
Had to vary
the lessons-In Summerscape, 3 hours of “same thing” would have failed. Need to vary in my college classes too.
What have I learned?
•
Better
to do ONE problem at a time and then go over it than to do 8-10 (or
more) and
then go over. Keeps the weaker students
interested longer (only one problem to tackle at a time).
• Use a whiteboard when possible.
• Let students show solutions when they find them.
• Let students work together often.
• Practice with buzzer, even as a team competition.
•
Need
a more consistent funding source than students
–
Too
hard to plan when funding determines selection of who participates
rather than
their ability.
–
Students
must commit early to pay.
–
Hard
to substitute (and who pays) if original student has a scheduling
conflict.
–
Hard
to incorporate students who may join later in the year.
•
I
am more a math “ambassador” than a math coach.
–
Coach
implies the goal is “obvious” success (winning).
–
Ambassador
implies more the increase of life-long appreciation.
–
Even
good athletic coaches are remembered more for being ambassadors than
for their
coaching.
–
Focus
more on the skills and enjoyment rather than “winning”.
•
Be
flexible.
–
In
meeting time.
–
In
how focused students will be.
–
In
how many contests you can/want to try and do.
–
Etc.
•
No
one can do it all in coaching (see MCTM bulletin, Oct. 2003, p. 11).
• Don’t show National MATHCOUNTS® Countdown round too early (can be intimidating).
•
Knowing
one way to do a problem and being able to explain it are two different
things. Often multiple ways to do the
same problem.
•
The method is more important than the
answer. Don’t give the answer too
soon. Part of mathematics is realizing
that learning can be a struggle.
•
Give
some problems where the answer is “It can’t be done” and the
explanation of WHY
NOT is the key component.
Will I do it again?
•
It
was rewarding to see the student’s interest in math.
•
It
was rewarding to see new math and the challenge that brings.
• The “ambassador” aspect encourages me to continue—it is not about the results I’ll see at a competition, but the results I’ll probably never fully see in the kids’ lives.
•
Yes—my
vested interest.