Recognizing and Nurturing Math Talent in Children

Copyright 2015 NAGC. Reprinted with permission of the National Association for Gifted Children. No further reprints are permitted without the consent of NAGC.
what is math talent?
Recognizing and Nurturing
Math Talent in Children
By Dr. M. Katherine Gavin, Dr. Janine M. Firmender, & Dr. Tutita M. Casa
R
ather than walking directly to the
gate at the airport, Jenna is always
dawdling but notices the most unusual things. She talks about the
patterns formed by the shapes in the
carpeting and the composition of the
mobiles hanging from the ceilings. She
asks the infamous question “Why?”
over and over. Why did they use cylinders to create the lighting mobiles?
Why did they decide on hexagons in
the carpeting pattern? She is so curious.
George loves to go to the supermarket. He makes a game out of figuring
the running total cost of items put into
the cart. He likes to look at the price
of different items to find the best buy.
He easily figures out the cost of a single
item when there are sales advertised.
His number sense and estimation skills
are amazing.
How can parents nurture their children’s interest in and talent for mathematics? There are many opportunities at home and outside of school in which children and their
parents can experience the joy in doing mathematics.
Recognizing Math Talent in Your Child
In Preparing the Next Generation of STEM Innovators: Identifying
and Developing Our Nation’s Human Capital, the National Science Board (2010) emphasized that “the U.S. education system
too frequently fails to identify and develop our most talented and
motivated students who will become the next generation of innovators” (p. 5). Parents have perhaps the best opportunity to spot
math talent and talent potential in their children.
What is math talent? Ten different educators will most likely pro-
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vide 10 different answers. One reason mathematical talent is difficult to
describe involves the different ways children manifest math talent. Vadim Krutetskii, a Russian psychologist, was interested in learning about
math talent, so he observed children in the process of doing mathematics for 8 years. He found children were of three different types: (a) those
who reasoned abstractly and had an “algebraic cast of mind”; (b) those
who had strong spatial skills with a “geometric” cast of mind; and (c)
those who had a combination of both. He found that speed in computation and/or the ability to memorize formulas, although useful, were
not necessary conditions for math talent (Krutetskii, 1976).
So often children with mathematical talent are identified as
those who know their times tables early and can do their math facts
quickly without errors. But it is important to realize that research-
ers have found that speed is secondary to
mathematical insight (Davidson & Sternberg, 1984; Krutetskii, 1976). A different
approach to identifying this talent includes
mathematical problem-solving ability and an
lems, and/or
saw puzzles, logic prob
inquisitive, intuitive mathematical mind.
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a strong interest in math and displays some
(e.g., the way it is set up
of the characteristics in the observation scale,
other problems)?
share this with his or her teacher. Educators
th talent.
on guide to recognizing ma
have additional measures to help give a more
Figure 1. Parents’ observati
comprehensive picture of your child’s ability.
These include standardized tests, classroom
performance, interviews, and math performance tasks. The important thing to remember is that identification should be an ongoing process rather than a procedure. There are
three important factors to consider during the process: (a) there
are different types of math talent, (b) multiple measures should be it already. Young children need to begin developing the habits of
used to provide a variety of sources of information, and (c) chil- mind of professional mathematicians right from the start (Gavin
dren demonstrate talent at different times and in different ways & Casa, 2012; Gavin, Casa, Adelson, Carroll, & Sheffield, 2009;
over the course of their schooling (Gavin, 2011).
Gavin et al., 2007; Renzulli, Leppien, & Hays, 2000; Tomlinson
et al., 2009). This is not accomplished by simply moving students
Nurturing Math Talent in Your Child
into the next grade-level math text, although this can be a good
Once signs of mathematical talent are recognized, what can done start. The kinds of problems posed to students and the discussions
to help your child develop this talent? As mentioned earlier, bring generated around these problems need to be challenging and mothis to the attention of his or her teacher, who may have spotted tivational in order to develop student mathematicians who are
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October 2013
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what is math talent?
innovative thinkers and
creative problem solvers.
Beyond math class, there
are other activities such
as math competitions,
math enrichment clubs,
computer clubs, and chess
clubs that provide challenge
and enjoyment within the
school environment.
There is much that can
be done outside of school. This does not
mean teaching your child more challenging arithmetic, such as multiplying 4-digit
numbers by 3-digit numbers. It also is not
about teaching procedures, such as solving
algebraic equations. Rather, it is about getting them to think about interesting and
challenging problems, to look for patterns,
to find mathematical structure in problems,
and to use math vocabulary to talk about
these problems.
Math Activities to Use With
Your Child
This section provides activities to do at
home. The games come from Unraveling the Mystery of the MoLi Stone (Gavin,
Chapin, Dailey, & Sheffield, 2006) in
the Project M3: Mentoring Mathematical
Minds series of units for mathematically
talented elementary students. Although
the activities are based on place value and
numeration, children go far beyond computation and think deeply not only about
place value but also addition, subtraction,
and even probability. They also are fun,
and children love to play them over and
over, learning something new each time.
6
9
7
How You Played
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Playing “Some Sum”
To play “Card Game Capers,” you will
need a total of 10 cards. Each card displays
one digit, 0–9. The object of the game is
to write the greatest two-digit number after
three digit cards are drawn, one at a time. It’s
not as easy as it sounds! Here are a few twists:
• You cannot look at the cards.
• The digit cards will be drawn one at a
time, and you must record where you
plan to place the digit: either in the tens
place, the ones place, or in the discard spot
before you draw the next card. You cannot
make a change after you write it down.
• The digit cards will not be placed back in
the deck once they are picked.
For example, say the first digit drawn is
a 6. Maybe you think that it will be the
greatest digit selected, so you put it in the
tens place. Your child feels that there is a
good chance that you will draw a greater
digit and records it in the ones place. In this
case (shown below), she beat you. However, the greatest possible combination would
have included the 9 that was drawn last.
At first, your child may think that this
game has to do with luck. In fact, to be successful with this game, you need to not only
7
9
How Your Child Played
6
Playing “Some Difference”
understand place value (for instance, the 6
in the tens place is worth more than the 6
in the ones place) but also probability. That
is, after you draw a 6, you have three out
of nine ways to pick a digit that is greater
(7, 8, and 9) and six out of nine ways (0, 1,
2, 3, 4, and 5) to pick a digit that is lesser.
As seen from the example above, this is not
always guaranteed! As one of our students
stated, “It depends on how much of a risktaker you are as well.” As play continues,
discuss digit placement and what the differences are in their values.
Try the “Think Beyond” activity for extension in which players make the greatest threedigit number using four digit cards and a discard option. You can also challenge yourselves
to try to create the least two- or three-digit
number. What strategies might you use that
are the same or different? A further extension
9 7
6
The Greatest Possible Number
challenges children to figure out how many
two-digit numbers are possible to create if the
tens digit cannot be zero and the same digit
cannot be repeated when writing the number.
There are many solution paths to the answer
besides writing down all the numbers!
“Some Sum” and “Some Difference” are
games that build off of “Card Game Capers.” You again will use the same 10-digit
cards and the same rules. The object of the
games is to make either the greatest or least
sum or difference. Over time, your child
may begin to realize the importance of the
digits recorded in the tens place when playing Some Sum. You sometimes also can get
the same sum with different addends (e.g.,
94 + 63 = 93 + 64). However, this does not
work for subtraction. Additional strategies
come up when playing “Some Difference”
when trying to get the greatest difference
(when the numbers have to be as far away
as possible) and least difference (when the
numbers have to be as close to each other
as possible).
Additional Activities
Did you know that by participating in
team sports, such as basketball and soccer, your child is developing spatial sense
as well as learning how to solve problems?
Players need to have a sense of where all
of the other players are on the court or
field and where they themselves need to
be to advance the ball. They need to think
quickly regarding adjustment of positions
and plays based on the strategy of the opposing team. So encourage your child to
try these and other sports.
Visiting science centers and math museums is another enjoyable way to experience mathematics. Look for free admission
days and special summer workshops, even
sleepovers. Make sure you and your child
take advantage of the activities. There are
often problems to solve and experiments
to explore, and you need to take the time
to do them together and discuss them.
Look for after-school math enrichment
programs, Saturday opportunities, and
summer math, computer, and robotics
workshops in your area. Often these programs provide scholarships, so do not be
deterred by the cost at the outset.
Finally, there are many excellent math
websites for children to hone their problemsolving skills. However, a word of caution
is in order. There are also many websites
that are not challenging and offer repetitive
practice and boring drill. Clearly, these are
not appropriate (see Resources to Nurture
Mathematical Talent).
Concluding Thoughts
To best identify mathematical talent in
your child, think of yourself as a talent
scout. Encourage an interest in mathematics. Let your child’s teacher know and
provide experiences at home to fuel the
spark. Play strategy games like Yahtzee and
Battleship, construct jigsaw puzzles, create
origami animals, and do Sudoku puzzles
together. Find interesting patterns in nature as you walk in the park or along the
beach. Most of all, have fun with math.
If children develop a love for mathematics, they will likely continue to pursue it.
And there is definitely a need to develop a
new generation of mathematicians to keep
our country globally competitive in this
increasingly technological world. You can
play an important part in this process.
Resources to Nurture
Mathematical Talent
• Davidson Institute (http://davidsongifted.
org). Type in “mathematics” in their
search engine. This website has extensive
listings of organizations, competitions,
games, problem-solving websites, printed
materials, summer and online programs,
and other links to develop math talent.
• Figure This! Math Challenges for Families
(http://www.figurethis.org/index.html).
Sponsored by the National Council
for Teachers of Mathematics, this site
provides real-world math challenges across
all mathematical areas for children and
families to investigate together.
• The Math Forum @ Drexel (www.
mathforum.org). The Math Forum offers
a wealth of problems and puzzles, online
mentoring, and team problem solving.
• MathSite (http://mathsite.math.berkeley.
edu/main.html). MathSite provides
interactive tasks and interesting activities
for investigating mathematics.
• Muggins! (http://www.mugginsmath.
com). The math board games available
here allow for creativity and flexibility in
developing number sense.
• Museum of Mathematics (http://momath.
org). This museum opened in 2013
in New York City and is dedicated to
the exploration of mathematics. Other
U.S. math museums are listed at http://
mathfactory.org/Similar+Institutions.
• National Library of Virtual Manipulatives
(http://nlvm.usu.edu/en/nav/vlibrary.
html). This award-winning website
features interactive, web-based virtual
manipulatives for math instruction (K–8
emphasis) in most topic areas.
• Project M3: Mentoring Mathematical
Minds (http://www.projectm3.org and
http://www.kendallhunt.com). This
research-based curriculum project is a
series of NAGC award-winning math
units across different content areas that
were designed for mathematically talented
elementary students. The Project M3
website also has a list of resources including
websites for parents and children.
• Project M2: Mentoring Young
Mathematicians (http://www.projectm2.
org and http://www.kendallhunt.com).
This National Science Foundation
curriculum project is a series of six units
for students in grades K–2. These NAGC
award-winning units focus on advanced
content in geometry and measurement.
The Project M2 website also has a list of
resources including websites for parents
and children.
• Set Game (http://www.setgame.com/set/
puzzle_frame.htm). This challenging game
of classification and visual perception is
available as a card game and is also online
with daily challenges.
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what is math talent?
Resource and Reference
Books
• Assouline, S. G., & Lupkowski-Shoplik,
A. (2011). Developing math talent: A
comprehensive guide to math education for
gifted students in elementary and middle
school (2nd ed.). Waco, TX: Prufrock
Press.
• Findell, C. R., Gavin, M. K., Greenes,
C. E., & Sheffield, L. J. (2000).
Awesome math problems for creative
thinking. Chicago, IL: Creative
Publications.
• Gavin, M. K. (2011). Identifying and
nurturing math talent. Waco, TX:
Prufrock Press.
• Saul, M., Assouline, S., & Sheffield,
L. J. (Eds.). (2010). The peak in the
middle: Developing mathematically gifted
students in the middle grades. Reston,
VA: National Council of Teachers of
Mathematics.
• Seeley, C. (2009). Faster isn’t smarter:
Messages about math, teaching, and
learning in the 21st century. Sausalito,
CA: Math Solutions.
Talent Searches
The following are some top universities
that conduct talent searches and offer a
range of programs for gifted students in
mathematics and math-related areas.
• Carnegie Mellon University—C-Mites
Institute
http://www.cmu.edu/cmites
• Duke University—Talent Identification
Program (TIP)
http://www.tip.duke.edu
• Johns Hopkins University—Center for
Talented Youth
http://cty.jhu.edu
•N
orthwestern University—Center for
Talent Development
http://www.ctd.northwestern.edu
References
•D
avidson, J. E., & Sternberg, R.
J. (1984). The role of insight in
intellectual giftedness. Gifted Child
Quarterly, 28, 58–64.
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• Gavin, M. K. (2011). Identifying and
nurturing math talent. Waco, TX:
Prufrock Press.
• Gavin, M. K., & Casa, T. M.
(2012). Nurturing young student
mathematicians. Gifted Education
International. Retrieved from
http://gei.sagepub.com/content/
early/2012/05/22/0261429412447711
• Gavin, M. K., Casa, T. M., Adelson,
J. L., Carroll, S. R., & Sheffield, L.
J. (2009). The impact of advanced
curriculum on the achievement of
mathematically promising elementary
students. Gifted Child Quarterly, 53,
188–202.
• Gavin, M. K., Casa, T. M., Adelson,
J. L., Carroll, S. R., Sheffield, L. J.,
& Spinelli, A. M. (2007). Project M3:
Mentoring mathematical minds: A
research-based curriculum for talented
elementary students. Journal of Advanced
Academics, 18, 566–585.
• Gavin, M. K., Chapin, S. H., Dailey,
J., & Sheffield, L. J. (2006). Project M3:
Unraveling the mystery of the MoLi Stone:
Place value and numeration. Dubuque,
IA: Kendall Hunt.
• Krutetskii, V. A. (1976). The psychology
of mathematical abilities in schoolchildren
(J. Teller, Trans.). Chicago, IL:
University of Chicago Press. (Original
work published 1968)
• National Science Board. (2010)
Preparing the next generation of STEM
innovators: Identifying and developing
our nation’s human capital (NSB-1033). Arlington, VA: National Science
Foundation.
• Renzulli, J. S., Leppien, J. H., &
Hays, T. S. (2000). The multiple menu
model: A practical guide for developing
differentiated curriculum. Mansfield
Center, CT: Creative Learning Press.
• Renzulli, J. S., Siegle, D., Reis, S.
M., Gavin, M. K., & Sytsma Reed,
R. E. (2009). An investigation of the
reliability and factor structure of four
new scales for rating the behavioral
characteristics of superior students.
Journal of Advanced Academics, 21,
84–108.
• Tomlinson, C. A., Kaplan, S. N.,
Renzulli, J. S., Purcell, J. H., Leppien, J.
H., & Burns, D. E., (2009). The parallel
curriculum: A design to develop learner
potential and challenge advanced learners
(2nd ed.). Thousand Oaks, CA:
Corwin Press.
Authors’ Note
M. Katherine Gavin, Ph.D., is an associate professor at the Neag Center for Gifted
Education and Talent Development at the
University of Connecticut. The main focus of her research is the development and
evaluation of advanced math curriculum
for elementary students. She works with
teachers nationally and internationally who
are interested in developing mathematical thinking and talent in their students.
Janine M. Firmender, Ph.D., is an assistant professor in the Teacher Education Department at Saint Joseph’s
University in Philadelphia, PA, where
she teaches courses in early childhood
(grades pre-K–4) education and is pursuing her research interests focused on
pedagogy and curriculum in the areas of
gifted and mathematics education. She
earned her Ph.D. in educational psychology with a concentration in gifted education from the University of Connecticut.
Tutita M. Casa, Ph.D., is an assistant
professor at the University of Connecticut.
She worked closely with teachers and the
authors of Project M3, a series of advanced
curriculum units for talented upper elementary students. She also served as the
co-principal investigator and co-author of
Project M2 units written for K–2 students.
A mother of three elementary-aged children, she focuses her work on high-level
math discussions.