# TEACHING MATHEMATICS TO GIFTED CHILDERN

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This book will teach you how to avoid common pitfalls and help you start on the journey to developing your gifted child’s ability to think mathematically and develop a greater love of math.
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Challenged in Math
7 Tips to Ensure Your Child Loves Math
By Raj Shah, Ph.D.
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Foster a Love of Math Using Games ..........................................................................4
Building a Routine ......................................................................................................9
Encourage Mental Math & Estimation .....................................................................11
Seek Math-Centric Opportunities ............................................................................13
The Surprising Benefits of Puzzling ..........................................................................18
Conclusion: Take a Broader View .............................................................................20
Resources .................................................................................................................21
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A child that has an affinity for math can be a challenge for parents who are not trained
to handle their child’s unique needs. All too often, parents make the mistake of trying
to push gifted students through math curricula too quickly which results in knowledge
gaps and saps the fun out of doing mathematics.
Sadly, because of how math has been traditionally taught, most people believe that
math is simply a collection of facts, definitions, and algorithms to be memorized. Those
people then resort exclusively to worksheets and flash cards to “teach” students the
basic skills. However, these are lousy tools to use if your goal it to try to challenge your
child because they are boring, repetitive, and no fun!
Your goal should be to use mathematics as a TOOL to teach your child how to
THINK, REASON, ANALYZE, MAKE CONJECTURES, FORMULATE NEW IDEAS
and form their own EXPLANATIONS and PROOFS. These are the skills that the 21st
century marketplace covets and the same skills that most students fail to develop
This book will teach you how to avoid common pitfalls and help you start on the
journey to developing your gifted child’s ability to think mathematically and develop a
greater love of math.
Raj Shah, Ph.D.
Founder
[email protected]
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4. Foster a Love of Math Using Games
As parents, we have been educated on Games are to Math as Books are
children every single day. Research shows The first thing you should do as a pro-
that these experiences help children active parent is to play games with your
develop early literacy skills. The best part children as often as possible. This is as
of a nightly reading time is that it is much true for pre-schoolers as it is for
relaxing and fun for parents and kids. middle schoolers.
Unfortunately, no one tells parents to do By playing games, you help children
the same for math because getting a develop mathematical thinking skills
head start on numeracy skills has also naturally without turning math into a
been shown to pay long-term dividends. chore.
Instead of finding ways to immerse kids Games Provide Many Benefits
in hands-on mathematical experiences, • They are fun for the whole family
parents often get workbooks or • They are interactive and collaborative
flashcards and use them to make kids • They take the pressure out of math and
memorize “math facts”. This would be put it into meaningful context.
like trading in nightly “reading time”, for • They involve problem solving, critical
studying the dictionary. Your child would thinking, and estimation, and arithmetic
hate that! And yet, that’s exactly what we skills
do to math — reduce it to repetitive Which Games are the Best?
drills. The good news is there is an Almost any game you can think of
analog to “reading time”, it’s “game requires strategy, spatial reasoning, and/
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5. or pattern recognition — all skills that are As you play more, you and your child will
vital to excellence in mathematics. discover new winning strategies.
Even a “word game” like Scrabble 3. Carcassonne (Ages 8+)
involves tons of mathematical thinking Carcassonne is a tile based game for 2 to
like where to place the tiles to maximize 5 players. Players build a landscape by
your score or placing tiles to prevent adding tiles to the board as the game
your opponent from high scores. goes on. After strategically placing a tile,
players have several options for placing
Five Games to Get You Started
their “followers” on the board. This
1. SET (Ages 7+)
allows the game to be played with a
This game takes a few minutes to learn
diverse set of competing strategies,
and enhances visual / spatial reasoning
which makes the game a lot of fun.
skills. Each player surveys the field of 12
cards looking for groups of 3 cards that
are all the same or all different with
respect to shape, color, number, and
pattern. You can play a single-player
online version to learn how the game
works. Full rules can be found here.
2. Qwirkle (Ages 6+)
Qwirkle is like Scrabble, but with shapes
and colors instead of letters. Players can
build on each others lines with new tiles 4. Settlers of Catan (Ages 8+)
and the creative player can find clever Settlers of Catan is the winner of several
ways to maximize their score. Qwirkle gaming awards and was called “the
can be played with school age students. board game of our time” by The
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6. Washington Post. Players try to build • Hive (Ages 7+) by Gen42 Games
colonies as they acquire and trade • Blokus by Mattel
resources. This is another game that • Zeus on the Loose (Ages 5-9) by
allows for multiple competing strategies. Gamewright
A typical games lasts 60 to 90 minutes. • Duck Duck Bruce (Ages 4-7) by
Gamewright
5. Forbidden Desert (Ages 8+)
Forbidden Desert is a cooperative game
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where each player takes the role of an These games provide kids with great
adventurer with a unique skill that will aid opportunities to develop their thinking
the team. Players work together, using and communication skills. Games present
each other’s unique skills to survive on an a wonderful and natural learning
ever-shifting game board. The teamwork opportunity.
needed to play this game makes it a nice
change from most competitive games.
Bonus Tip: Start a Family
Game Night
Family traditions are the glue that
holds families together. Choose
one night a week to play games.
Turn off the TV, the phone and all
other distractions and just have fun!
Many games build number sense
and mental math skills.
Other Games We Recommend
• Chocolate Fix (Ages 7+) by Think Fun Play these games with your kids, I
• Solitaire Chess (Ages 7+) by Think Fun promise you’ll love them!
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Stanford psychologist Dr. Carol Dweck given talents are fixed and can’t really be
has identified two mindsets, the fixed improved? In addition, people with fixed
mindset and the growth mindset, that mindsets avoid risks for fear of failure.
help explain why some people persevere Worse, they take constructive criticism as
and others don’t. Her research on this judgment about their self-worth rather
topic is summarized in her excellent than hearing the message and working
book, Mindset. to improve.
The Fixed Mindset Many gifted students suffer from a
She states that a person with a fixed fixed mindset which prevents them
mindset believes that traits like from attempting difficult problems.
intelligence or musical talent are fixed
A student with a fixed mindset who gets
and cannot be changed. People with a
a D on a math test thinks to himself, “I’m
fixed mindset would say that Tiger
just not good at math.” They don’t try go
back to see which problems were missed
Michael Jordan had an innate talent for
or reflect on how to study better next
basketball or that Einstein was born a
time.
genius. Many of us tend to believe this at
least a little. The Growth Mindset
A person with a growth mindset believes
Unfortunately, there is an insidious side
that abilities and talents can be
to having a fixed mindset. If you believe
developed with hard work. They see
talents are fixed, you tend to not work as
failures, not as a judgement on their
hard to increase your own talent. Why
talent or self-worth, but as
bother practicing or studying when your
opportunities to grow and improve.
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8. While they feel the sting of a failure, they go when the challenges get tougher and
can move on to figure out how to so they often give up.
perform better the next time. And they
The good news is that anyone can
accept most criticism as constructive.
change their mindset. Research shows
A student with a growth mindset who that just knowing these two mindsets
gets a D on a math test, goes back to the exist can help a person move toward the
teacher to find out what they growth mindset framework. This is true
misunderstood. They develop better even for children — it’s never too early to
study habits and seeks extra help until develop a growth mindset!
they achieve mastery of the concept.
Praise Effort over Outcomes
The Power of Praise When your child comes home with an A
These days, it seems that most parents, on a math test, try saying, “I can see how
educators and coaches often deliver your studying paid off. Great work.”
praise and rewards even for average rather than “Wow! You’re so smart!”.
results. Studies show the idea that
If your child didn’t put in much effort, but
everyone deserves a trophy or that we
still got a good grade, try saying “Looks
should continually praise our children to
like that test was too easy for you. Maybe
ensure they have self-worth are
we can work on more challenging
questionable at best.
problems together.” This way you’re
It turns out that if we praise children for letting them know you value effort over
being “smart” or “gifted” or “naturally talent. You are teaching them to value
talented”, we are feeding them the idea the process of learning as much as or
that talent is innate and fixed. With a even more than grades and that it’s OK
fixed mindset, a student has no where to to struggle with challenging ideas and
problems.
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9. Building a Routine
I spent months researching proven ways one tooth, you may choose to do them
to build daily habits like studying math. all, but you don’t have to. Who can’t floss
Here’s a summary of what I learned just one tooth every night?
(primarily from BJ Fogg of Stanford
University) and how you can apply it with
Make a list of the most frequent excuses
your kids. I’ve tried it and it works!
and defeat them in advance. For
1. Set the Bar Exceedingly Low example, if you’re trying to build a daily
This may sound counter-intuitive at first, workout habit, your excuses might
but creating a very low bar makes it include: Not having a gym membership,
easier to get started each day because not having clean workout clothes, and
the task won’t seem too daunting. Here’s lack of motivation to workout alone.
an example: Suppose you want to
Now find a solution for each one. Get a
develop a daily flossing habit because
membership, get more workout gear and
you believe it’s a good practice for dental
put it in your car at all times, then find
health. Make the goal to floss just one
someone to hold you accountable like a
tooth every night.
friend or personal trainer. You can do the
same with a daily homework habit by
having a notebook, pencil and eraser
handy along with books and problems
that you want to work on. If you want to
weekly game night, pick a night and a
! game in advance and have everything
Of course, once you start to floss that ready to go when the time comes.
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10. 3. Tie the New Habit to a 5. Use Rewards for Motivation
Developed One Turn the new habit development into a
If possible, tie the timing of the new friendly competition with your child.
habit to the timing of a daily habit that They’ll have a lot more motivation to
you are already successful with. In this keep going when their motivation wanes.
way, you make it much easier to Create some small rewards for doing the
remember and much harder to avoid the habit for 3, 5, 10 and 30 days in a row.
new habit. Find a daily activity that your
child does routinely after school like
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reading or watching a show and tie the
Bonus Tip: Keep It Short but
new routine to that activity.
Frequent
4. Track Their Progress (Don’t Short, frequent lessons are much
Break the Chain) better than longer, sporadic ones.
Print a calendar and have your child
In a short lesson, your child’s
simply mark an “X” every day that they
attention is less likely to wander,
complete the task. Encourage them to
and you’ll find that you can
try and build a chain of X’s as long as
accomplish more. Keep the lessons
possible. The longer the chain gets, the
upbeat and fast-paced and use
more motivated they’ll be to not “break
teaching tools and activities that
the chain”.
interests as much as possible.
For most students, I recommend
fifteen to twenty minutes of puzzles
or games per day, five times a
week.
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11. Encourage Mental Math & Estimation
One of the best ways to build a child’s encourage them to stretch their
working memory and computational skills capabilities.
is to challenge them to do math mentally.
Many times, you can teach patterns that
The ability to do mental math is an
make mental computation much easier.
overlooked, but extremely important
For example, when adding 9 to a
life skill your child will use everyday
for the rest of their lives.
10 and taking away 1 since 9 = 10 - 1.
Most kids are conditioned to doing This allows the student to take a more
arithmetic exclusively with pencil and difficult problem that often requires
paper. These kids are at a complete loss “carrying” or “regrouping” and turn it
when asked to make mental into two simple steps.
computations. Don’t let your child fall
Use Estimation to Build Number
into this trap.
Sense
Benefit of Mental Math Another great way to build number sense
Mental math has many benefits including is to practice estimating. The ability to
increasing creativity, working memory, estimate quickly can help students find
and improving number sense — the obvious computation errors and help
ability to intuitively understand numbers them greatly improve test scores. Later,
and reasonableness of answers. students will use estimation in real-life
situations at home and at work.
At first, your child may find mental math
frustrating, so start with simple Use the world around you to inspire
computations to build confidence and estimation activities you can do together.
then slowly increase the difficulty level to
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12. Estimation Examples To make things a little more fun,
• In the car, estimate how far it is from challenge your child to a contest to see
home to your destination or make a who can get closer to the correct answer.
reasonable guess at your average Every once in a while, make an “off-the-
speed and then estimate how long it wall” estimate and see if your child can
will take. explain if the estimate is reasonable or
• At the gas station, estimate the cost of not. You’ll be teaching valuable skills in
a fill up or how far you can expect to mental math, estimation, and checking
travel on one tank of gas. for reasonable answers.
favorite player’s shooting percentage. Bonus Tip: Provide
• While eating out, you can try to landmarks, but not answers.
estimate the final bill as well as the tax When students are struggling with
and tip. a mental math computation, you
can provide them with a
“landmark” that may help them.
For example, your child is stuck
while trying to compute 19 times 5.
You could reply with “I don’t know
what 19 times 5 is, but I do know
what 20 times 5 is. Then wait to see
if your child can make the
connection that 19 times 5 must be
5 less than 100 which is 95.
A child’s ability to make these kinds
of connections is vital to higher
level mathematical thinking.
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13. Seek Math-Centric Opportunities
When your child shows an interest in from about 8 years old and up. The kit
music or sports, you sign them up for comes with several example designs and
lessons or enroll them in a sports league. the flexibility to create an endless
You should try to do the same with your number of variations.
mathematically precocious child.
Through robotics students to develop
Students who excel at math tend to numerous skills including:
enjoy activities like robotics, computer
• Design and construction
programming, video game design, and
• Computer programming
• Problem solving
Robotics • Critical thinking
Even if you don’t have robotics or
search will yield a large variety of
Computer Programming
Learning to program a computer is
another activity in which kids can see the
fruits of their labor while developing
Working with robotics is a wonderful way computational thinking skills.
to see mathematics in action. One of the
I’ve found the best place to start is with a
best robotics kits for kids is the LEGO
computer language for kids created at
Mindstorms EV3. The EV3 offers a
MIT called SCRATCH (scratch.mit.edu).
wonderful hands-on experience for kids
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14. Another great resource is code.org. Start Search For Opportunities
your child on the “Hour of Code” and let Search your community for opportunities
them take it from there. The web is rich like a Math Olympiads Team, Chess
with resources to teach kids and adults Club, Robotics team, and Computer
how to code. Programming workshop. Often these are
offered at the local Science and Industry
Museum or as summer camps at the
community center. If you’re lucky, they
can be offered at school as well.
Math Plus Academy offers all of these
programs year-round. We are on a
mission to inspire kids to do great things
! and what better way to do that than
through amazing, fun enrichment classes
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“I have no special talents. I am just I’ve found the best answer to “Why
passionately curious.” — Albert …?” is “Why do you think?”. This
Einstein allows for you to have a productive
conversation where you can learn much
Did you know that an average 4 year-old
asks 65 questions per day? By age 8 that
knows as well as what concepts they are
number drops to 32 questions per day
missing.
and by age 40 we ask just 6 questions
per day. A Personal Story
My eight year old son asks a LOT of
Children are born with insatiable
questions. He’s very observant and highly
curiosity, but through school and life
inquisitive.
natural curiosity fades. It doesn’t have to
be this way. Allow your child’s curiosity to On a Saturday afternoon in late autumn,
flourish by encouraging them to our family went to a popular local
investigate the answers to some of their shopping mall. When we arrived it was
questions. cold and rainy so I decided to seek
shelter in a covered parking garage. The
The Best Way to Answer “Why?”
garage had an electronic sign that
indicated how many spaces were open.
First, realize that it is NOT your
My son noticed the sign and asked,
responsibility to answer all of your
“Dad, how do they know how many
child’s questions. Your role is to facilitate
spots are empty?”.
questions on their own. ME: “How do YOU think they know how
many spots are available?”
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16. THE BOY: (after a brief pause) “They He was stuck, temporarily out of
must have a camera over every spot, inspiration. So, I waited and then gave
then they can count the open spots.” him a gentle hint.
ME: “I don’t see cameras over every ME: “How many entrances and exits
spot, do you? Plus, I would imagine that does the garage have?”
a camera over every spot would be quite
THE BOY: “There’s only one way in and
expensive. Can you think of another
one way out.”
ME: “Hmmm… interesting… I wonder if
THE BOY: (another brief pause) “Maybe
the garage starts out empty early in the
they have a person at the end of every
morning.”
row that counts the empty spaces in that
row.” At this point, he had his “AHA” moment.
I know because he literally stopped in his
ME: “I don’t see anyone watching the
tracks and looked up at me smiling ear to
spots like that and how would they
ear.
communicate when something changed.
Any other ideas?” THE BOY: “I got it! They just count the
cars going in and out! When a car goes
in, that’s one less space and when one
comes out, that’s one more space.”
ME: “That makes sense, I bet that’s how
they do it!”
If I hadn’t been so excited at his
epiphany, I would have tried to extend
this even further with “Can you imagine
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17. other situations where you could know
what’s inside by counting what goes in
Interests to Your
and what comes out?”
Their Own Questions mysteries and other books that
The biggest benefit of this strategy is it include math or puzzles.
gets a child to accept the “discomfort”
• If your child likes art or animation,
of not knowing the answer and teaches
look for books or videos that can
them to persevere in the face of “not
connect art to architecture or
knowing” with the confidence that if they
computer animation to geometry.
keep trying, they will find a solution. Too
many students lack the ability to manage • If your child likes to play Minecraft
this “discomfort” and tend to beg for an or LEGOs, encourage them to
answer or just give up. build a scale model of your home
or any other building of interest.
Over time, this strategy will also teach
your child how to investigate questions • If your child enjoys cooking, then
on their own and it will enhance their following recipes is ripe for
creativity. Most of the great discoveries in conversations about
history are the result of passionately measurement, unit conversions,
curious people asking a new question and proportions.
The amazing thing about math is
Next time your child asks one of those that you can pursue it’s study just
“How does it work” type questions, try for fun or you can focus on it’s
answering with “How / Why do you practical application in almost
think?” and see what happens. every facet of human existence
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18. The Surprising Benefits of Puzzling
Why Do People Enjoy Puzzles? Puzzles Build Perseverance
Neuroscientist Daniel Bor, a research Many novice puzzlers give up. They will
fellow at the University of Sussex in say to themselves “I have tried
England, believes it’s because we take everything I can think of, this puzzle is
great pleasure in pattern-finding. In his impossible.” However, with puzzles, you
book, "The Ravenous Brain", he asserts have the opportunity to conquer the
that human brains are “ravenous” for impossible. What impossible really
new innovative solutions to problems. means in the puzzle context is that you
simply haven’t figured out how to get to
Puzzles are compelling because they
the solution *yet*. This is a great lesson
offer a complete problem-solving
that children can learn by playing with
experience, from defining the goal to
puzzles.
determining the characteristics of the
given information, and finally the Puzzles are Fun and Rewarding
solution. Many people find puzzles relaxing.
Puzzles provide you with a sense of
The Benefits of Puzzling
accomplishment which releases
Puzzles Enhance Creativity
dopamine in the brain, furthering your
Good puzzles require the solver to look
sense of happiness. The "Aha!" that
at the problem in multiple ways and from
happens when a person goes through a
different perspectives. As a natural
major shift in perception to achieve a
solution to a problem (puzzle) becomes
more questions and taps into their
just as satisfying as an ice cream cone.
imagination to find novel pathways.
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19. Puzzles Develop Critical Thinking • krazydad.com
The steps it takes to complete a puzzle • puzzles.com
incorporate elements of sequencing, • New York Times Numberplay blog
planning, logic, strategy and problem !
solving. These skills require the work of Looking for More Problem
your prefrontal cortex located in the Solving Opportunities?
frontal lobe. At Math Plus Academy, we are constantly
seeking out the best puzzles for kids.
The best puzzles are addictive just like a
Unique puzzles that will help students
well-designed video game. As soon as
build mathematical thinking skills and
you finish one, you want to reach for
offer just the right level of challenge.
Added Benefits of Our Problem Based
Try this puzzle for fun (It's a Programs
challenging one!)
The members of a math team • We help encourage students to
contributed a total of \$2.89 for persevere.
refreshments for their weekly practice. • We ask questions that spark their
Each member contributed the same creativity.
amount and paid for his or her share with • We teach kids how to organize their
exactly four coins. How many pennies thinking so that can be more
were contributed by all of the members productive and efficient problem
combined? solvers.
• Students work together to develop
Ready to do some puzzles with your
solutions and build teamwork skills
• We review every solution to make sure
Here are three great sources for a variety children retain the key insights.
of interesting puzzles. !
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20. Conclusion: Take a Broader View
As a parent, it’s natural to want your child their own and make mistakes without
to excel and to try and advance them being judged, then you will have created
through math curriculum as quickly as the ideal space for them to develop
possible to keep them challenged. mathematical thinking skills.
However, there is another way.
In the process, you should see your
Take a Broader View of child’s curiosity, perseverance, and
Mathematics problem solving skills grow by leaps and
If you believe that math is just a bounds.
collection of concepts, algorithms, and
Enjoy the journey with your child!
arithmetic, then you will miss out on all
it’s beauty and elegance. The pursuit of Dr. Raj Shah
mathematics through problem solving
thinking skills they will need to be
successful in the 21st century.
Mathematics is one of the best fields in
which one can develop the ability to
THINK, REASON, CREATE, ANALYZE,
FORMULATE IDEAS and SOLVE
If you create a culture in your home that
allows for your children to explore on
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21. Books for Kids Puzzle Websites
Grapes of Math - Gregory Tang puzzles.com - variety of logic puzzles
Math Appeal - Gregory Tang nrich.maths.org - games, lessons, ...
Math Curse by Jon Scieszka mathpickle.com - math explorations
How Much is a Million - David M krazydad.com - Japanese logic puzzles
Spaghetti and Meatballs for All - Marilyn
Games
Burns Visual / Spatial
The Greedy Triangle - Marilyn Burns SET
Sir Cumference and the First Round Swish
Table - Cindy Neuschwander Shape by Shape
Chasing Vermeer - Blue Baillett Blokus
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Books for Parents Strategy
Mindset - Dr. Carol Dweck Carcassonne
The Mathematician’s Lament - Paul Settler’s of Catan
Lockhart Qwirkle
So Good They Can’t Ignore You - Cal Hive
Newport !
! Logic
Problem Solving & Puzzle Books Chocolate Fix
Becoming a Problem Solving Genius - Ed Rush Hour
Zaccaro Solitaire Chess
Thinking Mathematically - J. Mason !
Creative Problem Solving - George Arithmetic / Memory
Lenchner Zeus on the Loose
My Best Mathematical and Logic Puzzles Duck, Duck, Bruce
- Martin Gardner Rat-a-tat-cat
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