Dr. Raj Shah [email protected]
How to Keep Your Child Challenged in Math Dr. Raj Shah [email protected]
Thursday, November 3, 11
What is Mathematics?
Thursday, November 3, 11
1 4 + 3 7 secant
Z
3 dx
x
s
x s o c x n i s 2 = x in 2
mixed number This is why most = i⇡ b 1=0 + e + a people think they 61 ⇡ r 2 don’t = polynomial like math! 4 6 44 = 2
2
c
2
x 2 + 4x
432
7⇥ Thursday, November 3, 11
6 5 8=
117 = 3
15
+ 17
prime
+5=0
8 2÷
51
perimeter
Traditional “Definition” • Numbers
• Trigonometry
• Addition
• Statistics
• Subtraction
• Algebra
• Variables
• Geometry
• Calculus
• Formulas
• Division
• Equations
Thursday, November 3, 11
Mathematics is the Art of Explanation Paul Lockhart, Mathematician
Thursday, November 3, 11
•
“If you deny students the opportunity to pose their own problems,
•
to make their own conjectures...,
•
to be wrong,
•
to be creatively frustrated,
•
to have an inspiration,
•
•
and to cobble together their own explanations and proofs, you deny them mathematics itself.” -- Paul Lockhart, Mathematician
Thursday, November 3, 11
A Different Kind of Math Problem
Thursday, November 3, 11
Problem: Color this Map using the fewest colors
Thursday, November 3, 11
Problem: Color this Map a simpler problem
3
2 1
2
Thursday, November 3, 11
1 3
Problem: Color this Map How can you extend this problem?
Thursday, November 3, 11
Problem: Color this Map • No mapmaker was ever limited to just 3 or 4 colors of ink!
• Yet, mathematicians studied this for fun for over 100 years!!!
• In 1976, “Four Color Theorem” was finally proven.
• There’s a Map Coloring Algorithm... Thursday, November 3, 11
Why Did We Just Spend 5 Minutes Coloring Maps?
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Simplifying
• Connecting
• Organizing
• Wondering
• Inventing
• Imagining
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Simplifying
• Connecting
• Organizing
• Wondering
• Inventing
• Imagining
Thursday, November 3, 11
Would You Rather Know How to Think or How to Compute? Which one do you think employers value?
Thursday, November 3, 11
Traditional Definition • Numbers
• Trigonometry
• Addition
• Statistics
• Subtraction
• Algebra
• Calculus
• Formulas
• Division
• Equations
This is mathematical knowledge • Variables • Geometry
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Organizing
• Wondering
• Inventing
• Imagining
This is mathematical thinking • Simplifying • Connecting
Thursday, November 3, 11
Knowledge is Important
Thinking is Essential
Thursday, November 3, 11
Knowledge Builders • Flashcards • Worksheets • Workbooks • Math Drill Websites
Thursday, November 3, 11
How much fun is this?
WARNING: Overuse may be hazardous to attitude and interest
Thursday, November 3, 11
Would this be more fun?
Can you color this map with just 3 colors? or 4? or 5?
Thursday, November 3, 11
School will teach the content Focus on mathematical thinking at home
Thursday, November 3, 11
Creating a Mathematical Culture at Home
Thursday, November 3, 11
Cultural Belief #1 Problem solving is challenging and fun
Thursday, November 3, 11
Cultural Belief #2 Failures are opportunities to learn
Thursday, November 3, 11
Cultural Belief #3 Celebrate effort regardless of outcome
Thursday, November 3, 11
Cultural Belief #4 Curiosity is always encouraged
Thursday, November 3, 11
Cultural Belief #5 Better to understand than memorize
Thursday, November 3, 11
Cultural Belief #6 Mental math trumps paper and pencil
Thursday, November 3, 11
Cultivate A New Attitude • Perseverance - “I refuse to give up.” • Confidence - “I can do it.” • Intuition - “I have an idea...” • Curiosity - “I wonder...”
Thursday, November 3, 11
Perseverance Reward effort not natural talent
Thursday, November 3, 11
Confidence Built through incremental successes (Be less helpful)
Thursday, November 3, 11
Intuition Do lots of problems (there’s no shortcut)
Thursday, November 3, 11
Curiosity Extend problems and always ask why
Thursday, November 3, 11
Tools for a Mathematical Culture
Thursday, November 3, 11
Leverage What Kids Already Enjoy Play Problem Solving Competition Exploration
Thursday, November 3, 11
Classic Games • Chess • Go • Backgammon • Dice games - Yahtzee, Shut the Box, ... • Card games - Rummy, Cribbage, ...
Thursday, November 3, 11
Tip: Verbalize your strategy
Thursday, November 3, 11
New Games • Think Fun • Rush Hour, Chocolate Fix, Tilt, Solitaire Chess... • Set • Gamewright • Loot, Zeus on the Loose, ... • Qwirkle • Blokus Thursday, November 3, 11
Tip: Establish a Family Game Night
Thursday, November 3, 11
Puzzles • Brain Teasers • Logic puzzles • Sudoku • KenKen • Kakuro • ... Thursday, November 3, 11
How Many Squares on a Chess Board?
Thursday, November 3, 11
Puzzle Sites • puzzles.com (try family brainstorms) • figurethis.org • nrich.maths.org • mathpickle.com • nikoli.com • krazydad.com Thursday, November 3, 11
Tip: Set aside regular “puzzle time” just like “reading time”
Thursday, November 3, 11
Everyday Life • Calculate recipe quantities • Estimate travel time • Calculate sports statistics • Estimate grocery bill • Compute taxes, sale prices, etc.
Thursday, November 3, 11
Tip: Challenge each other to make estimates.
Thursday, November 3, 11
Extra-Curricular • Math Olympiads (4th - 6th) • MATH COUNTS (6th - 8th) • Robotics (3rd+) • Computer Programming
Thursday, November 3, 11
Books • Becoming a Problem Solving Genius – Edward Zaccaro
• Creative Problem Solving – Dr. George Lenchner
• Math Oympiad Contest Problems
(Volume 1 & 2) – Dr. G. Lenchner
• Anything by Greg Tang Thursday, November 3, 11
Parent Book List • A Mathematician’s Lament - Paul Lockhart
• Mindset - Carol Dweck • Drive - Dan Pink • Bounce - Matthew Syed
Thursday, November 3, 11
Presentation Notes • MathPlusAcademy.com/challenge • Download PDF of presentation • Sign up for our eNewsletter to get more articles and useful tips.
Thursday, November 3, 11
If You Enjoyed This... • Field trips • Math Day (like COSI on Wheels) • Math Night • PTO partnerships • MathPlusAcademy.com/outreach • Games-a-palooza: Sat. Dec. 3, 2-5pm Thursday, November 3, 11
Q&A
Thursday, November 3, 11
Thursday, November 3, 11
What is Mathematics?
Thursday, November 3, 11
1 4 + 3 7 secant
Z
3 dx
x
s
x s o c x n i s 2 = x in 2
mixed number This is why most = i⇡ b 1=0 + e + a people think they 61 ⇡ r 2 don’t = polynomial like math! 4 6 44 = 2
2
c
2
x 2 + 4x
432
7⇥ Thursday, November 3, 11
6 5 8=
117 = 3
15
+ 17
prime
+5=0
8 2÷
51
perimeter
Traditional “Definition” • Numbers
• Trigonometry
• Addition
• Statistics
• Subtraction
• Algebra
• Variables
• Geometry
• Calculus
• Formulas
• Division
• Equations
Thursday, November 3, 11
Mathematics is the Art of Explanation Paul Lockhart, Mathematician
Thursday, November 3, 11
•
“If you deny students the opportunity to pose their own problems,
•
to make their own conjectures...,
•
to be wrong,
•
to be creatively frustrated,
•
to have an inspiration,
•
•
and to cobble together their own explanations and proofs, you deny them mathematics itself.” -- Paul Lockhart, Mathematician
Thursday, November 3, 11
A Different Kind of Math Problem
Thursday, November 3, 11
Problem: Color this Map using the fewest colors
Thursday, November 3, 11
Problem: Color this Map a simpler problem
3
2 1
2
Thursday, November 3, 11
1 3
Problem: Color this Map How can you extend this problem?
Thursday, November 3, 11
Problem: Color this Map • No mapmaker was ever limited to just 3 or 4 colors of ink!
• Yet, mathematicians studied this for fun for over 100 years!!!
• In 1976, “Four Color Theorem” was finally proven.
• There’s a Map Coloring Algorithm... Thursday, November 3, 11
Why Did We Just Spend 5 Minutes Coloring Maps?
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Simplifying
• Connecting
• Organizing
• Wondering
• Inventing
• Imagining
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Simplifying
• Connecting
• Organizing
• Wondering
• Inventing
• Imagining
Thursday, November 3, 11
Would You Rather Know How to Think or How to Compute? Which one do you think employers value?
Thursday, November 3, 11
Traditional Definition • Numbers
• Trigonometry
• Addition
• Statistics
• Subtraction
• Algebra
• Calculus
• Formulas
• Division
• Equations
This is mathematical knowledge • Variables • Geometry
Thursday, November 3, 11
Mathematical Thinking • Experimenting
• Strategizing
• Conjecturing
• Reasoning
• Estimating
• Proving
• Organizing
• Wondering
• Inventing
• Imagining
This is mathematical thinking • Simplifying • Connecting
Thursday, November 3, 11
Knowledge is Important
Thinking is Essential
Thursday, November 3, 11
Knowledge Builders • Flashcards • Worksheets • Workbooks • Math Drill Websites
Thursday, November 3, 11
How much fun is this?
WARNING: Overuse may be hazardous to attitude and interest
Thursday, November 3, 11
Would this be more fun?
Can you color this map with just 3 colors? or 4? or 5?
Thursday, November 3, 11
School will teach the content Focus on mathematical thinking at home
Thursday, November 3, 11
Creating a Mathematical Culture at Home
Thursday, November 3, 11
Cultural Belief #1 Problem solving is challenging and fun
Thursday, November 3, 11
Cultural Belief #2 Failures are opportunities to learn
Thursday, November 3, 11
Cultural Belief #3 Celebrate effort regardless of outcome
Thursday, November 3, 11
Cultural Belief #4 Curiosity is always encouraged
Thursday, November 3, 11
Cultural Belief #5 Better to understand than memorize
Thursday, November 3, 11
Cultural Belief #6 Mental math trumps paper and pencil
Thursday, November 3, 11
Cultivate A New Attitude • Perseverance - “I refuse to give up.” • Confidence - “I can do it.” • Intuition - “I have an idea...” • Curiosity - “I wonder...”
Thursday, November 3, 11
Perseverance Reward effort not natural talent
Thursday, November 3, 11
Confidence Built through incremental successes (Be less helpful)
Thursday, November 3, 11
Intuition Do lots of problems (there’s no shortcut)
Thursday, November 3, 11
Curiosity Extend problems and always ask why
Thursday, November 3, 11
Tools for a Mathematical Culture
Thursday, November 3, 11
Leverage What Kids Already Enjoy Play Problem Solving Competition Exploration
Thursday, November 3, 11
Classic Games • Chess • Go • Backgammon • Dice games - Yahtzee, Shut the Box, ... • Card games - Rummy, Cribbage, ...
Thursday, November 3, 11
Tip: Verbalize your strategy
Thursday, November 3, 11
New Games • Think Fun • Rush Hour, Chocolate Fix, Tilt, Solitaire Chess... • Set • Gamewright • Loot, Zeus on the Loose, ... • Qwirkle • Blokus Thursday, November 3, 11
Tip: Establish a Family Game Night
Thursday, November 3, 11
Puzzles • Brain Teasers • Logic puzzles • Sudoku • KenKen • Kakuro • ... Thursday, November 3, 11
How Many Squares on a Chess Board?
Thursday, November 3, 11
Puzzle Sites • puzzles.com (try family brainstorms) • figurethis.org • nrich.maths.org • mathpickle.com • nikoli.com • krazydad.com Thursday, November 3, 11
Tip: Set aside regular “puzzle time” just like “reading time”
Thursday, November 3, 11
Everyday Life • Calculate recipe quantities • Estimate travel time • Calculate sports statistics • Estimate grocery bill • Compute taxes, sale prices, etc.
Thursday, November 3, 11
Tip: Challenge each other to make estimates.
Thursday, November 3, 11
Extra-Curricular • Math Olympiads (4th - 6th) • MATH COUNTS (6th - 8th) • Robotics (3rd+) • Computer Programming
Thursday, November 3, 11
Books • Becoming a Problem Solving Genius – Edward Zaccaro
• Creative Problem Solving – Dr. George Lenchner
• Math Oympiad Contest Problems
(Volume 1 & 2) – Dr. G. Lenchner
• Anything by Greg Tang Thursday, November 3, 11
Parent Book List • A Mathematician’s Lament - Paul Lockhart
• Mindset - Carol Dweck • Drive - Dan Pink • Bounce - Matthew Syed
Thursday, November 3, 11
Presentation Notes • MathPlusAcademy.com/challenge • Download PDF of presentation • Sign up for our eNewsletter to get more articles and useful tips.
Thursday, November 3, 11
If You Enjoyed This... • Field trips • Math Day (like COSI on Wheels) • Math Night • PTO partnerships • MathPlusAcademy.com/outreach • Games-a-palooza: Sat. Dec. 3, 2-5pm Thursday, November 3, 11
Q&A
Thursday, November 3, 11
