Get ‘ em Involved: Problem Solve
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Get ‘em Involved: Problem Solve One of the world’s top mathematicians, Laurent Schwartz, reflected in his memoir that he was made to feel unintelligent in school because he was the slowest math thinker in his class. But he points out that what is important in mathematics “is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.” It is fortunate for Schwartz, and all of us, that he did not grow up in the speed and test-driven classrooms of the last decade that have
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Get ‘em Involved: Problem SolveOne of the world’s top mathematicians, Laurent Schwartz, reflected in his memoir that he was made to feel unintelligent in school because he was the slowest math thinker in his class. But he points out that what is important in mathematics “is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.” It is fortunate for Schwartz, and all of us, that he did not grow up in the speed and test-driven classrooms of the last decade that have successfully dissuaded any child that thinks deeply or slowly from pursuing mathematics or even thinking of themselves as capable.
Get ‘em Involved: Problem Solve
History –Problem Solving/TestingImportance of MindsetsCreating a Problem Solving AtmosphereIdeas (Links) for activities
Get ‘em Involved: Problem Solve•One Constant• involved• contrary to testing
•My History•“Traditional” Teaching• Show me how
•Learned “Hands On” in college • education not math classes
•Student taught traditional• UI, CI, CC, UC
•1st job – 6 classes – traditional•Nekoosa to teach math – traditional•Green Lake• new ideas and activities (deviate from the book) • Math Standards
Get ‘em Involved: Problem Solve
•Moved up•Pretest• Think about what I was doing• Taught to the test• Got them to perform• Had to show them first
•Found out I was UI and now I was CI•Teaching for Understanding•Sometimes I feel like I am being asked to be CI by teaching to the test.
•Mindsets• “I’m good/not good in math.”
•Intelligence is static and leads to a desire to look smart so therefore a tendency to:• Challenges• avoid challenges
• Obstacles• give up easily
• Effort• see effort is fruitless or worse
• Criticism• ignore useful negative criticism
• Success of others• feel threatened
Fixed Mindset
•Intelligence can be developed• leads to a desire to learn and therefore a
tendency to . . .• Challenges• embrace challenges
• Obstacles• persist in the face of setbacks
• Effort• see effort as a path to mastery
• Criticism• learn from criticism
• Success of others• find lessons and inspiration in the success
of others
Growth Mindset
•Not about the book you use, it’s how you use it – CMP• Figure out? Find own shortcuts and patterns.• Fraction pieces from Fraction Factory
•Cannot be afraid to make mistakes•Goal is NOT to “Get a Grade”•Goal is to Learn and Understand Math •Group/Partner work • We try to figure stuff out - answers are often
posted• We do problems on our own and compare• Fun to learn new stuff
•When you tell them “How”, the thinking process stops• Doesn’t mean you never tell them how• If you do, get them to tell others
•Effort Determines Success
Build a Problem Solving Atmosphere
•Introduction to Problem Solving• Guess a number • There are 350 pebbles in a jar. There are
50 more black pebbles than there are white pebbles. How many white pebbles are there?• Sometimes you have to get it wrong
before you get it right.
• The Problem Solver
Build a Problem Solving Atmosphere
•3 Act Math• Act One• What question do you have?
• Act Two• What information do you need from
me?• Act Three• Solve it
• Penny Problem• http://mrmeyer.com/threeacts/
pyramidofpennies/
Build a Problem Solving Atmosphere
Nana’s Chocolate Milk
Pyramid of Pennies• Act One• What question do you have?
• Act Two• What information do you need from me?
• Act Three• Solve it
•Messing with Numbers (Number Talks)• In place of Timed Tests• Memorizing is the only way• Ask “How”• Doesn’t mean “never”
• Computation : 198 + 479 Find as many ways as possible• Will do right to left like paper and pencil• L to R• Add 200 and subtract 2• round both then adjust• Move 2 from 479 to 198
• 600/4, 12x5 (6x10)• How many different ways can you do these?• Whole class, partner, and groups
Build a Problem Solving Atmosphere
•Messing with Numbers (Number Talks)
Build a Problem Solving Atmosphere
Input Output123 74567 158
100x
•LOGO (Be the turtle)• Polygon Activity• Groups: Turtle make triangle• fd 5, rt 60, fd 5, rt 60 fd 6 rt 60
• Intro to programming or coding• Make polygons, initials, and a house• Plan, write program, try it, debug
• Online and/or download from UCB•Hour of Code•Puzzle Tables• Handout• “Create” them (computation, fractions,
decimals, algebra)•“24” cards
Build a Problem Solving Atmosphere
•What is Algebra? • Letters for numbers• Symbols for numbers• Variables• Math for really smart people• Equations• Boring, frustrating• Extreme math, math on steroids
•Introduction to Algebra• Border Problem (Marilyn Burns)• Pastures (Beginning Algebra Thinking)• Puzzle Tables • Number Talks (Input, Output)
Build a Problem Solving Atmosphere
The Border Problem
How many squares are shaded?• (4x10) – 4• 10+9+9+8• 100-64• 10+10+8+8• (2x10)+(2x8)• 4x9
Edge Shaded
3 84 125 166 2010 36
100 396n (n-1) x
4
Pastures
Puzzle Tables
Number TalksInput Output
1234 ?567 208
100x
What is the output for 4 and how did you get it?
Coin Flip Activity
Figure out using manipulatives
Build a Problem Solving Atmosphere
•Mathalicious •Kids create videos• Willing to spend time• “Teaching Videos”• long division using manipulatives
• Taste Test commercials
Build a Problem Solving Atmosphere
If you allow kids to “create”, they must solve problems.
•“How to Teach Math”• (MOOC) Massive Open Online Course• 40,000 students• Phoenix Park and Amber Hill Schools Study• Traditional and Problem Based• Better problem solvers and test takers
•SO . . . If you are told “You need to teach to the test”, so then, according to the data, you must stop teaching to the test.
Build a Problem Solving Atmosphere
Get ‘em Involved: Problem SolveOne of the world’s top mathematicians, Laurent Schwartz, reflected in his memoir that he was made to feel unintelligent in school because he was the slowest math thinker in his class. But he points out that what is important in mathematics “is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.” It is fortunate for Schwartz, and all of us, that he did not grow up in the speed and test-driven classrooms of the last decade that have successfully dissuaded any child that thinks deeply or slowly from pursuing mathematics or even thinking of themselves as capable.
