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Revolutionizing Our Thinking About Math Instruction Building Mathematicians "The mind is not a vessel to be filled but a fire to be kindled." Plutarch, Greek Historian

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"We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility. -- Mary Beth Ruskai

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"Mathematics is no more computation than typing is literature." -- John Allen Paulos, Mathematics Professor, Temple, Author "Calculators can only calculate - they cannot do mathematics." -- John A. Van de Walle NCTM, Math Educator, Author aka or Mathematician Calculator Math Magician!!! Computer

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Building Mathematicians: Laying a Firm Foundation EQ: What is a mathematician? EQ: What are the fundamental skills a mathematician needs?

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the Science of Pattern and Order Math is "A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?" -- Martin Gardner, Mathematics Writer "Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders, designs, and harmonies. -- William L. Schaaf, Math Professor, Author "What humans do with the language of mathematics is to describe patterns..." -- Lynn A. Steen, Math Professor

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GeometryTrigonometry Differential geometryTopology Fractal geometry Measure theory Calculus Vector calculus Differential equations Dynamical systemsChaos theory Complex analysis Math is the Science of Pattern and Order

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the Pursuit of Laziness "The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder, Math Professor, Author "You know we all became mathematicians for the same reason: we were lazy." -- Max Rosenlicht, Mathematician Math is "Life is too short for long division."

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Math is the Pursuit of Laziness

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Many Paths, One Door Math is the Pursuit of Laziness

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Excerpt: Lets take a look at what the pursuit of laziness in mathematics might mean for our students and us. First of all, laziness does not mean an unwillingness to do work; rather, it speaks to an unwillingness to do pointless or unnecessary work in order to accomplish an objective. http://blog.aimsedu.org/2013/05/28/in-pursuit-of-laziness/ Math is the Pursuit of Laziness Second, laziness does not imply thoughtlessness or carelessness. Lazy mathematicians are extraordinarily thoughtful, but they take care to think on the right things and avoid irrelevant or unproductive approaches. Finally, laziness is not inactivity. While the pencil might be still, the mind is active and pursuing solutions to the problem at hand.

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Building Mathematicians: Laying a Firm Foundation EQ: What is a mathematician? EQ: What are the fundamental skills a mathematician needs?

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Content vs. Skill

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Standards of Mathematical Practice Activity: Name that Standard Strategy: Think, Pair, Pair Again

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Standards of Mathematical Practice Spider

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SMP 1 Make Sense of Problems and Persevere in Solving Them. LowHigh Learned Helplessness: I cant do this problem Fast Processors: This problem is wrong "Too many students give up upon encountering difficulties in math, when just trying a few strategies could mean the difference between succeeding and failing." -- Arthur E. Schwartz "If there is a problem you can't solve, then there is an easier problem you can't solve: find it." -- George Polya

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SMP 1 Make Sense of Problems and Persevere in Solving Them. I can solve problems without giving up.

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SMP 2 Reason abstractly and quantitatively. Students move from: tangible to intangible with units to without

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SMP 2 Reason abstractly and quantitatively. I can think about numbers in many ways.

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SMP 3 Construct viable arguments and critique the reasoning of others. Does the commutative property work for subtraction? Johnny: Yes, 2-2=0 and 2-2=0

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I can explain my thinking and try to understand others. SMP 3 Construct viable arguments and critique the reasoning of others.

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SMP 4 Model with mathematics.

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I can show my work in many ways.

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SMP 5 Use appropriate tools strategically. Dickerson Summer Math Packet 5 * $4.97.5 * $14.70 $4.97 =$5 - 3.5 = $14.70 =$14 + 70

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SMP 5 Use appropriate tools strategically. I can use math tools and show why I chose them.

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SMP 6 Attend to precision.

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I can work carefully and check my work.

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SMP 7 Look for and make use of structure. 1 + 2 = 3 10 + 20 = 30.1 +.2 =.3 1/10 + 2/10 = 3/10 1/5 + 2/5 = 3/5

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SMP 7 Look for and make use of structure. I can use what I know to solve new problems.

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SMP 8 Look for and express regularity in repeated reasoning. 2 + 2 + 2 + 2 + 2 + 2 = 6 x 2 5 = 10 2 so a x 5 = a x 10 2 or a 2 x 10 Multiplying 11s 11 x 23 2 3 5

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SMP 8 Look for and express regularity in repeated reasoning. I can discover and use shortcuts.

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Intro to Number Talks Students have the opportunity to:

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Intro to Number Talks Teachers have the opportunity to: Assess student understanding quickly Identify misconceptions or wrong thinking Build mental math skills Build computational fluency Allow students time to construct knowledge

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Math is a Foreign Language and it is not Dead Spoken and written Symbols Inferencing Context Clues Multiple meanings Things Get Lost in Translation Global