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West Virginias Next Generation Mathematics Content Standards and Objectives Spring Conference for Federal Program Directors and Chief Instructional Leaders Waterfront Place Hotel, Morgantown, WV March 10, 2011 Lynn Baker, Math Science Partnership Coordinator John Ford, Title I Mathematics Coordinator Lou Maynus, Mathematics Coordinator

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WVs Next Generation Mathematics Content Standards and Objectives Why do we need yet another set? Sets of state and national math standards have come and gone in the past twenty years. So, how are these different? These standards are truly the next generation of standards - their demand on teachers' content knowledge is substantial. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Previous sets of standards focused on: (1) whether to include a certain mathematical topic (e.g., the long division algorithm, logarithm), (2) whether certain activities receive the correct emphasis (e.g., use of manipulative or use of estimation), (3) whether to do topic x in grade n (e.g., x = data and n = 3, or x = algebra and n = 8). The underlying assumption has been that the mathematics of the school curriculum is well understood and it is only a matter of putting all the pieces together in the right way. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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K-12 Mathematics is NOT well understood and it is MUCH MORE THAN a matter of lining up the pieces in the right way. WVs next generation set of standards are written to ensure depth of understanding of the required topics in mathematics. Getting the math right is a serious issue. If we don't get it right, our students cannot learn. Garbage in, garbage out. We as a nation have been suffering from this mathematics mis- education for decades. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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You have all heard… Im just not a math person I taught it, they just dont get it They dont know their facts If they only knew fractions, they could do algebra These are all manifestations of garbage in, garbage out. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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We cannot teach what we do not know. We must KNOW the content. Knowing a concept means knowing its precise statement, when it is appropriate to apply it, how to prove that it is correct, the motivation for its creation, and, of course, the ability to use it correctly in diverse situations. We cannot claim to know the mathematics of a particular grade without also knowing a substantial amount of the mathematics of three or four grades before and after the grade in question. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Let us look at a simple topic: adding fractions. A set of state standards, long regarded as one of the best, has this to say: Grade 5. Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals. Grade 6. Students calculate and solve problems involving addition, subtraction, multiplication, and division. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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That is all. No need to go into details because we all know what to do, right? Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Another set of standards from a state that takes great pride in its work has this to say about adding fractions: Grade 4. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. Grade 5. 1. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. 2. Model addition and subtraction of fractions and decimals using a variety of representations. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Again, no need to go into details because we all know what to do, right? Wrong! Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Adding is supposed to combine things". The concept of combining" is so simple to children that it is always taught at the beginning of arithmetic. But did you see any combining" in the preceding description of how to add to ? If children have made the effort to master the addition of whole numbers as combining things, they should rightfully expect the addition of fractions to the same. So how can they learn this hard to figure out procedure? Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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NxG WVCSOs realizes that the business-as- usual kind of standards will not improve math education. So it approaches the addition of fractions as a progression from the simple to the complex, and spreads it across grades 3-5 to allow things to sink in. Its aim is to make students see that adding is combining things" Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Altogether, these standards guide students through three grades to get them to know the meaning of adding fractions: Addition is putting things together, even for fractions, and the logical development ends with the formula a/b + c/d = (ad + bc)/bd. There is no mention of Least Common Denominator. This is as it should be. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Teachers have to be aware how a child learns about combining things", and more importantly, have to know the mathematics so that they can teach in a way that respects the child's intuition about combining things". The same can be said for the teaching of fractions and whole number in general. This will requires extensive professional development. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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Professional development (PD) unfortunately means different things to different people at the moment. We must provide PD that teaches deeply the basic topics of the mathematics we teach with precision, reasoning, and coherence. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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There have been criticisms that such detailed specifications in the standards on how to teach many topics are an imposition of pedagogical ideology on the teaching of mathematics. You now know, of course, that such criticisms can only come from people who don't recognize mathematics when they see it. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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The detailed prescriptions in WVNGMS define the learning progressions and complexity of mathematical content required for career and college readiness in the 21 st century. Maynus - Adapted with permission from Hung-Hsi Wu, co author of CCSS Mathematics

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K-5 Mathematics Nuts and Bolts

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Provide greater focus and coherence. Are based on what is known today about how students mathematical knowledge, skill, and understanding develop over time. Focuses on the development of mathematical understanding and procedural skills using rich mathematical tasks.

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K-5 Mathematical Standards StandardsK12345 Counting & Cardinality Operations & Algebraic Thinking Number and Operations in Base Ten Measurement & Data Geometry Number & Operations Fractions

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M.2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 2 + 2 + 2 = 6

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Mathematical Content Moved to a Different Grade M.O.K.4.6 identify the name and value of coins and explain the relationships between: – penny – nickel – Dime M.O.1.4.6 identify, count, trade and organize the following coins and bill to display a variety of price values from real-life examples with a total value of 100 cents or less. – penny – nickel – dime – quarter – dollar bill M.O.2.4.7 identify, count and organize coins and bills to display a variety of price values from real- life examples with a total value of one dollar or less and model making change using manipulatives. M.O.3.4.5 identify, count and organize coins and bills to display a variety of price values from real-life examples with a total value of $100 or less and model making change using manipulatives. M.2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

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WV Content No Longer Included in Standards M.O.K.4.4 use calendar to identify date and the sequence of days of the week.

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6-12 Mathematics Nuts and Bolts

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Please Compute These Differences (-3) – (4) (17) – (4) (-2) – (6) (-7) – (-12) -7 13 -8 5

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Remember a Rule Subtraction means add the opposite (additive inverse); so 4 – 3 means 4 + (-3) = 1 4 – (-3) means 4 + (3) = 7 (Since the rule for adding is: signs same, find the sum, signs different, find the difference)

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Relate Subtraction (finding differences) to the Number Line -4 -3 -2 -1 0 1 2 3 4

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Relate Subtraction (finding differences) to the Number Line -4 -3 -2 -1 0 1 2 3 4 (4) – (3)1 What is the difference between 3 and 4? How far (how many spaces) between them? 1 space

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Relate Subtraction (finding differences) to the Number Line -4 -3 -2 -1 0 1 2 3 4 (4) – (3) What is the difference between -3 and 4? How far (how many spaces) between them? 7 spaces 7

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Compare WV CSOs to CCSS NxG WV CSOs 7 th Grade – Number Systems M.7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a number line. (c) Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show the distance between two numbers on the number line is the absolute value of their difference, and apply this in real world contexts. 21C WV CSO M.O.6.1.9 develop and test hypotheses to derive the rules for addition, subtraction, multiplication and division of integers, justify by using real- world examples and use them to solve problems

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High School and the Common Core NxG CSOs are organized by conceptual category, not by courses. Our work has been to group the standards into courses and the courses into pathways. Categories: Number and Quantity Algebra Functions Geometry Modeling Probability and Statistics West Virginia will be using this pathway

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Whats Different in High School? Current High School Pathways Algebra I * Geometry Algebra IIConceptual Mathematics Transition Math for Seniors Electives: Algebra III Trigonometry Probability and Statistics Pre-Calculus Calculus Other college level math courses NxG CSOsPathways in West Virginia Math I * Math II Math III(STEM) Math III (LA) Options for the required fourth math credit: Math IV Transition Math for Seniors Advanced Mathematical Modeling STEM Readiness Mathematics Technical Readiness Mathematics AP Calculus AP Statistics Other college level math courses * Available in 8 th grade

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The Key to Drive Successful Implementation Teacher Professional Development and On-Going Support

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Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

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