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Common Core State Standards for Mathematics: Shifts and Implications for Mathematics Instruction
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  1. Common Core State Standards for Mathematics: Shifts and Implications for Mathematics Instruction

  2. Schedule • 11:00-11:30 Auditorium- ALL • 11:30-2:00 Break-out rooms • Group A- Amy Room 108 A (Science comes 1:00-1:30) • Group B- Marilyn Room 108 B (Science comes 1:30-2:00) • Group C- Susan Room 209 (Science comes 12:30-1:00) • Group D- Drew Room 112 (Drew’s group stay in auditorium 11:30-12:00 for Science, then move to room 112

  3. Morning Session Focus, Coherence, and Rigor; Realizing the Common Core in Elementary Mathematics • Understand how the Common Core influences our Instruction • Identify the 3 major shifts in math education

  4. Last week, I was at a restaurant with a group of friends. The bill came and this is what was said… Out to lunch… “I’m not good at math, have Drew figure it out.”

  5. Next time we go… “I’m not good reading, can you read this to me?”

  6. Same Reaction? Illiteracy Innumeracy Why is it socially acceptable to be innumerate?

  7. Innumeracy 21% of Americans possess numeracy skills at the lowest level . . . [which] means that people cannot . . . work out the change from $2 when buying goods worth $1.58. (Murray, 2000. p. 2) www.lausd.net/District_8/math/secmath/0607/math_anx_ncsm.ppt

  8. Making Banners We have number lines, graph paper, and blank paper available. You have 9 yards of fabric. You need 2 of a yard to make a banner. How many banners could you make? Approaches? Now let’s change the numbers…

  9. Making Banners We have number lines, graph paper, and blank paper available. You have 9/4 yards of fabric. You need 1/2 of a yard to make a banner. How many banners could you make? Solve 2 ways– number line/picture AND then computation • Under every other chair there is a solution to this problem. With a partner, show how how a student might arrive at this solution.

  10. Making Banners Find your group How are your solutions the same? How are they different?

  11. Making Banners Listen as groups share what they noticed

  12. A Lesson in the “old” Days What did math class look like when you were a student? • First, invert the 1/2 so you now have 9/4 x 2/1 • Next, multiply 9x2 to get 18, then 4x1 to get 4. • Now we need to reduce so you take 18 divided by 4 to get 4 r 2 or 4 2/4 that needs to then be reduced to 4 1/2 • Which answer does method this lead to?

  13. “Don’t Ask Why, Just Invert and Multiply!” During and after reading a selected text, we ask… After solving a math problem, we ask… “Did you get the right answer?” “What do you notice in the text?” “Do you agree with the characters decision to…/why?”

  14. Numbers…. 9 divided by 2??? 9/4 divided by 1/2 • How did changing the numbers influence the “difficulty” of the task?

  15. How did changing the numbers influence the “difficulty” of the task? Procedures = Understanding 17 - 6 10 - 6

  16. By place value…start at the right… Ones column: 7- 6 = 1. Tens column: Bring down the 1. I have a 1 in both places. Answer is 11. Procedures = Understanding 17 - 6

  17. By place value…start at the right… Ones column: I can’t do 0 minus 6. Go next door… change the 1 to a 0 in the tens Change the 0 to a 10 in the ones. Ones: 10 – 6 = 4 Tens: 0 – 0 = 0. I have 0 tens and 4 ones. My answer is 4. Do they understand? Procedures = Understanding 10 - 6

  18. Turn and Talk • Think of a mathematical procedure you learned as a student. • How does that make it difficult for you to explain your mathematics behind your solution? Foil Butterfly Standard Algorithm for … Change mixed numbers to improper fractions

  19. Break

  20. Welcome Back • What is MOST IMPORTANT at your grade level? • Answer by placing one sticker on the chart.

  21. The Three Shifts in Mathematics • Focusspecificity and concentration on fewer “big ideas” • Coherence: Think across grades and link to major topics within grades • Rigor: Require conceptual understanding, fluency, and application

  22. Shift One:Focusstrongly where the Standards focus • Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom • Focus deeply only on what is emphasized in the standards, so that students gain strong foundations

  23. It starts with Focus • The current U.S. curriculum is ‘a mile wide and an inch deep.’ • Focus is necessary in order to achieve the rigor set forth in the standards

  24. The following graphs refer to mathematics instruction With a partner, predict what these represent

  25. Mathematics topics intended at each grade By at least 2/3 of US States By at least 2/3 of A+ Countries The Shape of Math Instruction 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

  26. Comparing Charts Compare our school chart to this one What do you notice?

  27. Traditional U.S. Approach

  28. Complete the Diagram Below -Number and Operations—Fractions -Expressions and Equations -Operations and Algebraic Thinking -Number and Operations—Base Ten -The Number System

  29. Focusing attention within Number and Operations

  30. How do they compare?

  31. Content Emphasis • Released by Achieve.org • Non-profit group of educational leaders who have committed to provide resources at no cost. • Designed to help teachers focus on what is most important at each grade level. Focus

  32. Sample Content Emphases What do you notice? What’s missing?

  33. Focus – your grade level • With your grade level team • Look at the Content Emphasis • In YOUR copy of the Common Core –highlight areas of focus at your grade level. Focus

  34. What is vital at my grade level? Complete this sentence with only one mathematical concept; “By the end of ___ grade, if my students knew _____ they would be considered mathematically proficient.” Focus

  35. Walk and Trade

  36. Shift Two: Coherence • Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. • Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new set of events, but an extension of previous learning.

  37. Coherence Within Grade • Look within your grade and find where important concepts are connected across domains. • Create a product that communicates your findings

  38. Coherence Within Grade • Grade Levels Share

  39. Shift Three: Rigor • The CCSSM require a balance of: • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations • This requires balanced intensity in time, activities, and resources in pursuit of all three

  40. Rigor Hundreds, Tens, and Ones

  41. Hundreds, Tens, and Ones Compare the two Hundreds, Tens, and Ones activities thinking about how each provides… • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations

  42. DPI 3-5 Released Item • Mrs. Gregory assigned a project that required each of her 20 students to use 36 toothpicks. How many toothpicks did the students use? • A 72 • B 620 • C 720 • D 7,200

  43. Common Core

  44. Rigor • Compare the two items, which provides for… • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations

  45. Three Mathematical Shifts • Which shift will have the greatest impact on student learning? • Decide with your team and be prepared to share!

  46. Realizing the Promise of the Common Core To This! It will take hard work on our part to move a society from this… 10 - 6

  47. Afternoon Session • Ensuring the Standards for Mathematical Practice at the student level.

  48. Illustrating the Mathematical Practices

  49. Afternoon Session • Ensuring the Standards for Mathematical Practice at the student level.

  50. A pen for Great Danes is shown below. Amy wants to add a safe place for her Chihuahua to run around the great Danes (and not get stepped on!). If she adds 2 ½ feet from the perimeter of the Dane’s pen shown below, how much fencing will she need? 7 ¼ 3 5 2