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

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##### Common Core State Standards for Mathematics: Shifts and Implications for Mathematics Instruction

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**Common Core State Standards for Mathematics: Shifts and**Implications for Mathematics Instruction**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**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**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.”**Next time we go…**“I’m not good reading, can you read this to me?”**Same Reaction?**Illiteracy Innumeracy Why is it socially acceptable to be innumerate?**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**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…**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.**Making Banners**Find your group How are your solutions the same? How are they different?**Making Banners**Listen as groups share what they noticed**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?**“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?”**Numbers….**9 divided by 2??? 9/4 divided by 1/2 • How did changing the numbers influence the “difficulty” of the task?**How did changing the numbers influence the “difficulty”**of the task? Procedures = Understanding 17 - 6 10 - 6**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**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**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**Welcome Back**• What is MOST IMPORTANT at your grade level? • Answer by placing one sticker on the chart.**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**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**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**The following graphs refer to mathematics instruction**With a partner, predict what these represent**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).**Comparing Charts**Compare our school chart to this one What do you notice?**Complete the Diagram Below**-Number and Operations—Fractions -Expressions and Equations -Operations and Algebraic Thinking -Number and Operations—Base Ten -The Number System**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**Sample Content Emphases**What do you notice? What’s missing?**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**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**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.**Coherence Within Grade**• Look within your grade and find where important concepts are connected across domains. • Create a product that communicates your findings**Coherence Within Grade**• Grade Levels Share**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**Rigor**Hundreds, Tens, and Ones**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**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**Rigor**• Compare the two items, which provides for… • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations**Three Mathematical Shifts**• Which shift will have the greatest impact on student learning? • Decide with your team and be prepared to share!**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**Afternoon Session**• Ensuring the Standards for Mathematical Practice at the student level.**Afternoon Session**• Ensuring the Standards for Mathematical Practice at the student level.**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