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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**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, you 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**Explain to your partner how you would use the traditional**algorithm to solve this Procedures = Understanding 17 - 6**Now explain to your partner how you would use the**traditional algorithm to solve this Procedures = Understanding 10 - 6**How did changing the numbers influence the “difficulty”**of the task? Procedures = Understanding 17 - 6 10 - 6**Xtranormal video- I will email the link as soon as it is**released. If it’s not released in time, you can simply say “What do I do first? I can’t take 6 away from 0, so I have to cross off the 1 and …”. Teachers always get a chuckle out of this. Do they understand? Procedures = Understanding 10 - 6**Procedures & Algorithms**At your table, fill your large paper with examples of algorithms/procedures you learned as a student. Examples: Foil method in algebra Butterfly to compare fractions Standard Algorithm for multiplication or division**Algorithms**• Choose one procedure or algorithm that you learned as a student. • E.g., Finding common denominator, FOIL, Butterfly to compare fractions, multiplication or division algorithm, dividing fractions • Do a sample problem using it… • Then explain it to your neighbor – explain the process and why it works**Algorithms**• What algorithms did you explain? • How does understanding the math relate to following the steps of the algorithm?**Break**• When you come back, please sit in grade level groups.**Welcome Back**• According to the Common Core, What is MOST IMPORTANT at your grade level? • Answer by placing one sticker on the chart.**The Three Shifts in Mathematics**• Focus • Coherence • Rigor Authors of the Common Core Math Standards have emphasized 3 shifts from old state standards (like the NCSCOS)**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**Why Focus?**• The U.S. curriculum before the Common Core was known as ‘a mile wide and an inch deep.’ • What did this look like in the NCSCOS? • Focus is necessary in order to achieve the rigor set forth in the standards**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).**Content Emphasis**Designed to help teachers focus on what is most important at each grade level. Focus**Content Emphases by Cluster**• Not all of the content in a given grade is emphasized equally in the standards. • Some clusters require greater emphasis based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. • An intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice. • Focus does not mean neglecting certain standards. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.**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**With your grade level team, discuss…**K-2 Teachers • Look at the supporting standards at your grade level. • Generate specific examples of how each supporting standard relates to major standards • 3-5 Teachers • Identify major changes within your grade level. • How has the focus changed from the 2003 NCSCOS? Focus**Focus**• Would you change where you placed your sticker? Focus**Coherence Within Grade**• Use the handout of your Grade Level Clusters • Analyze how these clusters are classified • How do these clusters overlap or address similar “larger concepts”? • How do Supporting Clusters align with Major Clusters.**Coherence**• Pick a unit from Investigations that incorporates multiple clusters • What are the pre-requisite skills you hope students have before this unit starts? • As students are doing the work in the unit, what is the Major Cluster? • What other clusters are also incorporated?**Coherence**• Move and group with teachers from multiple grade levels • Exchange ideas and discuss what your grade level came up with**Coherence Wrap-up**• When teaching the Common Core, teachers should: • 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.**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**Place Value… Why do we need rigor when we work with place value concepts?**Hundreds, Tens, and Ones**In groups with teachers from different grade levels, analyze the two Hundreds, Tens, and Ones activities. How does each provide… • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations**Hundreds, Tens and Ones**• Do these promote Conceptual Understanding? • Why or why not?**Hundreds, Tens and Ones**• Do these promote Procedural Skill and Fluency? • Why or why not?**Hundreds, Tens and Ones**• Do these promote skill application in problem solving situations? • Why or why not?**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 previous multiplication items, and discuss how each does/does not provide the opportunity for students to demonstrate… • 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 Aramis and Elise (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 a fence that is 2½ feet from the current perimeter, how much fencing will she need for the Chihuahua’s run? The Chihuahua run must be built 2½ feet from the edge of the Great Dane pen! 7 ¼ 3 5 2**Standards for Mathematical Practice**• 4 and 5 • In pictures and words, show how you used either mathematical practice 4 or 5 as you solved this task • (you might have to pull these out and re-read )**An Experience with Students**• The following slides are from DPI.