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Standards for Mathematical Practice 1. Make sense of complex 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.
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
https://www.teachingchannel.org/videos/subtraction-as-a-confidence-builder?fd=1https://www.teachingchannel.org/videos/subtraction-as-a-confidence-builder?fd=1 Do they understand? Procedures = Understanding 10 - 6
SMP Integration Traditional U.S. Problem Which fraction is closer to 1: 4/5 or 5/4 ? Same problem with SMP integration 4/5 is closer to 1 than is 5/4. Using a number line, explain why this is so… Discuss the shift with this question…
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).
Teach Less, Learn More! https://www.teachingchannel.org/videos/common-core-state-standards-for-math?fd=1 How will teaching fewer “topics” in each grade change your planning?
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!
C.C. Item ExamplesInside Mathematics http://insidemathematics.org/index.php/home • Tools for Educators • Choose your grade level • Mars Tasks These should be similar to future Common Core assessment Items…
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
Choose 3 Ways! 4 Teachers $20.00 Burrito - $4.12 Soda - ?
February 21 • Ensuring the Standards for Mathematical Practice at the student level.
February 21 • Ensuring the Standards for Mathematical Practice at the student level.