Math Common Core Standards: Towards Greater Focus and Coherence!Elementary Principals’ OrganizationMay 17, 2013
Objectives • Develop a understanding of the Common Core Sate Standards in Mathematics by relating their implementation to the past, current and future work of Networks. • Identify the implications of the CCSS Math Standards to instruction, assessment, leadership and professional development.
Why Common Core? I Choose “C” http://www.youtube.com/watch?v=dY2mRM4i6tY
Why do we study mathematics in school? • Because it’s hard and we have to learn hard things at school. We can learn easy stuff at home like manners. Carrine, K • Because it always comes after reading. Roger, 1 • Because all the calculators might run out of batteries or something. Thomas, 1 • Because it’s important. It’s the law from President Bush and it says so in the Bible on the first page. Jolene, 2 • Because you can drown if you don’t. Amy, K
Why do we study mathematics in school? • Because what would you do with your check from work when you grow up? Brad, 1 • Because you have to count if you want to be an astronaut. Like 10…9…8…blast off. Michael, 1 • Because you could never find the right page. Mary, 1 • Because when you grow up you couldn’t tell if you are rich or not. Raji, 2 • Because my teacher could get sued if we don’t. That’s what she said. Any subject we don’t know – Wham! She gets sued and she’s already poor. Corky, 3
Let’s talk about Miguel • Miguel begins kindergarten this year and will graduate from high school in 2026 and from college in 2030. What will Miguel's world be like in 2030? We can’t know for sure, but a few things are certain: • It's likely that the career Miguel chooses doesn't exist today. • Advanced technology will be more central to Miguel's life and that of his peers than for any previous generation in human history. • Miguel's generation will grapple with the impact of global challenges using understandings that have not yet been achieved and with technologies and solutions that have not yet been invented. • The exponential pace of change means the world in which Miguel lives today will likely bear little resemblance to the world he will know in 2030.
What are standards? • Standards define what students should understand and be able to do. • Standards must be a promise to students of the mathematics they can take with them. • We haven’t kept our old promise and now we make a new one. • What difference will it make?
Lessons Learned After two decades of standards based accountability: • Too many standards • Lack of student motivation • “Cover” at “pace” is a failure • Tells teachers to ignore students • Turn the page regardless • Shrug your shoulders and do what “they” say • Mathematics is not a list of topics to cover • Singapore: “Teach less, learn more”
Lessons Learned • TIMSS: math performance in the US is being compromised by a lack of focus and coherence in the “mile wide, inch deep” curriculum • Hong Kong students outscore U.S. students on the grade 4 TIMSS, even though Hong Kong only teaches about half of the tested topics. U.S. covers over 80% of the tested topics. • High-performing countries spend more time on mathematically central concepts: greater depth and coherence.
Answer Getting vs. Learning Mathematics United States How can I teach my kids to get the answer to this problem? Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management. Japan How can I use this problem to teach mathematics they don’t already know?
Math Standards • Mathematical Performance: what kids should be able to do • Mathematical Understanding: standards for what kids need to understand • Mathematical Practices: behaviors students need to exhibit in mathematics
Performance • Performance: what kids should be able to do • multiply and divide within 100 • 3rd grade sample
Understanding • Understanding: what kids should understand about mathematics. The ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. • 3rd grade sample • Understand properties of multiplication and the relationship between multiplication and division. • Table Talk: • Why is that our kids do not perform as well as students in other countries do?
2.15 + 3.1 215 + 31
24 x 5 = 120 4 x 1/2 = 2
Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.
… US textbooks do a much worse job than the Singapore textbooks in clarifying the mathematical concepts that students must learn. … the presentation becomes more mechanical than is ideal. …we found this conceptual weakness …in both traditional and non-traditional textbooks used in the US. • Leinwand, S., and Ginsburg, A., "Measuring Up: How the Highest Performing state (Massachusetts) Compares to the Highest Performing Country (Hong Kong) in Grade 3 Mathematics," American Institutes for Research, 2009, p. 2; Ginsburg et al. (2005, op cit), p. xii.
There are 125 sheep and 5 dogs in a flock. How old is the shepherd?
A Student’s Response There are 125 sheep and 5 dogs in a flock. How old is the shepherd? 125 x 5 = 625 extremely big 125 + 5 = 130 too big 125 - 5 = 120 still big 125 5 = 25 That works!
Math Standards • Mathematical Performance: what kids should be able to do • Mathematical Understanding: standards for what kids need to understand • Mathematical Practices: varieties of expertise that math educators should seek to develop in their students.
Take the number apart? • Tina, Emma, and Jen discuss this expression: • 6×5 1/3 • Tina: I know a way to multiply with a mixed number that is different from the one we learned in class. I call my way “take the number apart.” I’ll show you. First, I multiply the 5 by the 6 and get 30. Then I multiply the 1/3 by the 6 and get 2. Finally, I add the 30 and the 2 to get my answer, which is 32.
Take the number apart? Tina: It works whenever I have to multiply a mixed number by a whole number. Emma: Sorry Tina, but that answer is wrong! Jen: No, Tina’s answer is right for this one problem, but “take the number apart” doesn’t work for other fraction problems. Which of the three girls do you think is right? Justify your answer mathematically?
Table Talk • What are your reactions to the sample assessment item? • How does the sample assessment item compare to tasks being assigned in your school? • How does the sample assessment item assesses the three types of standards (performance, understanding and practices)? • What are the implications for mathematics teaching and learning?
Overview of K-8 Mathematics Standards • The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals • The 6-8 standards describe robust learning in geometry, algebra, and probability and statistics • Modeled after the focus of standards from high-performing nations, the standards for grades 7 and 8 include significant algebra and geometry content • Students who have completed 7th grade and mastered the content and skills will be prepared for algebra, in 8th grade or after
How to Read the Standards: K-8 • introduction (see page 13)
How to Read the Standards: K-8 • Overview (see page 14)
How to Read the Standards: K-8 • Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. • Standards define what students should understand and be able to do. • Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. DOMAIN STANDARD CLUSTER
Miguel and the CCSS • While school can't prepare Miguel for every challenge he will face in the future, a quality and inspired CCSS-aligned education can empower Miguel to: • Demonstrate independence and self-directed learning • Value evidence, reason logically, and think conceptually and abstractly • Analyze and use data • Comprehend as well as critique • Construct and present viable arguments • Use media and technology strategically • Persevere in making sense of and solving problems • Understand and appreciate different perspectives and cultures • Develop the skills and dispositions necessary to the responsible exercise of citizenship in an advanced democratic republic • These capacities, developed in the context of a well-rounded education, will ensure that Miguel can engage with and contribute to the 21st -century world effectively and with purpose.
Content Emphases by Cluster--Kindergarten* *Emphases are given at the cluster level. Refer to the Common Core State Standards for Mathematics for the specific standards that fall within each cluster.
Selected ResponseMultiple Correct Options Which of the following statements is a property of a rectangle? Select all that apply. ☐ Contains three sides ☐ Contains four sides ☐ Contains eight sides ☐ Contains two sets of parallel lines ☐ Contains at least one interior angle that is acute ☐ Contains at least one interior angle that is obtuse ☐ All interior angles are right angles ☐ All sides have the same length ☐ All sides are of different length
Constructed Response The table below shows the number of students in each third-grade class at Lincoln School. There are 105 fourth-grade students at Lincoln School. How many more fourth-grade students than third-grade students are at Lincoln School? Show or explain how you found your answer.
Constructed Response Item A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5,000. 496 + 1,404 + 2,605 + 489 = One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning. Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated.
Example of Technology-Enabled Item Gregory is installing tile on a rectangular floor. • He is using congruent square tiles that each have a side length of ½ foot • The area of the floor is 22 square feet. • The width of the floor is 4 feet. Use the grid and the tile below to model the floor. What is the length, in feet, of the floor?
Technology-Enhanced Items The graph on the right shows a triangle. Draw the triangle after it is reflected over the y-axis. Draw a line of symmetry through the figure below. Classify each shape below based whether it contains at least one pair of parallel sides. Reorder the fractions below so that they are ordered from smallest to largest. 3/5 3/4 2/6 1/2 2/3
4th Grade Performance Task PLANTING GUIDELINES The distance between tulip bulbs should be 3 times the width of the bulb. • Planting Tulips, Part 3 • The class finds a bag containing bulbs that are each 1 ½ inches wide and decides to use them in their rectangular planter. Following the planting guidelines, answer the questions and show your calculations. • This picture shows a tulip bulb that is 1 ½ inches • wide. Use your ruler and mark an “X” where the • next bulb could be planted. • Using your drawing, calculate the total length • of space that is needed for each bulb with • a 1 ½ -inch width. Your answer should include • the width of the bulb shown. • How many tulip bulbs with a 1 ½ -inch width • can be planted in a single row that is 5 fee long? • How many tulip bulbs with a 1 ½ -inch width can • be planted in a single column that is 2 feet long? • How many tulip bulbs with a 1 ½ -inch can be planted • in the 5-foot by 2-foot rectangular planter? Explain or show your reasoning.
Turn and Talk • With your elbow partner review the sample Math assessment items. • Discuss the implications of these new assessment items as it relates to curriculum, instruction, assessment and professional development.