The Common Core Standards

1. The Common Core Standards Doug Holley dholley@hinghamschools.com

2. Common Core State Standards for Mathematics • Council of Chief State School Officers • National Governors Association Center • 48 states, two territories, District of Columbia • No federal involvement But…

3. Race to the Top In Phase 2 states receive extra points for agreeing to adopt the Common Core Standards and to participate in the Common Assessment Consortium. Massachusetts plans to do this “if the Common Core Standards are at least as strong as our current standards.”

4. Mathematics Work Team • Deborah Loewenberg Ball (University of Michigan) • Skip Fennell (Past-President of NCTM) • Sol Garfunkel (COMAP) • Ken Gross (University of Vermont) • Barbara Hughes Hallett (Reform Calculus text author) • Barbara Libby (Mass DESE) • Andrew Schwartz (The College Board) • Sharyn Sweeney (Mass DESE) • Many Others

5. Common Core Standards “These draft standards define the knowledge and skills students should have within their K-12 education careers so that they will graduate high school able to succeed in entry-level, credit-bearing academic college courses…” “States will be asked to adopt the Common Core State Standards in their entirety and the core must represent at least 85% of the state’s standards in English language arts and mathematics.”

6. Common Core State Standards for Mathematics “…aim for clarity and specificity.” “There is a world of difference between the student who can summon a mnemonic device such as “FOIL” to expand a product such as (a + b)(x + y) and a student who can explain where that mnemonic comes from… Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”

7. Mathematics Standards for Mathematical Practice “Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content.” • 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.

8. NCTM Statement “The Standards for Mathematical Practice are consistent with the NCTM Process Standards… But these mathematical practices are not connected with the specific core standards. Without consistent, explicit, recommendations for the mathematical practices, it is unlikely that future assessments, and consequently instruction, will address them.”

9. NCTM Statement “…there are references to mathematical connections both across content and with contextual real world settings. But there are few explicit connections made in the standards and consequently we again fear that assessment and instruction won’t address them.”

10. Massachusetts Board of Elementary and Secondary Education March 22, 2010 – 1½ hours for eleven invited speakers to give their views on the core standards and for members of the board to ask questions. March 23, 2010 – the board discussed the standards among themselves. Speakers and questions on March 22 were devoted entirely to the specific standards. There was no discussion of assessment or professional development.

11. Memo from Dr. Chester, 5/14 • June 1: Public comment invited to compare rigor of Common Core Standards with 2000 Mass Mathematics frameworks • June 15: “Independent expert panel” appointed to compare rigor of Common Core Standards with 2010 Mass Mathematics frameworks

12. Memo from Dr. Chester, 5/14 • June 22: Public comments and expert panel reports to Board of Elementary and Secondary Education • By August 2: Board votes on adopting Common Core Standards • By end of 2011-2012: “we will expect all districts to have aligned their curriculum to these new standards.”

14. K-5 Standards Massachusetts • Number Sense and Operations • Patterns, Relations, and Algebra • Geometry • Measurement • Data Analysis, Statistics, and Probability Core Standards • Number – Counting and Cardinality (K only) • Number – Operations and the Problems they solve • Number – Base Ten • Number – Fractions • Measurement and Data • Geometry

15. K-5 Standards “The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals – which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.”

16. K-5 Standards The “data” in the Measurement and Data Strand refers to bar graphs, and line plots, together with arithmetic operations performed using the data. “Make a dot plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions to solve problems involving information presented in dot plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers would contain if the total amount in all the beakers were redistributed equally.” (5-MD 6)

17. K-5 Standards 5-NBT-2 Explain why division strategies and algorithms work, using place value and the properties of operations. Include explanations supported by drawings, equations, or both. A range of reasonably efficient algorithms may be covered, not only the standard algorithm. 5-NBT-3 Use the standard algorithm to compute quotients of two-, three-, and four-digit whole numbers.

18. NCTM Statement “If the phrase ‘standard algorithm’ must be used for political purposes in reference to the four operations, it should be referred to as ‘a standard algorithm.’ There are numerous such algorithms in international educational settings that are also mathematically appropriate and correct… We cannot send a message to teachers, parents, and students that an efficient algorithm that is already well understood and mastered by a child must be unlearned in favor of a single mathematical algorithm chosen by this writing team. Of concern is that the current statement invites assessment of a student’s ability to use the exact steps in an algorithm that someone else had in mind – not an ability to execute the required computation.”

19. The K-5 Standards Greater emphasis is needed on mental arithmetic, rounding, and estimation There is no exposure to statistics and data analysis until Grade 6. NCTM says a review of international curricula, and statements by professional bodies in the Untied States, confirms that is too late. There seems to be excessive attention given to fractions and relatively little to decimals.

20. The K-5 Standards There are symbols in the draft that indicate standards that are important in the development of algebraic thinking. But there needs to be a stronger statement that teachers need to understand how these standards are related to algebraic thinking. We need to have elementary teachers understand that they really are teaching algebraic concepts. There need to be standards such as input-output tables and number theory (composites, factors, etc.) that integrate understanding of arithmetic in ways that prepare for algebraic thinking.

21. The K – 5 Standards • The Common Core Standards push much work on place value into K -1 where it is not age appropriate. This may be perceived as increasing rigor. But it is likely to lead to rote memorization.