We have the Common Core Standards for Mathematics – what now and how should we start?

Recently, I participated in a webinar that addressed “Getting Started with the Common Core State Standards, First Steps for Mathematics Education Leadership.” I needed to hear what the experts are saying about the Common Core Standards (CCS) and needed advice about assisting teachers/schools/districts that we serve regarding translating the Standards instructionally. Often times in our work as mathematics educational consultants we have CCS status discussions that circle from we have mapped our mathematics curriculum to match the Common Core Standards to we are thinking about the CCS but do not know where to start to we have heard about the CCS but have never seen them.

Where are you in this curricular circle? Has your mathematics department begun to research the Standards? What are the next steps?

Let’s look at the suggestions/main points made by the experts (National Council of Teachers of Mathematics and National Council of Supervisors of Mathematics) discussed in their most webinar (That webinar can be accessed through http://ncsmonline.org/events/webinars.html).

  • Do not map the CCS point by point to your curriculum maps but rather get to know and understand the Standards. (The assessments that accompany the CCS are not due to roll out until 2014.)

Instead, decide which of the CCS Mathematics Practices* are currently embedded into your instruction. Each of them provide opportunities for students to demonstrate proficiency in understanding the mathematics, so the question remains – why not use and promote each instructionally?

Determine which of the large Domains and their accompanying Clustered Standards ** are currently what you want students to know and be able to do. How do these two pieces fit into your current practice and curriculum?

For gaps in either practices and/or curriculum standards, is there something you could begin to introduce/use; if you do not understand, what help is available to get you going, can other colleagues help?

  • Take a Domain or big idea and follow that thread all the way through (K – G8 and then onto high school) and attend to the conceptual understanding area of mathematical development . Where is your curriculum in that regard? Do you use big ideas in planning units of study? Do you make connections for students so that there is opportunity to fit the pieces together; versus “the lesson for the day” that is not connected to any concepts? CCS place a greater emphasis on conceptual understanding so that procedural fluency follows.

An example from the webinar:

curriculum map

  • Provide opportunities for students to reason and for sense making: For example, in getting students to remember that 3 x 2 is 6 you get to understand that 3 x 2 means 3 groups of 2 or 2 x 3 with 2 groups of 3 (by the commutative property) giving a product or sum of objects of 6. So, for students who forget what 3 x 2 is, he/she has multiple paths to understand/recall the answer.

area model of multiplication

Think of this reasoning and sense making Grade 4 example that was provided in ASCD, Educational Leadership, December/January 2011, “Teaching Skillful Teaching.” The question is posed, which of the two examples would provide greater opportunities for students to think through a wide range of mathematical concepts:
“What fraction of this rectangle is shaded brown?

area model comparison

For grades/high schools students who are solving multi-step equations such as:

multiple represenations of systems

  • Analyze if your students have opportunities to communicate in mathematics: There is substantial research that supports that it is through communicating about the mathematics, students can organize their thinking, construct meaning, and become independent thinkers. Two simple suggestions come from Fisher and Frey in their ASCD book Checking for Understanding: Formative Assessment Techniques for Your Classroom (2006). In student to student and student to teacher dialogue press students to:
    • Clarify and explain their thinking
    • Justify statements made or strategies used.

So from the experts, we have four starters as you begin to understand and interpret the CCS relating to your curriculum and instruction. What if we have dialogue regarding each of these starter points? What is your school doing to embed and/or understand the CCS?

The next webinar to provide additional support is Deeper Dive into the Common Core State Standards, Focus on Standards for Mathematical Practice on February 23, 2011: http://ncsmonline.org/events/webinars.html

*  CCS for Mathematics Practice for all Grade levels:
1. Make sense of 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.

** Sample Grade 4, Large Domain and Cluster Standards for Operations and Algebraic Thinking (there are five Domains for Grade 4):
Operations and Algebraic Thinking 4.OA

  • Use the four operations with whole numbers to solve problems.
  1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
  3. Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • Gain familiarity with factors and multiples.
  1. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
  • Generate and analyze patterns.
  1. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

The underlying framework for the CCS are:

  • NCTM five process standards: Problem Solving, Reasoning & Proof, Communications, Connections, and Representations;
  • NRC’s, Adding It Up, strands of mathematical proficiency: Strategic Competence, Adaptive Reasoning, Productive Disposition, Procedural Fluency, and Conceptual Understanding.

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