As we begin to consider how to design and deliver instruction that meets the requirements of the Common Core State Standards for Mathematics, it is critical that we not progress with business as usual.  These new standards offer an opportunity to refocus our mathematics instruction in a manner that allows more students to achieve.  They offer us an opportunity to re-energize the instructional delivery so that it makes sense to more students clearly linking procedural rules to the conceptual understanding and to meaningful problem solving.  Mathematics, after all, is a language used to describe and solve real events and problems.

What's in a Name?

To begin to understand the common core, one only needs to examine the name. The word common signifies that students throughout the United States are expected to achieve the same learning outcomes.  No longer do the expectations vary from state to state, well at least not in the 42 that have adopted the Common Core.  Now the word core, which has synonyms such as essential, central, fundamental, and primary, conveys how standards outlined at one grade level are essential skills students need to acquire in order to be successful at subsequent levels and beyond.  This national focus and rigor allows for a greater community of educators to collaborate on instruction that moves all students toward greater levels of achievement.

What characteristics make the Common Core State Standards different?

1. Less Is More 

The overwhelming number of topics and skills presented in very optimistic pacing guides leads many teachers to rush through content often relying on very basic demonstration of skills or methods for recalling rules and procedures that shortcut deep understanding.  Keep in mind that keeping up has been greatly reinforced.  We can always go back reteach, right?  Well not with the new standards.  The Common Core State Standards require instruction that goes deeper into concepts rather than cover more content.   

2.  Explaining What and How

The second characteristic that I notice is the way the standards are written to describe not only what the student will learn but how the students will demonstrate mastery.  These standards are very descriptive, more so than the previous NCTM standards and Focal Points.  For example in grade 5 the standard states:

"Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

3.  Emphasis on conceptual understanding

The new standards use words such as understand, recognize, explain and compare to describe a conceptual understanding of numbers and procedures.  For example in grade 3 the standard states:

"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model."

Some standards specify the use of visual models to develop and express concepts.  For example in grade 3 the standard states:

 "Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8." 

When will the standards begin to impact instruction? 

Several states such as North Carolina are moving toward implementing some of the CCSS in the 2011-2012 school year.  Others will wait until the 2014-2015 scheduled time for implementation.  Others such as Kentucky have developed crosswalk resources, which show alignments of present state standards to the CCSS.  

Many educators already realize that teacher preparation is critical to delivering the type of instruction that aligns their learning outcomes with the new standards. Although many of the standards describe how a student will demonstrate achievement, they do not tell teachers how to teach. 

For teachers with a deep understanding of mathematics, the CCSS will refine what they teach.  For others, the emphasis on conceptual understanding and reasoning will be difficult to translate into different teaching practices. Others may believe that the standards simply represent another change in a long line of reform efforts. Whatever the belief, change will bring about higher levels of anxiety and uncertainty that will need to be addressed with both strong leadership, well-designed professional development and high quality methods and tools.

Certainly transition to the Common Core State Standards will be a focus of the upcoming NCSM and NCTM national conferences that begin next week in Indianapolis.  Both conferences should provide a great avenue to learn more about the standards and methods for delivering instruction in which the learning outcomes of all students match the expectations within the new Common Core.

Click here to learn how Conceptua Fractions aligns to the CCSS.