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Common Core: Now What?
December 6, 2012 | Volume 8 | Issue 5
Table of Contents
Common Core Quick-Start
Focus High School Math on Practices, Critical Areas, and Connections
Of all content areas, across all grade levels, it's safe to say that none provoke quite as immediate a reaction as math. But whether you're a "math person" or not, we all need math skills to succeed in school, postsecondary education, and the workforce.
Implementation of the Common Core State Standards in mathematics is likely to represent a significant change for most states (Schwols & Dempsey, 2012; Center on Education Policy, 2012). First, they're structured differently than most existing state standards: in addition to the more familiar content standards, which focus on students' conceptual and procedural understanding of mathematics, the Common Core standards include mathematical practice standards intended to help students develop the approaches, or practices, of mathematicians. By persevering to solve problems, using accurate terminology, and justifying solution strategies, students begin to think and act like mathematicians. While in the past, students may have been able to get by with simply knowing how to solve a math problem, they now need to be able to describe the what and the why of the mathematics skill.
For students and teachers alike, this can be a tall order. Students who may be accustomed to simply memorizing a formula now have to be able to explain and justify their thinking and apply their learning to new situations and problems. And teachers—who, despite their other superhero powers, can't be expected to be mind-readers—have to find ways to verify that students genuinely understand the concepts behind the mathematics being taught.
How can teachers do that? By combining a focused, strategic approach to the Common Core standards with time-tested, research-based instructional strategies. Common Core Standards for High School Mathematics: A Quick-Start Guide (ASCD/McREL, 2012) provides three recommendations for beginning implementation of the Common Core math standards: focus on the standards for mathematical practice, focus on critical areas, and focus on connections.
Focusing on Mathematical Practices
The Standards for Mathematical Practice, which are intended to be applied across grades, focus on problem solving; reasoning and proof; communication; representation; connections; adaptive reasoning; strategic competence; conceptual understanding; procedural fluency; and productive disposition, which speaks to students' attitudes about math's usefulness and their own math ability (Common Core State Standards Initiative, 2010).
Remember that the Standards for Mathematical Practice, and their focus on deep conceptual knowledge, will be new to most teachers and students. We all remember what it's like to have that one class—for many of us it was math; for others, language arts or science—that was, well, hard. As a result, it's important to create an environment for learning in which objectives are clear, teachers reinforce students' effort and provide recognition, and cooperative learning can take place (Dean, Hubbell, Pitler, & Stone, 2012).
Focusing on Critical Areas
Appendix A (PDF) of the Common Core math standards categorizes standards into "critical areas," which can help provide a focus for teachers' unit and lesson planning. Schwols and Dempsey (2012) recommend that math courses focus on four to six critical areas, which "allows teachers to guide students to a deeper, richer understanding of mathematical concepts" (p. 12). One way that teachers can determine whether or not students are reaching this deeper understanding is to ask them to make their knowledge visible through multiple representations, such as modeling, equations, in writing, and through oral discourse via cues and questioning, as described in the instructional strategies from Classroom Instruction That Works, 2nd edition (Dean et. al, 2012).
Focusing on Connections
The Common Core math standards are intended to function as an integrated whole across grade levels, building on foundational knowledge to facilitate deep understanding of key concepts. As Schwols and Dempsey note, "each standard is best understood not as completely new knowledge or skills but as an extension of ideas presented in previous grades" (p. 12). Recognizing these connections across grade levels and standards means that teachers can use the instructional strategies that are already in their toolboxes to help students extend and apply knowledge, whether by identifying similarities and differences through comparison and classification or by generating and testing hypotheses (Dean et. al, 2012). Additionally, teachers might use these connections to either identify gaps in knowledge or speed up instruction as appropriate (Schwols & Dempsey, 2012).
The Common Core standards represent a change and a challenge for math teachers. But as we begin to implement the standards, we don't need to throw out the baby with the bathwater. The fundamentals of good teaching aren't going to change, and research-based instructional strategies that worked before the Common Core standards will still stand with teachers in good stead for years to come.
Center on Education Policy (2012). States' progress and challenges in implementing Common Core State Standards (PDF). Washington, D.C.: Center on Education Policy.
Common Core State Standards Initiative (2010). Common core state standards: Mthematics. Washington, DC: CCSSO & National Governors Association. Retrieved from http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf
Dean, C. B., Hubbell, E. R., Pitler, H., & Stone, B. (2012). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: ASCD.
Schwols, A., & Dempsey, K. (2012). Common Core standards for high school mathematics: A quick-start guide. Alexandria, VA: ASCD.
Kirsten Miller is lead communications consultant at McREL.
ASCD Express, Vol. 8, No. 5. Copyright 2012 by ASCD. All rights reserved. Visit www.ascd.org/ascdexpress.
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