by Andrew Foster
I have been interested in the structure of the Common Core Standards since the day I heard about them. The way I heard it, the CCSS were supposed to be controversial, scary, and intimidating, and in some ways they fit those descriptions. I’ve found, however, that the simplicity and strength of the CCSS structure may encourage the opposite reactions: acceptance, relief, and even excitement. If you’ve never really explored the Math Standards in detail, maybe this article will help get you started.
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Straightforward Introduction to Math Theory: 8 Practices
The Math CCSS begin with an important discussion of theory, research, and assumptions that are the foundation of the standards. Whether you agree with the premise of the CCSS or not, this section is a fairly straightforward statement of purpose that deserves a close read. The general idea is to clarify the purpose of the standards and explain what they are not intended to address, such as focused intervention or differentiation for special needs.
You will want to seriously study the “Standards for Mathematical Practice”. Many have observed that these practices may require more deliberate shift in classroom instruction than the content standards themselves. Each of the eight practices include details and examples about the kind of thinking, speaking, questioning, manipulating, and research in which students should participate regularly. The goal is to develop true understanding of math concepts instead of relying on memorized processes. In my view, much of the professional development connected to implementation of the Common Core will necessarily focus on these eight math practices.
Math Content Standards
The content standards for each grade level have a very deliberate and practical structure: a synopsis of the big ideas, an overview in outline form, and then the detailed performance standards.
While there is much debate about the quality and emphasis of the English Language Arts Common Core (specifically the focus on nonfiction, informational text), the Math standards are more often recognized as a well-developed progression of mathematical skill. The biggest complaint I have heard is that the expectations for students are not developmentally appropriate – that the Math standards expect students to think and reason at a very sophisticated level at an early age. A similar argument is made concerning the English Language Arts standards.
The greatest benefit of the Content Standards seems to be the focus on depth of knowledge as opposed to breadth of knowledge. For example, the old New Mexico Math standards for 7th grade include 5 strands, 17 benchmarks, and 86 Performance Standards; from scientific notation to the Pythagorean Theorem to line of best fit! In contrast, the Common Core Math Standards for 7th grade include 5 strands, but only 9 benchmarks and 24 performance standards. Another nice change is the clarity of each performance standard, which often includes examples of student tasks or class activities.
Make no mistake: fewer standards do not indicate less rigor. These standards are serious reading, even for college-educated adults accustomed to teaching the content year after year. Each standard will need to be examined, pulled apart, and introduced to students with careful and deliberate skill. Dive in and see for yourself. If you get lost, look for the structure. It is simple but strong, and will help you find your way to practical implementation of the Math CCSS.