Potential Impact of the Common Core Mathematics Standards on the American Curriculum
In June of 2010, the Common Core State Standards in Mathematics (CCSSM) were introduced in the U.S. Long before the advent of the CCSSM, American schools had a de facto national mathematics curriculum, namely, the curriculum dictated by school mathematics
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Abstract In June of 2010, the Common Core State Standards in Mathematics (CCSSM) were introduced in the U.S. Long before the advent of the CCSSM, American schools had a de facto national mathematics curriculum, namely, the curriculum dictated by school mathematics textbooks. While there are some formal differences among these books, the underlying mathematics is quite similar throughout. The resulting curriculum distorts mathematics in the sense that it often withholds precise definitions and logical reasoning, fails to point out interconnections between major topics such as whole numbers and fractions, and employs ambiguous language that ultimately leads to widespread non-learning. The CCSSM make a conscientious attempt to address many of these problems and, in the process, raise the demand on teachers’ content knowledge for a successful implementation of these standards. This article examines, strictly from an American perspective, some of the mathematical issues (primarily in grades 4–12) that arise during the transition from the de facto curriculum to the curriculum envisioned by the CCSSM. Although the CCSSM would seem to be strictly an American concern, these mathematical issues transcend national boundaries because there are very few deviations in the K-12 curriculum across nations (for the K-8 curriculum, see p. 3-31 to p. 3-33 of National Mathematics Advisory Panel 2008). Keywords Common Core Standards · Curriculum · Content knowledge · Definition · Reasoning
Introduction In the unending search for improvement in mathematics education in the U.S. for the last half century, one thing seems to have been consistently overlooked; namely, the fact that there has been a de facto American mathematics school curriculum since the demise of the “New Math” in the early 1970s. This is the curriculum encoded
H.-H. Wu (B) Department of Mathematics #3840, University of California, Berkeley, CA 94720-3840, USA e-mail: [email protected] Y. Li, G. Lappan (eds.), Mathematics Curriculum in School Education, Advances in Mathematics Education, DOI 10.1007/978-94-007-7560-2_7, © Springer Science+Business Media Dordrecht 2014
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in school textbooks. There are many textbooks, of course, and they are guided by quite different philosophical outlooks ranging from “traditional” to “reform”. Nevertheless, the underlying mathematics is, overall, quite similar. While such a claim may startle some, the element of surprise will disappear the minute one considers for instance, the uniform lack of emphasis in school textbooks on giving precise definitions to concepts1 and, even more significantly, the same lack of emphasis on basing logical reasoning on precise definitions. If even this does not drive home the point, consider further the ambiguity of the meaning of fraction, multiplication or division of fractions, “variable”, congruence, similarity, etc. How many textbooks explain how to multiply two fractions strictly on the basis of the definition of a fraction?2 How many textbooks explain why any two circles are simila
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