Learning Paths and Learning Supports for Conceptual Addition and Subtraction in the US Common Core State Standards and i
The results of the Fuson and Li (ZDM Math. Educ. 41:793–808, 2009 ) analysis of the major early numerical aspects and learning supports for single-digit and multi-digit adding and subtracting in a representative Chinese textbook series and a US textbook s
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Abstract The results of the Fuson and Li (ZDM Math. Educ. 41:793–808, 2009) analysis of the major early numerical aspects and learning supports for single-digit and multi-digit adding and subtracting in a representative Chinese textbook series and a US textbook series (Math Expressions) are related to the Chinese standards and to the US Common Core State Standards for these topics. Similar learning paths and visual-quantitative supports for mathematical thinking were identified in the textbooks from both countries, the US standards, and the experimental Chinese standards (2001). The new Chinese standards (2011) were less specific about learning paths and supports, though these appeared in examples. Criteria for judging the best variations of the multi-digit adding and subtracting variations were proposed and used. This analysis identified the best variations as the “New Groups Below” for adding and the “Ungroup First” for subtracting. The somewhat different levels in the adding and subtracting learning paths for East Asia and the US are summarized. Keywords Addition · Subtraction · Language effects · Learning supports · Cross-cultural textbook analysis · Standards
Introduction Several studies document ways in which East Asian mathematics textbooks support conceptual understanding by students (Cai 2008; Li 2007, 2008; Li et al. 2009a,b,c; Murata 2004, 2008; Murata and Fuson 2006; Watanabe 2006). Some of these studies also describe ways in which mathematics textbooks from the US fail to support conceptual understanding in these ways. One exception (Fuson and Li 2009) is the support for single-digit and multi-digit addition and subtraction in the most-used Chinese text and in a US second-generation NSF math textbook Math Expressions K.C. Fuson (B) Northwestern University, Evanston, IL, US e-mail: [email protected] Y. Li Texas A&M University, College Station, TX, US Y. Li, G. Lappan (eds.), Mathematics Curriculum in School Education, Advances in Mathematics Education, DOI 10.1007/978-94-007-7560-2_25, © Springer Science+Business Media Dordrecht 2014
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(Fuson 2006/2009). In that study, Fuson and Li reported extensive linguistic, visualquantitative, and written-numeric supports for mathematical thinking in the Chinese textbooks and for the US textbook for the grades analyzed (Grades 1, 2, and 3 in both countries and Kindergarten for Math Expressions). The diverse results from textbook analyses across countries suggest the need to examine and understand possible influences from curriculum standards that help guide the development of textbooks and possible learning paths embedded in textbooks. In many countries textbooks are a commonly used teaching resource that embodies the mandated curriculum. Therefore, it is also important to analyze the curriculum documents themselves as they are the primary source on which teachers and textbook writers draw in creating learning resources and planning learning experiences. Thus a major objective of this chapter is to analyze the extent to which curri
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