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The introduction emphasizes greater focus and coherence by concentrating instruction on number, geometry, spatial relations, and measurement, while integrating mathematical process goals. 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Mathematical process goals should be integrated in these content areas.  \n— Mathematics Learning in Early Childhood, National Research Council, 2009  \nThe composite standards [of Hong Kong, Korea and Singapore] have a number of features that can inform an international benchmarking process for the development ofK–6 mathematics standards in the U.S. First, the composite standards concentrate the early learning of mathematics on the number, measurement, and geometry strands with less emphasis on data analysis and little exposure to algebra. The Hong Kong standards for grades 1–3 devote approximately half the targeted time to numbers and almost all the time remaining to geometry and measurement.  \n— Ginsburg, Leinwand and Decker, 2009  \nBecause the mathematics concepts in [U.S.] textbooks are often weak, the presentation becomes more mechanical than is ideal. We looked at both traditional and non-traditional textbooks used in the US and found this conceptual weakness in both.  \n— Ginsburg et al., 2005  \nThere are many ways to organize curricula. The challenge, now rarely met, is to avoid those that distort mathematics and turn off students.  \n— Steen, 2007  \nFor over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.” These Standards are a substantial answer to that challenge.  \nIt is important to recognize that “fewer standards” are no substitute for focused standards. Achieving “fewer standards” would be easy to do by resorting to broad, general statements. Instead, these Standards aim for clarity and specificity.  \nAssessing the coherence of a set of standards is more difficult than assessing their focus. William Schmidt and Richard Houang (2002) have said that content standards and curricula are coherent if they are:  \narticulated over time as a sequence of topics and performances that are logical and reflect, where appropriate, the sequential or hierarchical nature of the disciplinary content from which the subject matter derives. That is, what and how students are taught should reflect not only the topics that fall within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline. This implies  \nI ntrodUCt Ion  \nCommon Core State StandardS for matHematICS  \nthat to be coherent, a set of content standards must evolve from particulars (e.g., the meaning and operations of whole numbers, including simple math facts and routine computational procedures associated with whole numbers and fractions) to deeper structures inherent in the discipline. These deeper structures then serve as a means for connecting the particulars (such as an understa","cbCaifEFj2983cg9","https://ap.wps.com/l/cbCaifEFj2983cg9","pdf",1237460,93,"English","# Introduction\n## Toward greater focus and coherence\n## Understanding mathematics","[{\"question\":\"What learning areas are prioritized in early childhood mathematics experiences?\",\"answer\":\"Early childhood math experiences should concentrate on number and on geometry, spatial relations, and measurement, with more time devoted to number than to other topics.\"},{\"question\":\"Why does the document emphasize focus and coherence in the standards?\",\"answer\":\"The standards aim for clarity and specificity so the curriculum becomes substantially more focused and coherent, addressing a problem described as being “a mile wide and an inch deep.”\"},{\"question\":\"What does mathematical understanding require, according to the document?\",\"answer\":\"Mathematical understanding includes the ability to justify why a statement is true or where a rule comes from, not just to use mnemonics or procedural shortcuts; it should be assessable through sufficiently rich mathematical tasks.\"}]","Common Core State Standards for Mathematics - Introduction - Toward greater focus and coherence | PDF",1791600696,234]