Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Whole- Number Concepts and Operations

摘要: IntroductionConsider a prospective elementary teacher (PT] solving 527 - 135, using the standard algorithm and explaining regrouping as follows:You put 1 over next to number that gives you 10____I don't get how can become 10. One 10 are two different numbers. How subtract from here then add here? Where did other 9 come from?This PT clearly followed correct procedure arrived at answer, but she was not able provide an explanation for why this solution method results in answer. Figure shows her written work.Now consider another PT's reflection describing inability explain regrouping:I learned [at beginning of my mathematics methods class] there lot more concept [of place value] than I aware of. am use math effectively everyday life, such balancing checkbook, when presented with questions carry out procedures carrying1 borrowing addition subtraction, stuck. could any these or rules. just knew do them. This came huge shock me considering well most classes. felt terrible simple subtraction.Both PTs have determined they want teach children, yet point neither them would be conceptually help elementary-aged child make sense works algorithms taught United States. Moreover, problem is sufficient knowledge teaching children. In States, National Council Teachers Mathematics (NCTM, 2000a] Common Core State Standards (CCSSM] (National Governors Association Center Best Practices, Chief School Officers, 2010] call children develop conceptual understanding (Hiebert & Lefevre, 1986] encounter. Procedural fluency one several aspects being mathematically proficient Research Council, 2001]; four understanding, strategic competence, adaptive reasoning, productive disposition. order equipped support students' development mathematical proficiency, inservice teachers also need mathematics. Researchers highlighted deep multifaceted (Hill, Ball, Schilling, 2008; Ma, 1999]. Less clear, however, improvement teachers' accomplished.At core school concepts operations. NCTM (2000a] stressed all pre K-12 students should "[a] understand numbers, ways representing relationships among systems; [b] meanings operations relate another; [and c] compute fluently reasonable estimates" (p. 32]. A underlies learning future STEM subjects. "Number pervades areas The Content [other Number Operations] five Process grounded number" 2000b, HI]. CCSSM, Operation Base Ten" focal domains each grade K through 5, by "The System" Grades 6-8 Quantity" high school.Even strong focus on throughout curriculum, States countries "experience considerable difficulty constructing appropriate multidigit numeration arithmetic" (Verschaffel, Greer, De Corte, 2007, p. …