By Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup
This quantity emerges from a partnership among the yankee Federation of academics and the educational examine and improvement heart on the college of Pittsburgh. The partnership introduced jointly researchers and professional lecturers for extensive discussion periods concentrating on what each one neighborhood is familiar with approximately powerful mathematical studying and guide. The chapters take care of the learn on, and conceptual research of, particular mathematics issues (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching topics that pervade the early curriculum and represent the hyperlinks with the extra complex subject matters of arithmetic (intuition, quantity experience, and estimation). Serving as a hyperlink among the groups of cognitive researchers and arithmetic educators, the e-book capitalizes at the fresh study successes of cognitive technological know-how and experiences the literature of the maths schooling neighborhood as well.
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Additional resources for Analysis of Arithmetic for Mathematics Teaching
36 SOWDER Decimal Numbers Decimals (in tenths) are introduced in CAPl, Grade 3, cis a new way to write fractions with denominators of 10. Adding decimal numbers is introduced next, with the rule given to line up decimal points. 7 give 1 whole and 3 tenths. No attempt appears to be made in this grade to relate decimals to previously acquired place-value concepts. 8 cm long). Money is also used to develop the concepts of decimal pcu-ts. A lesson then is given on comparing decimal numbers. The rules given for comparing decimal num bers tell students to line up the decimal points and, starting from the left, to compare digits.
Interposed between these two reports, the landmark position paper of the National Council of Supervisors of Mathematics (1977) on basic skills included estimation and approximation among the 10 basic skill areas in need of development. Both the NAEP reports and the position paper sparked a great deal of interest in learning more about how children (and adults) estimate and how estimation skills develop. In order to acquire a better understanding of children’s thinking while answering NAEP prob lems, 1(Threadgill-Sowder, 1984) selected 12 representative NAEP or NAEPlike items and asked 26 sixth through ninth graders to work these problems individually.
A seventh-grade teacher used discussion of estima tion techniques, pattern searching, and cognitive conflict in a unit that focused on making reasonable estimates, particularly with traditionally difficult topics such as estimating products and quotients involving ration 1. MAKING SENSE OF NUMBERS 19 al numbers. Students become much more flexible when estimating. ). An indirect approach to instruction on estimating operations on fractions was also successful for Mack (1988). Whether estimation strategies should be directly taught to students or whether students should be encouraged to explore and invent strategies through an indirect instructional approach is an important instructional question.
Analysis of Arithmetic for Mathematics Teaching by Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup