By Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup
This quantity emerges from a partnership among the yankee Federation of lecturers and the training learn and improvement heart on the college of Pittsburgh. The partnership introduced jointly researchers and professional lecturers for extensive discussion classes targeting what every one group understands approximately powerful mathematical studying and guideline. The chapters take care of the study on, and conceptual research of, particular mathematics issues (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching issues 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 booklet capitalizes at the contemporary learn successes of cognitive technological know-how and studies the literature of the mathematics schooling group as well.
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Extra info for Analysis of Arithmetic for Mathematics Teaching
CAPl first shows sets of objects with more than 10 but fewer than 100, with sets of 10 in groups or bundles, and students identify these as, for example, 2 tens and 3 ones, 23. Besides writing the number of elements pictured, students are required to fill in numbers missing from sequences of count ing numbers and to tell what comes before and after a number. In Grade 1, trading (one ten for ten ones, and vice versa) is introduced in preparation for adding and subtracting two-digit numbers, and three-digit numbers are introduced via pictures of flats (of 100 squares), longs (of 10 squares), and ones (squares), and also with money.
CAP2 also considers larger numbers in higher grades, in addition to other lessons focusing on place-value concepts. , using 6, 7, 1, make the biggest number you can). Many games at various grades in this program also call for placevalue understanding. In Grade 1 of SMP numbers larger than ten are divided for instructional purposes into the numbers 11 through 20 cind the numbers 21 through 100. Students are expected to acquire the concept of 10 while working with numbers 11 through 20. One bundle of 10 sticks and individucd sticks are used to display these numbers.
This study, although it provided some insight into performance on NAEP-type items, did not provide information on the range of strategies students use to solve (or attempt to solve) estimation problems. A more comprehensive study of student performance on computational estimation was undertaken by Keys, Rybolt, Bestgen, and \^^att (1982), who sought to identify and characterize the computational processes used in estimation by in-school students and out-of-school adults. Good estimators were identified as those scoring in the top 10% of each group of students in Grades 7-12 who completed a 55-item computational estimation test.