By Gaea Leinhardt, Ralph Putnam, Rosemary A. Hattrup

This quantity emerges from a partnership among the yankee Federation of academics and the training study and improvement middle on the collage of Pittsburgh. The partnership introduced jointly researchers and specialist lecturers for extensive discussion classes targeting what every one neighborhood understands approximately powerful mathematical studying and guideline. The chapters take care of the examine on, and conceptual research of, particular mathematics themes (addition, subtraction, multiplication, department, decimals, and fractions) or with overarching subject matters that pervade the early curriculum and represent the hyperlinks with the extra complex issues 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 contemporary study successes of cognitive technological know-how and reports the literature of the mathematics schooling group as well.

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**Example text**

In CAP2, these ex ercises appear in the teachers’ pages of each lesson under the heading “Mental Arithmetic” and are intended as a “lively drill” to begin each class. Only a small percentage of these problems require mental computation as defined and discussed earlier in this chapter, particularly if we do not consider review and drill of basic facts as mental computation. Many of the problems require making both gross and fine estimates of sums, differ ences, products, and quotients. The majority of lessons call for thinking about reasonable answers rather than simply applying a rule or a number fact.

The second reason is that estimation is important in its own right and is a skill worth having. Many would argue that direct instruction on strategies is the most efficient and reasonable way to reach this goal. But if the skill we want students to acquire is to be able to use intuitive, sometimes non routine methods to check the reasonableness of answers, then we might want to consider an indirect approach as a way of assisting students in developing number sense and computational estimation ability.

Her instructional focus is on making reasoned connec tions between what students assume about mathematical structure and what she wants them to learn. For example, students in the class used drawings and stories as a symbol system in which they could argue that “it is legitimate to figure out 28 x 65 by first finding 30 x 65, and subtracting the product of 2 x 65 from that” (p. 145). As part of the Primary Instruction in Mathematics Education (PRIME) project in England (Shuard, 1986), a calculator-aware numbers curriculum is being developed with the following as its main goals: the ability to translate between a situation and the corresponding calculation, a “friend ly” feeling for numbers, an understanding of “how numbers work,” an un derstanding of place value, an ability to calculate in the head, the ability to use the calculator sensibly when mental calculation is not appropriate, the early development of algorithmic thinking, and the ability to tackle new 1.