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Judith Sowder and Diana Wearne

The national assessment of Educational Progress (NAEP) is used by the federal government and by states to gauge achievement in several subject areas, including mathematics. The results of the NAEP tests in mathematics at the eighth grade are used here to help us explore students' mathematics achievement over the decade from 1990 to 2000. In particular, we use these data to counteract the media portrayal of students' achievement in mathematics as steadily declining.

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Zvia Markovits and Judith Sowder

Few students exhibit number sense when solving arithmetic problems in school. This study examined the effects of an intervention in the instruction of seventh-grade students for the purpose of developing number sense. Students were taught by the classroom teacher from experimental units on number magnitude, mental computation, and computational estimation. Instruction was designed to provide rich opportunities for exploring numbers, number relationships, and number operations and to discover rules and invent algorithms. Written measures and interviews before instruction, immediately after instruction, and several months later revealed that after instruction students were more likely to elect to use strategies that reflected number sense and that this was a long-term change. It appeared to the investigators that the students reorganized and used existing knowledge rather than acquiring new knowledge structures.

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Frank K. Lester Jr. and Judith T. Sowder

The field of mathematics education bas witnessed dramatic changes in its nature and complexion during recent years and there is every indication that the pace of change is likely to accelerate in the future. Naturally, the JRME has been changing as well, most notably with respect to the types of articles being published and the move toward an electronic version of the journal. Collectively, most evidence indicates that the journal is thriving, that it has been adapting well to changes in the field. But, unfortunately, not all of the changes have been for the good! rn particular, one negative change has been an increase in the size of the backlog of accepted manuscripts.

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Judith Sowder, Bonnie Schappelle and Diana Lambdin

In Everybody Counts, a document from the National Research Council (1989), we are told that the major objective of elementary school mathematics should be to develop number sense. This strong statement, if taken seriously, can change the way many—but not all—teachers teach mathematics in elementary school.

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Judith A. Threadgill-Sowder and Patricia A. Juilfs

The purpose of the present study was to investigate the interaction of mathematical achievement with manipulative and symbolic approaches to teaching logical connectives to seventh-grade students. The 147 participants were randomly assigned to a manipulative treatment, a symbolic treatment, and a control treatment. The manipulative and symbolic treatments were designed to be parallel in format, and instruction on logical connectives was given by videotape. An analysis of variance revealed significant differences (p<.01) between the main treatments and control treatment, but not between the manipulative and symbolic treatments. Mathematical achievement was found to interact disordinally with the two main treatments, p<.05. Low-achieving students benefited more from the manipulative approach, whereas high-achieving students found the symbolic approach to be more effective.

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Judith T. Sowder and Margariete M. Wheeler

Twelve students at each of Grades 3, 5, 7, and 9 were individually given tasks that presented problems with solutions from hypothetical students, accompanied by questions requiring students to contrast and compare the solutions. These tasks were followed by open-response estimation problems. The older children understood better than the younger children what was asked but were uncomfortable with estimation processes and outcomes. Acceptance of multiple estimates and rounding-then-computing rather than computing-then-rounding were both slow to develop. Recognition of the need to compensate for rounding errors increased with grade level. Schooling factors such as emphasis on unique answers and instruction on rounding and computional procedures seemed to influence results. Careful development of foundational concepts is recommended to prevent learning computational estimation as a set of algorithmic rules

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John C. Moyer, Margaret B. Moyer, Larry Sowder and Judith Threadgill-Sowder

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John C. Moyer, Larry Sowder, Judith Threadgill-Sowder and Margaret B. Moyer

Eight story problems in a drawn format, eight matching problems in a verbal format, and eight matching problems in a telegraphic format were administered to 854 students in tests at each grade from 3 to 7. Scoring was based on the choice of correct operations to solve the problem. Readers of high ability, as measured by a reading test, chose correct operations more often than low-ability readers. The drawn format was easier than the other two formats. A significant format-by-reading-ability interaction revealed that the advantage of the drawn format was greater for low readers than for high readers.

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Larry Sowder, Judith Threadgill-Sowder, Margaret B. Moyer and John C. Moyer

Interviewer (after the pupil had correctly solved a story problem): How did you know to do it that way?

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Analúcia Dias Schliemann

Edited by Judith Sowder, Larry Sowder and Terezinha Nunes Carraher

Children learn much mathematics in everyday life. When they buy things, for example, they have to count their money and calculate their change. Counting money is a special type of counting. On the one hand, when children count objects, they establish a one-to-one correspondence bet ween objects and number words; only absolute value, as opposed to relative value, is involved. On the other hand, when counting money children must bear in mind both types of value; while they deal with the coins one by one (absolute value), they must also take into account the relative value of the coins. Counting money thus helps children understand the decomposition of numbers; a large amount (for example, sixty-eight) is made up of smaller amounts—tens and ones—that can be repeated (six tens and eight one). All these ideas—relative and absolute value, decomposition, and repetition of equal values—are basic both to the understanding of the decimal system and to the undertanding of important properties of arithmetic operations.