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Jane O. Swafford

The study investigated sex-related differences among first-year algebra students with respect to achievement, attitude, and consumer problem-solving skills. The subjects were 329 females and 294 males enrolled in first-year algebra courses in 17 schools across the country. In the fall, no sex-related differences were evident in arithmetic computational skill or attitude about the usefulness and enjoyment of mathematics. Males showed a slight advantage on consumer items. In the spring, no sex-related differences in algebra achievement were found; a decline in attitude was observed for both groups; and the differences on consumer exercises became more pronounced.

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Jane Swafford

Computers and calculator are here to stay. The challenge facing us, as stated in An Agenda for Action, is to “take full advantage of the power of calculator and computer at all grade levels.” Much has been written and said about how this goal might be accomplished, about what we should add to the curriculum or how we can enhance the existing curriculum. But where will we find the room?

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Jane Swafford and Robert McGinty

The students could tell a prime number when they saw one, but they could not tell why it was a prime number. Obviously, the definition, “a prime number is a whole number with exactly two factors — itself and one,” did not mean much to fifth graders.

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Cynthia W. Langrall and Jane Swafford

Ellen, Jim, and Steve bought three helium-filled balloons and paid $2 for all three. They decided to go back to the store and buy enough balloons for everyone in the class.

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Jane O. Swafford and Henry S. Kepner Jr.

Experimental first-year algebra materials, Algebra Through Applications, were developed by Zalman Usiskin of the University of Chicago under a grant from NSF. This study was a field evaluation of the materials conducted in 20 schools across the country. The effectiveness of the materials was evaluated in terms of achievement, attitude, transfer to consumer problem solving, readability, and implementability. Overall, it was found that the experimental materials could be used effectively in a variety of school settings. Recommendations are made concerning the use and implementation of the materials.

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Jane O. Swafford and Cynthia W. Langrall

The purpose of this study was to investigate 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Ten students were presented with a series of similar tasks in 6 different problem contexts representing linear and nonlinear situations. The students in this study showed a remarkable ability to generalize the problem situations and to write equations using variables, often in nonstandard form. Although students were often able to write equations, they rarely used their equations to solve related problems. We describe students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra.

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William E. Schall, Jane O. Swafford, Jacob Gendelman and E. Harold Harper

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Curtis C. McKnight, Kenneth J. Travers, F. Joe Crosswhite and Jane O. Swafford

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Jane O. Swafford, Graham A. Jones and Carol A. Thornton

This study examined the effects on instruction of an intervention program designed to enhance teachers' knowledge of geometry and their knowledge of research on student cognition in geometry. Forty-nine middle-grade (4-8) teachers participated in a 4-week program consisting of a content course in geometry and a research seminar on van Hiele theory. The pretest and posttest results showed significant gains in content knowledge and in van Hiele level. The analysis of a lesson-plan task revealed a significant shift in goals and expectations to the next higher van Hiele level. Follow-up observations of 8 teachers found marked changes in what was taught, how it was taught, and the characteristics teachers displayed. Teachers attributed these changes to increased geometrical content knowledge and research-based knowledge of student cognition.

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Catherine A. Brown, Thomas P. Carpenter, Vicky L. Kouba, Mary M. Lindquist, Edward A. Silver and Jane O. Swafford

This article is the first of two articles reporting on the seventh-grade and eleventh- grade results of the fourth mathematics assessment of the National Assessment of Educational Progress (NAEP) administered in 1986. The elementary school results appear in companion articles in the Arithmetic Teacher (Kouba et al. 1988a, 1988b). Secondary school data from previous national assessments have been reported in the Mathematics Teacher (see, e. g., Carpenter et al. [1980, 1983))