Title: Comparisons of a physical model and computer representations in reasoning and learning about linear functions
Abstract: This study examined reasoning and learning about the concepts of variables and functions with three learning environments: a physical device, a computer simulation of the physical device, and a computer-based numerical representation. The physical system, called the winches, has two tracks where blocks are pulled by winding strings around spools when a handle is turned. The position reached by a block is a linear function: y = b + mx, where b is the starting position, m is the size of the spool, and x is the number of turns. The analyses focused on characterizing the differential effects of features of the physical and computational representations.
Twelve pairs of seventh graders participated in the study. The sessions consisted of four sections: a pre- and posttest, a structured interview about the device, and a workbook which presented equations as a way of symbolizing events on the device.
Reasoning about the device during the interviews was characterized by: (1) early use of numerical properties by the computer groups; (2) more relational and ordinal statements by the winch groups; (3) strategies used by the winch groups that relied on the structure of the device, with equations more likely to be produced by the numerically-based computer group.
Reasoning about equations during the workbook sessions was characterized by: (1) more references to device quantities by the winch simulation group; (2) more explanations in terms of the device by the winch groups; (3) more transformation of equations to isolate variables in the computer groups.
Work on the posttest was characterized by: (1) significant improvement in the pre-algebra students from pre- to posttest; (2) more use and discussion of equations by the winch students.
These findings indicate that the physical device and computer simulation are environments in which students understand the quantitative structure of the device, and that this structure can provide a foundation for reasoning about the concepts of variable and function. This suggests that a beginning algebra curriculum could be designed in which the concepts of variable and function are grounded in concrete physical or computational activities.
Publication Year: 1993
Publication Date: 1993-01-01
Language: en
Type: article
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Cited By Count: 5
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