A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students |
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Authors: | Bryan Moseley Mary E Brenner |
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Institution: | (1) Chaminade University of Honolulu, Brogan Hall Rm 117, 3140 Waialae Avenue, Honolulu, HI 96816-1579, USA;(2) The Gevirtz Graduate School of Education, University of California at Santa Barbara, Santa Barbara, CA 93106, USA |
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Abstract: | This research examines students’ ability to integrate algebraic variables with arithmetic operations and symbols as a result
of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from
arithmetic to algebraic reasoning. It presents data from pre and post instruction clinical interviews administered to a sample
of middle school students experiencing their first exposure to formal pre-algebra. Roughly half of the sample (n = 15) was taught with a standards-based curriculum emphasizing representation skills, while a comparable group (n = 12) of students received traditional instruction. Analysis of the pre and post interviews indicated that participants receiving
a standards-based curriculum demonstrated more frequent and sophisticated usage of variables when writing equations to model
word problems of varying complexity. This advantage was attenuated on problems that provided more representational support
in which a diagram with a variable was presented with the request that an expression be written to represent the perimeter
and area. Differences in strategies used by the two groups suggest that the traditional curriculum encouraged students to
continue using arithmetic conventions, such as focusing on finding specific values, when asked to model relations with algebraic
notation.
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Keywords: | Curriculum Mathematics education Problem solving Cognition Constructivism Schema integration |
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