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.
The new issue of Instructional Science (January, 2009) has an article related to mathematics education: A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students, by Bryan Moseley and Mary E. (“Betsy”) Brenner. Here is their article abstract: