Implementing a Novel Computer-Related Algebra Course
Recent concern about the quality of American education led the National Council of Teachers of Mathematics (NCTM) to propose a new set of standards for K-12 mathematics instruction which suggests a variety of fundamental content changes for mathematics education. At the most general level, NCTM standards emphasize the need for students to learn higher-order thinking and problem-solving skills. Since 1988 the RAND Algebra Tutor Project has been working on developing and piloting intelligent computer tools for first-year algebra students. It developed an intelligent tutoring system (ITS) to help students learn symbol manipulation skills for solving problems in basic algebra. Consistent with the NCTM standards, subsequent versions of the ITS have focused on helping students learn more "strategic" reasoning skills in algebra, leaving the "tactics" of symbol manipulation to the computer. Inadequate training, new instructional, pedagogical and organizational goals, and logistical problems all contributed to the difficulty of effectively implementing computer-assisted instruction. The classroom culture places priority on covering a given set of topics in a certain amount of time. Topics are taught didactically, at a fast pace, driven by the textbook. This note describes the curriculum module for beginning algebra that the authors developed to address in an integrated rather than piecemeal way, some problems of mathematics curriculum content reform, the novel use of computers in the classroom, and implementation problems that arise from these content and technology changes. It describes the development and content of the curriculum; discusses the overall approach to curriculum development, the specific novel mathematical topics targeted, as well as the design of the computer software and teacher and student materials; describes the implementation of the module, student and teacher training procedures, and assessment procedures; and evaluates the curriculum and its implementation. The classroom observations and teacher feedback suggest several needed changes to the curriculum and supporting tutor software: the connection between the qualitative and quantitative components of the curriculum needs to be made clearer; new graphical representations need to be designed and integrated with existing quantitative representations; students need more coaching on the construction of equations to represent natural situations; more noticeable messaging techniques (e.g. computer-generated voice messages) need to be investigated to overcome student reluctance to read textual instructions; students need more instruction in inquiry techniques and systematic ways to collect data; course terminology needs to be made more meaningful so that attention can be focused on the reasons for mathematical processes rather than the name for them; students need more direct practice in symbol-manipulation skills; we must continue to develop interesting and realistic natural situations for students to explore.