This study examined the effects of two inductive multimedia programs, one including the teaching and using of the coordinate graph and its language, on university students' ability conceptualize variables and create equations from word problems. The programs were designed to address the problem of syntactic and semantic translation misconceptions in world problems. For both treatments, posttest scores were significantly higher on both function construction and variable conceptualization than on the pretest. However, students receiving instructions via the inductive multimedia with graph program scored significantly higher on function construction than did those receiving the multimedia only program. This result is consistent with propositions recognizing the conceptual richness of visuals, specifically the coordinate graph, in mathematics education learning. Results suggest using inductive multimedia program treatments that incorporate many instructional strategies including inquiry learning from data, tutorial, schema, and core representational systems. This study also suggests using inductive multimedia programs that include the coordinate graph teaching strategy for the problem of translation, specifically creation of linear function.
In today's work environment, the ability to think critically, to communicate basic mathematical ideas, and to develop problem-solving strategies is essential (Smith, 1994). Furthermore, for students building toward a career, research indicates that a strong relationship exists between mathematical skills and success in college, regardless of major (Waits & Demana, 1988). However, despite the proven short- and long-term value of such skills, student underpreparedness in mathematics is a continuing and growing problem in higher education (Berenson, Best, Stiff, & Wasik, 1990).
In algebraic problem-solving situations, students find algebraic applications difficult. Most students cannot, in fact, translate rational word problems into simple linear functions (Clement, 1982; Lewis & Mayer, 1987; Lochhead & Mestre, 1988; Mayer, 1982; Wollman, 1983). Further, students simply have difficulty with the concept of variables (Leinhardt et al., 1990; Philip, 1992; Usiskin, 1988); variables are an integral part of the concept of function.
Misconceptions are a typical source of errors. Students maintain are incorrect conceptual systems regarding specific concepts in mathematics. These misconceptions may or may not have been intentionally instructed and have been misunderstood repeatedly by learners (Leinhardt et al., 1990). A considerable amount of research has been done in the area of algebraic misconceptions (e.g., Carlson, 1998; Kaur & Boey Peng, 1994), specifically misconceptions during translation tasks from problem situations to equations (Clement, 1982; Kaput & Sims-Knight, 1983; Lewis & Mayer, 1987; Mayer, 1982; Rosnick & Clement, 1980). Generally speaking, misconceptions, evidenced by persistent error patterns, have a psychological base. According to Piagetian learning theory, learners use their existing cognitive structures and construct new knowledge that will be adapted. The problem is that "learner's existing cognitive structures are difficult to change significantly" (Herscovics, 1989, p. 62).
Misconceptions can also be viewed via current cognitive psychology. Mayer (1992) explained the matured (the 1970s and 1980s) cognitive learning theory as a three-part process: "selecting, organizing, and integrating." According to Mayer, integrating is "connecting the organized [new] information to other familiar knowledge structures already in memory" (1984, p. 33). The problem again may be that learners have difficulty opposing their already-existing cognitive structures during the connecting process, especially if their prior knowledge structures make sense to them. The following paragraphs identify two misconceptions that occur consistently during translation from problem situations to equations. …