THE EFFECTS OF TABLE-BUILDING PROBLEM-SOLVING PROCEDURES ON STUDENTS' UNDERSTANDING OF VARIABLES IN PRE-ALGEBRA.

摘要

Research has indicated students have misconceptions about variables and difficulty in solving word problems. Most algebraic approaches develop the concept of variable using translation and deductive reasoning. This teaching experiment examined alternative approaches to variables. Two Table-Building (TB) Methods of teaching word problems and use of variables were compared with a Translation (T) Method.;Ninety-seven ninth grade pre-algebra students enrolled in four classes of an inner-city high school were randomly assigned to treatments in eight matched groups of approximately 13 students. The experimental design was a completely randomized one-factor design with three levels of treatments. The data were analyzed by MANOVA, correlational analyses, and Dunn's post-hoc comparison procedures.;The Investigator met each group forty minutes once a week for eleven weeks. Understanding and use of variables were assessed by a pretest and posttest. A problem-solving test assessed ability to use variables and problem-solving procedures.;Analyses revealed the following: (1) There were no statistically significant differences among the three treatment groups on their abilities to understand and use variables. Subjective data indicated the TB1 group had a better understanding of variables than the TB2 and T groups, and the TB1 and T groups used variables more than the TB2 group. (2) The time a variable was introduced affected students' use of variables but did not affect their understanding. No significant effect was made on a student's ability to use variables to solve problems. (3) TB instruction yielded better problem-solving than T instruction. (4) Students' levels of cognitive development were correlated with problem-solving abilities (p (LESSTHEQ) .01). Concrete thinkers taught via translation were less successful with problem-solving than those taught by table-building.;The Table-Building (TB) treatment consisted of two experimental groups (TB1, TB2) and the Translation (T) treatment (a comparison group). The difference between the instruction of the TB groups was the timing of the introduction of a variable in the table-building process. TB approaches utilized numerical problem-solving with guess and check, and inductive techniques. The T approach required use of rules about translation to write equations for problems.