An intervention to advance Piagetian levels of cognitive development and algebraic reasoning in high-school students.

摘要

This dissertation addressed the relationship between levels of Piagetian cognitive development and algebraic reasoning. A correlational analysis was conducted to show the relationship between levels of Piagetian cognitive development and algebraic reasoning and also to show the relationship between levels of Piagetian cognitive development and algebra course grades. High-school students were chosen because they are at the age approximation Piaget predicted children would transition from concrete operations to formal operations. An intervention followed with a small group of students to accelerate their transition to formal operations. The types of strategies used and the errors made during the intervention were observed and calculated.; The objectives of this study were as follows: (1) to determine whether there is a relationship between Piagetian levels of cognitive development and the level of algebraic reasoning in high-school freshmen, (2) to determine whether there is a relationship between Piagetian levels of cognitive development and grades in algebra class in high-school freshmen, (3) to determine whether the intervention group had a statistically significantly greater change in level of Piagetian cognitive development from the transitional stage between concrete operations and formal operations to formal operations than the comparison group, (4) to determine what types of strategies the intervention students used who successfully shifted to formal operations, and (5) to determine the patterns of errors of the intervention students who did not successfully shift to formal operations.; The results indicate that there is a significant positive relationship between the Piagetian level of cognitive development and levels of algebraic reasoning in high-school freshmen but not between Piagetian levels of cognitive development and algebra course grades. The results did not show that the students who participated in the intervention had a greater change in the level of Piagetian cognitive development than the students who did not receive the intervention. The results showed that the intervention students who successfully shifted to formal operations used algebraic strategies more than 50% of the time. The students who participated in the intervention and did not successfully shift to formal operations primarily made pattern errors or made errors when writing arithmetic equations to solve problems.