An investigation of fourth graders' conceptual understanding of and procedural fluency with rational numbers

The purpose of this study was to compare two groups of fourth grade students' conceptual understanding and procedural fluency in the area of rational numbers. One group of students will be provided instruction based upon a constructivist approach utilizing an operational manipulative and the second group was provided instruction based on a constructivist approach without the use of an operational manipulative. Whereas the constructivist model supports the global use of manipulatives to foster students' understanding, there is little research that distinguishes specific instructional purposes of various manipulative models.; Data was gathered from one independent school in a suburban area of a major metropolitan city in the Midwest. Data included pre and posttests of conceptual understanding and procedural fluency of rational numbers of fourth graders. There were 18 students in the control group and 18 students in the experimental group. Students in the control group received a constructivist approach to teaching rational numbers using the reform-based curriculum, Everyday Mathematics (1986). Students in the experimental group received the same instruction employing a set of lessons in which the constructivist approach was taught with the enhancement of a specific manipulative.; The study utilized a true experimental design with a pretest-posttest. (Campbell & Stanley, 1963) A two-factor analysis with repeated measures on one factor was used for data analysis (Winer, 1971).; There were two research hypotheses in the study. The first was that fourth grade students gain greater conceptual understanding in using rational numbers after being taught lessons from a constructivist approach supported by the use of a specific manipulative designed to enhance operational understanding and skill as compared to students taught lessons from a constructivist approach that does not include the use of a specific manipulative designed to enhance operational understanding and skill. The data indicated that the experimental group showed significantly higher growth of conceptual understanding than the control group. The effect size was 0.75.; The second research hypothesis was that fourth grade students gain greater procedural fluency in using rational numbers after being taught lessons from a constructivist approach supported by the use of a specific manipulative designed to enhance operational understanding and skill as compared to students taught lessons from a constructivist approach that does not include the use of a specific manipulative designed to enhance operational understanding and skill. The data indicated that the experimental group showed significantly higher growth of procedural fluency than the control group. The effect size was 0.59.