Algebra for sixth graders: An investigation of the perceived difference in subsequent learning in algebra attributed to the Hands-On Equations Learning Systems

The purpose of this qualitative study was to examine the perceptions of high school graduates who experienced the mathematics education materials from the Hands-On Equations Learning System (Hands-On Equations) when the students were in the sixth grade. The investigation also included the perceptions about mathematics of students who did not experience these manipulative materials.; The participants for this research had attended school and graduated from high school in a small, public school district in eastern Kansas. Of the 19 students who were interviewed, 10 had experienced 21 lessons that involved Hands-On Equations when they were in the sixth grade in January 1997. Ten of the students were male and nine were female. The data consisted of the interviews that were conducted with these students in 2005, solutions to six one-variable linear equations completed by each student, and GPA and ACT information for each student.; Students recalled positive reactions and valued the Hands-On Equations experience. They recommended that other sixth-grade students be taught algebra with these materials. The reasons for valuing the Hands-On Equations materials included the access to foundational algebraic knowledge that helped students when they got to their first algebra class, alignment with visual or hands-on learning styles, and the promotion of student interest in mathematics.; Several areas of comparison between the two groups of students were analyzed. No obvious difference in present mathematics self-efficacy between the students in the two groups was discerned. Differences were noted when student attitudes were examined. Hands-On Equations students favored mathematics noticeably more than the non-Hands-On Equations students did. The Hands-On Equations group had both a lower mean GPA and lower mean ACT mathematics score, however the students in the Hands-On Equations group solved the six one-variable linear equations with more success (72% accuracy) than did the non-Hands-On Equations group (59% accuracy).; The results from this study confirm the information from other studies (Barclay, 1992; Busta, 1993; Leinenbach & Raymond, 1996) that suggest that Hands-On Equations may help middle level students learn algebra.