An investigation of proportional thinking among high school students

摘要

The National Council of Teachers of Mathematics suggests that formal proportional reasoning instruction take place during grades five through eight (1989). While extensive research has explored both pre-instructional and intra-instructional student proportional thinking strategies, little research has been done on post-instructional proportional thinking strategies used by high-school aged students. As proportional reasoning is fundamental for success in Algebra and other advanced mathematics, it seems relevant to verify that these students retain their reasoning abilities and can apply them in both high school and college mathematical situations.;This study sought to: (1) determine whether high-school students from specific rural, low-income school environments possessed advanced proportional reasoning abilities, (2) explore students' conceptual understanding of the "cross multiply and divide algorithm," and (3) evaluate the impact of manipulatives on student thinking. This systematic investigation of the participants' proportional reasoning abilities was comprised primarily of interviews and observations.;One hundred and seven high school students were involved in the study, twenty-one of whom participated in one-on-one in-depth interviews. The research found: (1) only two of the twenty-one interviewees (9.5%) exhibited advanced proportional reasoning skills, (2) nineteen of the interviewees (90.5%) were unable to apply their knowledge of proportions and the "cross multiply and divide" algorithm to solve nontraditional problems, and (3) evidence indicated that using manipulatives helped students move toward solutions to the proportional reasoning problems.