
06561726
j
2016c.00648
Doyle, Kathleen M.
Dias, Olen
Kennis, James R.
Czarnocha, Bronislaw
Baker, William
The rational number subconstructs as a foundation for problem solving.
Adults Learn. Math. 11, No. 1, 2142, electronic only (2016).
2016
Adults Learning Mathematics (ALM)
EN
F48
F88
D58
adult education
higher education
university teaching
colleges
institutes of technology
adult learners
remedial teaching
research
concept formation
concepts
rational numbers
subconstructs
fractions
proportion
ratio
operator
quotient
percentages
measure
problem solving
competency
transfer of learning
transfer of training
informal proportional reasoning
formal proportional reasoning
http://www.almonline.net/images/ALM/journals/almijvolume111january2016.pdf
Summary: One of the many roles of two year community colleges in the United States is to bridge the gap between secondary school and college for students who graduate from high school with weak mathematics skills that prevent them from enrolling in college level mathematics courses. At community colleges remedial or developmental mathematics courses review the prealgebra and/or algebra skills required for college level mathematics. Fractions are often cited as the most difficult topic for students due to their abstract nature. This study with adult prealgebra students is based upon a teaching research experiment in which the Kieren's fraction subconstructs of partwhole, ratio, operator, quotient, measure and the fractional equivalence were used as foundational concept knowledge during problem solving. In the first quantitative part of this study, students' proficiency with Kieren's rational number subconstructs are used as independent variables in a multiple linear regression model to predict or explain students' competency in formal problem solving. This part of the study supplies hypothetical or statistical suggested pathways for students learning and transition from fraction concepts to proportional reasoning. Then in the second qualitative part of this study, transcripts from classroom lectures during the teaching research experiment are reviewed in order to understand how students used these rational number subconstructs during problem solving with ratio, quotient, proportion, and percent.