How do college students solve proportion problems?

Abstract

Problems which could be solved using proportional reasoning were administered nationwide by college faculty to their own science classes during a three year period. The reasoning of more than 8000 students covering three sections of the country was classifi ed as concrete, transitional, or formal using Piagetian categories. Data from the West closely replicated that from the Midwest on similar metric conversion tasks. Student performance changed noticeably with a different problem format. The percentages of students using a ratio formula, ratio attempt, or intuitive methods of solution held approximately constant over time, task, and section of the country. The data shows the use of additive and conversion methods of solution depends upon the problem presentation.

Intuitive Conceptions of Probability and the Development of Basic Math Skills

“…Indeed, additive reasoning is used in a qualitative, intuitive way, not just by seven-year-olds, but by students from the ages of 11 through 16 who have been taught something about proportions (Hart 1981). Furthermore, research shows that children do not "grow out" of erroneous addition methods (Thornton and Fuller 1981) and that this additive error may actually cause a delay in the development of multiplicative thinking (Markovits and Hershokowitz 1997) which can disrupt work with rational number and ultimately with more advanced topics such as slope and probability. For example, students inappropriately apply additive thinking when judging the equivalency of two fractions with different numerators and denominators (Behr et al 1984).…”

Can one book really transform your career?

“…We frequently gave the Frog Puzzle (Figure 1), a simple test of proportional reasoning, to our ADAPT students in an English class. In general, we found about half used proportional reasoning on this task (Thornton & Fuller, 1981).…”

Complex instructional analogies and theoretical concept acquisition in college genetics

“…Accordingly, successful acquisition of theoretical genetics concepts requires students to reason hypothetico-deductively. Yet, research indicates that substantial percentages of college undergraduates have failed to acquire such reasoning skills (Cantu & Herron, 1978;Gipson, Abraham, & Renner, 1989;Killian, 1979;Lawson, 1982;Thorton & Fuller, 1981;Walker, Hendrix, & Mertens, 1980;Walker, Mertens, & Hendrix, 1979;Ward & Herron, 1980). Not surprisingly, genetics has been recognized as one of the most difficult topics for undergraduates (Lawson, 1992;Mitchell & Lawson, 1988).…”