Abstract

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated with rational numbers all around them, from the “% Daily Values” on nutrition labels to sales and discounts in stores to the constant ups and downs of gas prices. From an early age, humans have a rather robust concept of natural number, but this earlier knowledge seems to act as a barrier to future learning of rational number. While participants performed better on one-statement problems with a single percent, they ignored the principles of rational number when presented with two-statement percent problems. For example, using rational numbers involves dropping the successor principle, a principle that applies to the natural numbers. Problems presented algebraically gave participants great difficulty, though performance improved when subjects were able to replace the variable y with a natural number. When using a numerical hint, participants still did not improve their performance on algebra problems in posttest. Error analyses revealed a strong tendency for students to interpret the problems as novel examples of natural number problems. This research discusses the failure to understand percents in light of overuse or failure to apply the natural number successor principle, division, false cognates, and the absence of knowledge that relates multiple rational number representations to a common underlying knowledge structure. The amount of previous math experience is also correlated with the ease of moving between natural number and rational number concepts.