| Popis: |
Fractions are important in mathematics but notoriously difficult to learn. One obstacle for learners is the “whole number bias,” in which the whole numbers in fractions (i.e., in numerators and denominators) overshadows fractional magnitudes in numeric reasoning. How to overcome the “whole number bias” and make use of prior whole number knowledge? Here we investigated whether comparison to whole numbers on the number line can facilitate children’s learning of fraction magnitudes. In Experiment 1, 30 children identified a number (integer or fraction) from a mark on a number line or placed a mark on a number line to indicate a target number. Estimates of integers were as much as 2x more accurate than estimates of fractions. Therefore, we hypothesized that comparing fraction to integer scales might improve representations of fractions as much as 2x. Using a pretest-training-posttest design (Experiment 2), 64 children were trained to estimate and compare positions of fraction and integers on number lines (e.g., 3/8:1::3:8). At post-test, children solved number-line problems either with (Cue group) or without (No Cue group) visually-aligned cues to facilitate source retrieval. Children in the Cue groups did improve their estimates from pretest to post-test as much as 2x, suggesting that children’s understanding of fractional magnitudes came from the comparison to integers. Further, visually-aligned cues activated inert knowledge at post-test. Together, the two experiments suggest that comparisons of integers and fractions on number lines can reduce the whole number bias and teach fractional magnitudes. |
