Poster #36 - Malleability of whole-number and fraction biases in decimal comparison

• In Event: 1-115 - Poster Session 03
  In Poster Session: PS 03 Section - Cognitive Processes

Integrative Statement

In numerical development, decimals share the same important status as whole numbers and fractions. However, the similarities among whole numbers, fractions, and decimals often lead children to overgeneralize whole-number and fraction logic to decimals, where misconceptions and biases appear. The whole-number bias refers to the false belief that decimals share the same properties as whole numbers (Ni & Zhou, 2005). People who hold this bias think decimals with more digits are larger in magnitude, a property that is true of whole numbers but not fractions (e.g., this leads to the belief that 0.32 is larger than 0.7 because it has more digits than 0.7).The fraction bias involves generalizing fraction rules to decimals, including treating decimals that are shorter in length as larger in magnitude (e.g., 0.64 is smaller than 0.3 because 1/64 is smaller than 1/3). According to overlapping waves theory, children can have multiple strategies available simultaneously when handling novel problems (Siegler, 1998). The dynamic strategy choice account suggests that saliency, recency, prior knowledge, and other factors contribute to strategy use when reasoning about decimals (Alibali & Sidney, 2015). However, to our knowledge, this has never been experimentally tested. We hypothesized that whole-number priming would increase whole-number bias in decimal comparisons, whereas fraction priming would increase fraction bias.
Sixth- to 8th-graders (N=149, 76 girls) and adults (N=175, 105 females) were randomly assigned to one of four priming conditions: whole-number comparisons, fraction comparisons, decimal comparisons, or a flanker control task. Participants first completed numerical magnitude comparisons according to their priming condition (or control task) with feedback (prime block), then all conditions completed decimal comparisons without feedback (test block). Decimal comparisons were either whole-number congruent (e.g., .64 versus .3) or whole-number incongruent (e.g., .32 versus .7). We considered better performance on congruent than incongruent decimal trials as evidence for a whole-number bias. We analyzed accuracy and RT in the decimal-comparison test block, with condition and congruency as factors, separately for children and adults. Adults showed significant whole-number bias in RT and accuracy (main effect of congruency, ps.001), a significant main effect of condition on accuracy only (p=.024; accuracy was lower after fraction priming), and no condition x congruency interactions. Sixth- to 8th-graders showed significant condition x congruency interactions for both RT (p=.018) and accuracy (p<.001) (Figure 1). Compared to the control, fraction and decimal priming significantly reduced whole-number bias in both accuracy and RT, and decimal priming showed the highest accuracy overall. We also conducted analyses at the individual level by categorizing children according to their pattern of performance on the test block (Table 1). Compared to the control condition, fraction priming increased the percent of children with a fraction bias, χ2(1)=6.19, p=.013, and decimal priming increased the percent of children with high decimal-comparison accuracy, χ2(1)=17.53, p<.001. These results provide the first experimental evidence that increasing the saliency of fractions leads to fraction bias in decimal comparisons. Moreover, performance in the control and whole-number-priming conditions was characterized by strong whole-number bias, but relatively brief feedback with decimal comparisons substantially improved performance.

Authors

• Kexin Ren, Temple University
  Presenting Author

• Elizabeth Gunderson, Temple University
  Non-Presenting Author