| Popis: |
Understanding number magnitudes is important in life and for math achievement, yet little is known about children’s and adults’ metacognitive awareness of the accuracy of their whole number and fraction estimates. In Study 1, fourth and fifth graders estimated whole numbers (0-1,000 and 0-100,000) and fractions (0-1) on number lines, made a confidence judgment immediately after each estimate, and rated their familiarity with each number. In Study 2, I randomly assigned third through fifth graders and adults to either a number- or word-familiarity manipulation to test the hypothesis that experiences with numbers increase familiarity and confidence. Older children estimated more precisely than younger children across numerical ranges, yet there were few differences in their item-by-item confidence and familiarity judgments. Additionally, children and adults relied on their familiarity to monitor their estimates of fractions, but not whole numbers. Monitoring accuracy was low across all numerical ranges and grades, inconsistent with evidence that suggests monitoring accuracy is greater in older than younger children. A brief experience with unfamiliar fractions did not lead to greater familiarity or confidence, likely because of participants’ extensive prior experiences with numbers. However, in a secondary data analysis, a more time-intensive fraction board game intervention increased children’s confidence, despite having no effect on performance on different fraction tasks. Thus, children’s and adults’ experiences with whole numbers and fractions may influence their confidence judgments. In Study 3, I tested whether monitoring accuracy was greater when there was systematic variability in estimation accuracy and a cue that identified this variability. I randomly assigned participants to estimate fractions on 0-1 number lines in either a non-diagnostic cue condition or a diagnostic-cue condition. In the non-diagnostic cue condition, participants estimated small-component (e.g., 2/9) and large-component (e.g., 16/25) fractions. In the diagnostic-cue condition, participants estimated the same magnitudes, but large-component fractions were raised to a power (e.g., [9/18]3). As expected, adults were less familiar with, less confident in their estimates of, and less accurate in estimating fractions raised to a power compared to small-component fractions. As a result of the differences in confidence and performance between small-component and large-component fractions raised to a power, adults more accurately judged their estimation accuracy in the diagnostic-cue compared to non-diagnostic cue condition. I also expected that adults’ monitoring accuracy was limited due to noise associated with spatial-localization skills. However, accounting for spatial-localization accuracy did not increase the relation between confidence and number-line estimation accuracy. Finally, participants’ confidence and estimation accuracy were related to the likelihood they asked for help on any given item. However, the relation between confidence and help-seeking was stronger in the diagnostic-cue condition than the non-diagnostic cue condition. These results are consistent with the cue-utilization framework and suggest that adults can identify when there are salient differences in their estimation accuracy. Further, their monitoring accuracy is important because adults relied on their confidence judgments to ask for help on individual items. |
