The Effects of Equiprobability Bias and Representativeness Heuristics on the Performance in Probability Comparison and Calculation Tasks Among Middle School Students in China

Abstract

<p><em>Students expose various intuitions in probability comparison and calculation tasks.</em></p><p><em>Large volumes of research looked into these intuitions by categorizing learners’</em></p><p><em>strategies, but fewer studies considered how these intuitions may be associated</em></p><p><em>with learners’ judgments. Even fewer examined the mixed effects of multiple intuitions</em></p><p><em>held by the same individual. Despite calls from scholars to explore students’</em></p><p><em>understanding of probability in different cultural contexts, there has been a dearth</em></p><p><em>of research on how Chinese students understand probability. This study explores</em></p><p><em>the relationship between students’ multiple probability-related intuitions and their</em></p><p><em>judgments in the probability contexts among middle school students in China. In</em></p><p><em>this study, we sampled 707 7th–9th graders from Qingdao, China. We measured</em></p><p><em>students’ performance in probability comparisons and calculations and their probability-</em></p><p><em>related intuitions about equiprobability bias and representativeness heuristics.</em></p><p><em>With chi-square tests and multinomial logistic regression analysis, the relationship</em></p><p><em>between the 2 intuitions and students’ judgments in probability comparison and calculation</em></p><p><em>tasks was examined in detail (including dual effects). The findings of this</em></p><p><em>study include, first, that at the middle school level, students’ equiprobability bias and</em></p><p><em>representativeness heuristics fade with age, but they do not disappear completely.</em></p><p><em>Second, students’ intuitions may play a role in solving probability problems, where</em></p><p><em>equiprobability bias may induce them to make an “equal probability” judgment</em></p><p><em>and representativeness heuristics may make them consider a mixed outcome more</em></p><p><em>likely to occur. Third, the 2 intuitions coexisted and influenced students’ responses</em></p><p><em>together, but the sensitivity of these dual effects to the students’ judgments in the</em></p><p><em>qualitative comparison and quantitative calculation tasks differed. This study will</em></p><p><em>contribute to the fast-iterating policymaking in probability education in China by</em></p><p><em>advocating that curriculum standards pay more attention to students’ limitations in</em></p><p><em>conceptual understanding and their exposed intuitions or misconceptions. This study</em></p><p><em>may, to some extent, complement previous works focusing on Western students’ </em></p><p><em>probability intuitions by confirming that, even for Chinese students who performed</em></p><p><em>well in PISA, their probability perceptions are also accompanied by intuitions.</em></p><em></em>