| Current reform efforts in mathematics call for making probability and statistics (stochastics) a fundamental component of the school mathematics curriculum. Factors have been found that may limit students' understanding of and performance in stochastics. Students' misconceptions are particularly problematic as they result in a lack of conceptual understanding of the nature of stochastics. However, little is known about the current state of high school students' misconceptions in this area. The purposes of this study were (a) to determine if certain defined misconceptions in stochastics are present in students attending one particular high school and if so, which misconceptions, (b) to determine if demographics (i.e., ethnic background, gender, grade, and family socioeconomic level) are related to these students' misconceptions in stochastics, and (c) to determine if academic factors (academic track, on or off mathematics grade level, and taking honors classes) are related to these students' misconceptions in stochastics. Two hundred high school students were given an assessment that addressed reasoning in stochastics. A total of 12 misconceptions were covered in this study including "Anchoring & Adjustment," "Availability," "Conditionals," "Conjunction Fallacy," "Correlation implies Causation," "Equal Groups to Compare Means," "Equiprobability," "Law of Small Numbers," "Means & Averages," "Outcome," "Representativeness," and "Sample Size" (See Appendix A for definitions.). The students were asked to provide demographic data that included gender, grade level, ethnic background, and socioeconomic status and academic information which included identifying their academic track, whether they were on or below mathematic grade level, and whether they were enrolled in honors mathematics classes. Quantitative measures were employed. Comparing means from the students previously given the assessment showed that these high school students had higher levels of misconceptions. Additionally, multiple regressions and bivariate correlations were performed on each of the 12 misconception scales against the seven independent variables. The results showed that gender and that students who were enrolled in honors mathematics classes were contributing factors to the misconception of Availability. Females and students enrolled in honors mathematics classes had higher misconceptions in Availability. Students who were identified as being below mathematics grade level had higher misconceptions in Anchoring and Adjustment; and students who were enrolled in honors mathematics classes had a higher misconception in Equiprobability. |
