Grade-continuum trajectories of four known probabilistic misconceptions: What are students’ perceptions of self-efficacy in completing probability tasks?

• We examined 7th, 9th, and 11th grades, and 3rd year preservice mathematics teachers in a high achieving population.
• Four unique probability tasks were studied with respect to self-reporting self-efficacy.
• Two probability misconceptions increased across grade levels.
• Two probability misconceptions decreased across grade levels.
• Self-efficacy increased with respect to two misconception responses as grade level increased.

This study introduces a new line of research that examines the cross-sectional interaction between student self-efficacy of completing probability tasks. Our study was completed in a high achieving, middle to upper middle class school district and a research university in Alabama. Through our study, we can begin to understand and organize probability misconception trajectories across grades 7, 9, 11, and 3rd year preservice mathematics teachers. In this study we examined four misconceptions: recency effects, the distinction between compound and simple events, the effect of sample size, and representativeness. Our findings indicate probability misconception trajectories slightly increase beginning in 7th grade with respect to distinguishing simple-compound events and the effect of sample size. Recency effect and representativeness misconception trajectories were found to dissipate as grade level increased. We found preservice secondary mathematics teachers to have high self-efficacy with probability misconception answers very similar to 11th graders. Recommendations include assessing for misconceptions and designing mathematics lessons and/or curricula that authentically explore these probability concepts. Preservice programs can use these findings in a manner that models authentic probability task explorations to model effective pedagogical methods. Future research on student self-efficacy with respect to mathematical misconceptions is recommended.