ABSTRACT
In statistics education, students' thinking about various statistical concepts, such as central tendencies, probability, and covariance, has also received attention in education research. Research on students' pre-instructional thinking and reasoning about variability can be conceived to include two main areas: one that examines students' reasoning with variability, and another that investigates students' notions of how variability is measured. Productive failure (PF) engages students in generating solutions to novel problems first before teaching them the concept. In the generation and exploration phase of the PF learning design, the focus was on affording students the opportunity to leverage their formal as well as intuitive prior knowledge and resources. Researchers have previously highlighted that the measure of variance and variability is computationally complex and difficult to motivate in instruction. The PF design affords the generation of problem-solving strategies because it is designed to activate the formal and informal, intuitive prior knowledge structures.
