Innovative pedagogical approaches based on solving a disjunctive probability problem

Probability remains a pedagogically problematic topic in mathematics at both primary and secondary levels (Way and Ayres, 2002). Topics in statistics and probability require special attention, mainly because the underlying misconceptions students hold about probability are often not addressed by their teachers. Students find the abstract expressions, complex terms, and nested relationships contained in probability laws hard to understand and tend to rely on everyday reasoning skills that may be flawed (Tomlinson and Quinn, 1997). Developing sound reasoning skills is important in probabilistic thinking because many students and adults hold misconceptions about the likelihood of events based on their feelings (Stepans & Hutchison, 1998; Green, 1982). Additionally, students' understanding of probability does not improve naturally with age - teaching plays an important role (Li and Pereira-Mendoza, 2000). Furthermore, the difficulty of unlearning faulty beliefs lies in the fact that such beliefs are often grounded in the principles of probability but include subtle misconceptions that can be difficult to explain (Costello, 2008).