Using conversions and treatments to understand students’ engagement with problems based on the normal distribution curve

Including probability and statistics in the core curriculum of mathematics in South African schools has made it necessary to train teachers to teach statistics at high school level. This study concentrates on practising mathematics teachers who were students in an in-service programme. The purpose of the study was to investigate students’ success rates on different questions of a multi-part task based on the normal distribution curve. The theory that I used to understand the students’ difficulties is Duval’s theory about movement within and between semiotic representation systems, called treatment transformations and conversion transformations respectively. The first two parts of the problem were unknown percentage problems and involved a treatment followed by a conversion. The third was an unknown value problem and required a conversion before the students could undertake a treatment transformation. The findings reveal that the success rates the students achieved in treatment transformations were higher than those they achieved in conversion transformations. The study also revealed that the direction of the conversions played a role in success rates. Recognising the different challenges the two types of transformations pose requires that teachers pay particular attention to actions that involve movement between different representation systems.