Using an Apos Framework to Understand Teachers’ Responses to Questions on the Normal Distribution

This study is an exploration of teachers’ engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an “unknown percentage” problem, which required the application of properties of the standard normal distribution curve. Responses to the task were analyzed using the Action, Process, Object, Schema (APOS) framework that specified a standardization and a probability layer of understanding. The success rates were 27% and 14% in the two questions, with most teachers experiencing problems in the probability layer because of a failure to link the probability values with the area covered by the curve.