Knowledge of Binomial Distribution in Pre-service Mathematics Teachers

The binomial distribution is one of the most important discrete distributions in probability and statistics; however, research identifies weaknesses in teachers’ and students’ application of binomial distributions for solving tasks beyond the direct use of the formula. Based on historical epistemological study and notions from the onto-semiotic approach to mathematical knowledge and instruction, we designed and administered a questionnaire to secondary school mathematics teachers in training. In our results, we identify and describe a lack of articulation among historical epistemological elements of the binomial distribution. Teachers can correctly use concepts such as combinatorics, probability, and the binomial distribution formula to model and identify binomial phenomena but cannot answer questions about a random variable or expected value. They show a lack of consideration of alternative representations.