Exploring grade 10 learners’ errors and misconceptions involved in solving probability problems using different representations

A research project submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Masters in Science Education. 2015The Curriculum Assessment Policy Statements (CAPS) re-introduced some mathematics topics such as probability. An immediate effect of this re-introduction is that most teachers and learners were not well equipped to deal with this topic. To at least begin addressing this problem, this research explored the errors and misconceptions that learners have when solving probability problems using different representations. The study draws from Nesher’s (1987) theory of errors and misconceptions as well as Sfard’s (2007) theory of commognition in explaining representations and prevalence of errors in learning mathematics. Twenty two Grade 10 learners wrote probability tasks after which their scripts were analysed for errors. Six of those learners were interviewed on the errors they made in solving probability problems with different representations. The findings reveal five main categories of errors and misconceptions. These are: (1) difficulty with construction of visual representations; (2) improper distinction between simple and compound events; (3) application of inappropriate routines; (4) errors associated with familiarity; and, (5) misinterpreted language. The findings also showed that inappropriate choice of representations was caused by misinterpretation of probability terminology. Concurring with Zahner and Corter (2010) the researcher found that learners made a multitude of errors if they constructed and used their own probability representations. Further, learners committed fewer errors where the task provided representations. Results also show that learners were most confident in using tree diagram representations even though they struggled to construct them from scratch. Most learners avoided Venn diagrams, outcome listings and matrix representations even though they would be the most useful in answering the questions. As a result many errors and misconceptions resulted when learners tried to use these representations. The study recommends that teachers take time to discuss probability terminology and the use of different representations with their learners. This promotes both the conceptual and procedural knowledge of probability. Also, to reduce learners’ errors and misconceptions on the topic, teachers need to scaffold the construction of representations by providing partially constructed representations and gradually encourage learners to construct their own probability representations