Tasks used in mathematics classrooms

Abstract

The current mathematics curriculum in South Africa require that learners are provided with opportunities to develop abilities to be methodical, to generalise, to make conjectures and try to justify and prove their conjectures. These objectives call for the use of teaching strategies and tasks that support learners’ participation in the development of mathematical thinking and reasoning. This means that teachers have to be cautious when selecting tasks and deciding on teaching strategies for their classes. Tasks differ in their cognitive and difficulty levels and opportunities they afford for learner to learn mathematics competently. The levels of tasks selected by the teachers; the kinds of questions asked by the teachers during the implementation of the selected tasks and how the questions asked by the teachers and the teachers’ actions at implementations affected the levels of the tasks were the focus of this research report. The study was carried out in one high poverty high school in South Africa. Two teachers were observed teaching and each teacher taught their allocated grades. One teacher was observed teaching Grade 9s while the other taught Grade 11s. Both teacher taught number patterns at the time their lessons were observed. The research was qualitative. Methods of data collection and instruments included lesson observations; collection of tasks used in the observed classes, audio-taping and field notes. Pictures of the teachers’ work and copies of learners’ workbooks also provided some data. The analysis of data shows that the teachers not only selected and used lower-level cognitive demand and ‘easy’ tasks, that did not support mathematical thinking, but also did not lift up the levels and/or maintain the ‘difficulty levels’ of the task at implementation. Teachers were unable to initiate class discussions. Their teaching focused on ‘drill and practice’ learning and teaching practices.