Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom

Abstract

This qualitative case study examined similarities and differences between circle geometric proof development tasks set up in the Malawian Grade 11 mathematics textbook, and those that are set up and implemented by teachers in the classroom. Data generation included analysing the content of circle geometry proof tasks from the mathematics textbook and video recordings of geometric proof development lessons taught by three teachers. The Mathematics Discourse in Instructional Framework for Textbook analysis (MDITx) by Ronda and Adler and the framework for analysing the level of cognitive demands of mathematical tasks by Smith and Stein were used to identify and analyse the mathematical tasks as set up by the textbook and as set up and implemented by three Malawian secondary school mathematics teachers in the classroom. The findings revealed that the textbook presented the geometric proof development tasks at a high level as they included both empirical exploration tasks and formal proof tasks. Despite this task setup in the textbook, only one teacher involved the learners in empirical exploration tasks and maintained the high cognitive level of the tasks during instruction. The other two teachers only presented the formal proof tasks. Although the formal proof tasks that were set up by the two teachers were of a high cognitive level, the procedures that were used during task implementation resulted in reduction of the cognitive level of the proof tasks. I therefore conclude that teachers’ ability to set up and implement high cognitive level tasks that promote learners’ understanding and discovery of deductive geometric proofs depends not only on the availability of a good quality textbook, but also on the teacher’s conceptual ability to make effective use of textbook content.