Sensitivity to Student Learning: A Possible Way to Enhance Teachers’ and Students’ Learning?

Abstract

To calculate with negative numbers seems to be one of the hardest topics in mathematics courses for 13–14 year old students to learn. Our experience is that this very often is taught by ‘telling the rules,’ and even adults when given a task like ‘ - 3 - (-5) =’ try to remember some kind of ‘trick’ to solve the problem. How could this be taught for understanding? What is necessary to be aware of in order to understand? What is critical for learning this? Questions like these were addressed by a group of teachers who collaboratively used a systematic approach to investigate what it takes to learn to subtract negative numbers in grade seven and eight in a Swedish compulsory school. In this approach, student learning and their understanding of that which was taught was the main concern and in the forefront of the teachers’ attention. In an iterative process of planning, observing and revising a single lesson, they in depth analysed and inquired the progress of student learning before, in and after the lesson. In this process the teachers tried to learn about the particular difficulties their students had for learning what was intended. This was done from an analysis of students’ written tests and from a close observation of video recorded lessons. In this observation, they tried to understand students’ learning outcomes in the light of how the content taught was handled in the lessons. Through the process they gained some insights from which they successively could change their teaching in a way that had an effect on students’ learning. We also demonstrate how reflection on teaching and the learning from teaching can take its point of departure from sensitivity to students’ understanding and perceptions of that which is to be learnt.