Teaching one thing at a time or several things together? – teachers changing their way of handling the object of learning by being engaged in a theory-based professional learning community in mathematics and science

Abstract

Twelve lower secondary schoolteachers in mathematics and science were asked to teach a topic of their choice during a lesson that was video-recorded. We were able to analyse 10 of the cases and we found that all of them were similar in one respect: concepts and principles were introduced one at a time, each one followed by examples of the concept or principle in question, apparently to highlight its essential meaning. All the teachers participated in three modified lesson studies with three cycles in four different groups during three semesters. The modified lesson studies were built on a theoretical idea supported by a large number of recent studies. The theory states that new meanings (of concepts and principles, for instance) are learned through engaging with instances of contrasting concepts and principles. The core idea is that new meanings derive from differences, not from sameness. After the three modified lesson studies, the teachers were asked to once again teach the same topic as in the recorded lessons before the lesson studies. The new lessons were also recorded and the analysis showed that there was one thing in common in all cases: all of the 10 teachers dealt with the relevant concepts and principles in relation to each other (i.e. simultaneously) and not one at a time. By thus bringing out the differences between them, their meaning was made possible to grasp for the students. The study lends support to the conjecture that the modified lesson study is a powerful tool for enabling teachers to structure the content of their teaching in accordance with a principle that is more powerful in making learning possible, even if this contradicts their taken-for-granted practice.

Keywords:

• Teacher learning
• learning study
• variation theory
• mathematics and science
• professional learning communities (PLC)

Acknowledgements

We thank the anonymous reviewers whose feedback has contributed to a stronger article.

Notes

1. For details about the LS cycle see e.g. Lo, 2012.

2. For more details on patterns of variation, see Marton, 2015, p. 53.

3. The balance method implies that you do the same operations on both sides of the equal sign in order to get x.