Mathematics

Learning on three levels
In the knowledge synthesis of PLC, made by the National Commission on
Teaching & America’s Future in 2010, it is said that “few studies can on a
rigorous ground support student learning outcomes related to teachers
engagement in PLC, but the trend is positive”. It might not be possible to
directly related changes in learning outcomes that are robust, in the sense of
statistical significance, to teachers’ participation in PLC. However, evaluation
of a number of Learning studies in Hong Kong indicates progress in student as
well as teacher learning (Cheng & Lo 2013)
After evaluating the effect of teacher learning, National Commission on
Teaching & America’s Future points to effects important for teachers’
professional growth:
Participation in PLCs can successfully engage teachers in discussion about
content knowledge or knowledge about how to teach it (pedagogical content
knowledge or PCK), positively impacting their understanding of or
preparedness to teach content, or attitudes toward teaching methods.
Participation in PLCs increased teachers’ deliberation about students’
mathematics or science thinking.” (p. 8)
These are findings similar to what has been identified from studying teachers
participating in Learning study, but specified by Cheng and Lo (ibid.) in that it
concerns a common language to talk about teaching and learning, knowledge
about the object of learning and how to teach it in a way that can promote
learning:
Throughout the project, the teachers learned and used a common language -
the jargon of variation theory - to talk about teaching and learning, referring to
the object of learning (OL), critical features (CF), variation in students’
understanding of the OL, variation in teachers’ ways of dealing with the OL
(V2), and using variation as a guiding principle of pedagogical design (V3).
They learned to negotiate patterns of variation, to help students to discern
critical features and together planned teaching activities that could best allow
students to experience the variation patterns themselves. In doing this, they
had to draw on their own experience and knowledge of teaching. (p. 20)
Our suggestion is that by the theory based inquiry, thus that there is an explicit
theoretical framework involved in the process, adds values to Learning study.
Learning after Learning study?
So far, I have suggested what teachers can learn when they are involved in
Learning study, but what happens outside and after participating in Learning
study? Does the participation have any influence on what teachers do outside
Learning study? In a current study we explore the long term effects of Learning
study (Kullberg,et al., under revision). Before participating in three Learning
studies, 12 mathematics and science teachers were asked to teach one lesson
free of choice. One and a half year later they were asked to teach the same
lesson again. That is, they taught the same topic. However this topic was
297