Abstract
Teacher learning through professional development is a complex process and is not yet well understood. Some features of professional development programs are known to be important, such as a focus on learner needs, design of and reflection on classroom artefacts, and the creation and sustaining of communities of support for teacher professional learning. In this paper, we describe the workings of such communities in a teacher professional development program, which focused on learner errors in a well-researched mathematical topic—the equal sign. Drawing on data from program sessions where teachers discussed their lesson designs and reflections on their teaching with each other, we develop the notions of challenge and solidarity as important in developing accountability conversations among teachers. We show how our program supported teachers to challenge each other and to build solidarity with each other and in so doing to develop accountability to each other and the profession, for their practices and their learning.
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Notes
In South Africa the word learner is used instead of student or pupil. We use these words interchangeably as appropriate in context.
When we use the terms “account” and “accounting” we use it as the verb of this form of accountability.
See Brodie et al. (2010) for a discussion of the second activity.
In choosing the concepts we used a number of criteria. First, the concepts should have leverage, that is, they should be central to the curriculum and should support teachers to work in a range of topics across the curriculum, and in all grades from grade 3–9. Second, the concepts should have well-researched errors that teachers are most likely not aware of. Third, the concepts should support teachers to make their tacit knowledge explicit and in so doing develop new ways of thinking about learner thinking and planning lessons to take account of learner errors. In sum, the concept should have the potential to develop teachers’ mathematical knowledge for teaching and illuminate the intersection between the two practices of mathematics and mathematics teaching.
In total 64 teachers have been involved in the project and 18 have left. Of these, 8 left after the first three months. The teachers are paid for the time spent in meetings.
At any one time there were 14 team-leaders in the project, one per group. Over the 3 years, 23 team leaders worked in the project and 8 have left.
For example in the test item analysis activity team-leaders were trained to keep a focus on the reasons underlying particular errors and in the video analysis activity they were trained to keep the focus on the teachers’ interaction with learner errors rather than focusing on where the learners had done well. Team leaders were also trained more generally to support patterns of constructive critique and rigorous inquiry by acknowledging and working with the strengths of teachers’ ideas and at the same time pushing teachers to move beyond their taken-for-granted assumptions and into uncharted territory.
In total there were 14 pre-lesson and 14 post-lesson presentations, one each for each small group. The teacher who taught the lessons presented the post-lesson presentation, while another member of the group (not the teacher) presented the pre-lesson presentation. Sometimes two group members presented together for support. The facilitators of the large group sessions were the project leaders, including the first author of this paper.
This point raises the question as to whether relational understandings replace, subsume or conflict with operational understandings. It may be the case that mature mathematicians work flexibly between operational and relational meanings, as the context requires, while learners may struggle to reconcile the two, creating conflicts between them (Seo and Ginsburg (2003)).
An analysis of their answers suggests that many were aware of the errors that learners with operational understandings make although they were not aware of the reasons for these errors. Some were not aware of the errors and were surprised to have discovered something new.
In this extract, K is the member of group 1, S is the presenting member of group 2 and F is the facilitator.
This move was planned for in group 1’s lesson plans and it formed the basis of challenge 1 to group 2 discussed above.
We remind the reader that in the post-lesson presentations, the teacher her/himself presented to the large group.
The teacher in the episode did not actually come back to the manholes in the episode above, however the point remains that the teacher in group 1 saw leading questions as useful because they take the teacher and learner back to previously shared knowledge.
In a set of interviews following the presentations, teachers struggled to distinguish leading questions from probing questions but in subsequent sessions and interviews they articulated the differences clearly in a number of ways.
We remind the reader that the group had changed this task after a challenge from group 1 in the pre-lesson presentation.
Grade 7 is in primary school in South Africa.
T is the teacher who taught the lesson and S and M are two teachers from the large group.
L, N and A are teachers from other groups.
An important feature of the small-large group structure was the presence of cross-grade groups. Having teachers from different grades in the larger discussions added to the possibilities for new ways of thinking. Having primary school and high school teachers together in the same group, was particularly useful. It mitigated against a “blame the primary school teacher” approach, often seen when high school teachers discuss learner errors. More importantly, the primary school teachers appreciated the insight into what high school teachers expect learners to know, and the high school teachers came to see why concepts are taught in particular ways in primary school and how they need to work in relation to what learners know.
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Brodie, K., Shalem, Y. Accountability conversations: mathematics teachers’ learning through challenge and solidarity. J Math Teacher Educ 14, 419–439 (2011). https://doi.org/10.1007/s10857-011-9178-8
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DOI: https://doi.org/10.1007/s10857-011-9178-8