E. van Es, "A framework
for learning to notice student thinking," in Mathematics
teacher noticing: Seeing through teachers' eyes, edited by M. G. Sherin, V. R.
Jacobs, and R. A. Philipp (Routledge, New York, 2011), pp. 134-151.
What first struck me in this paper was vanEs’s idea that in
order to learn how to attend to students’ ideas, teachers needed to first “know
what counts for evidence for effective practice” (p 134). Van Es points out
that decisions about evidence are closely tied to a person’s theory of
learning. This struck me as a different way to think about the process of
teaching teachers to notice. It isn’t about teaching teachers to notice, but
about teaching teachers what to notice. Therefore, if a teacher’s theory of
learning is that students will learn whatever information they hear and take
in, then it makes sense to focus on whether the information was presented in a
coherent way and if the students were facing the teacher and listening quietly.
If a teacher’s theory of learning states that students will learn if they are
enjoying the activity and engaged in it, then it makes sense to pay attention
to whether the students appear to like the activity and be having fun. Yet, if
a teacher has a constructivist theory of learning then they will need to notice
the ideas a student is expressing and whether the instructional response
aligned with the student’s ideas and moved the student toward the scientific
idea.
Given this perspective, the purpose of the video club isn’t
to teach teachers to argue their ideas with evidence. The point is to teach
teachers what evidence to use to argue their point. For instance, during the
first video club meeting, the teachers were using evidence to argue their
point, but it wasn’t the kind of evidence that the facilitators felt
demonstrated learning as they understood it. I’m not sure that this means the
teachers thought engagement was sufficient for learning, though. I do think
these teachers’ valued using students’ ideas to help them learn; otherwise I
don’t think they would have been so willing to be directed toward that focus by
the facilitators. Instead I think these teachers had a disconnect between how
they thought students’ learned and to what they had trained themselves to pay
attention when teaching.
A second thing I really appreciated about this article was
the result shown in Table 9.2 and the accompanying analysis. As researchers I
think we expect learning to be linear, especially given the large grain-size of
this study. And while this data
definitely shows an upward trajectory (as represented by a downward slope, but
that’s another issue entirely), the middle of the data is nothing short of a
mess. To me, this “mess” is a great example of Vygotsky’s theory of learning.
Vygotsky thought that learners would try on and try out new ideas before they
fully caught on or committed to an idea. I think this is what is happening
here. This brings up the question, though, of what would have happened if the
video club had ended on week 8? And when we’re teaching how often are our
students tested during their “week 8” instead of on their “week 10”?
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