For the last 6 weeks I’ve been teaching a 6-hour face to face class on Saturdays to a group of pre-service teachers in an MAT program and in-service teachers getting advanced degrees. This has been brutal for everyone concerned, to say the least. I’ve had to pare down my expectations because after about 4 hours nobody can absorb much, no matter how many times I asked them to get out of their seats and try something different.
I decided to focus on Stigler & Hiebert’s The Teaching Gap, which is old news, but not to the students, so that they would be open to questioning their cultural assumptions about what it means to teach science and mathematics. My plan was this would allow them to be open to reform ideas, such as those embodied in the Tools 4 Teaching Science out of the University of Washington.
I think this pretty much worked. In our last class today I asked the students to make concept maps. I gave each person a page of stickers with 60 nouns culled from a variety of class readings:
- The biology people read The Beak of the Finch, which most hated because it is tedious in spots. The math people read either Jacqueline Leonard’s book on multicultural mathematics education or the Joy of X. The purpose was to increase content knowledge, which I think was modestly successful.
- Magdalene Lampert, “When the Problem is not the Question and the Solution is not the answer.” We used the theoretical framework of this article to think about what it means to do mathematics (and science).
- Hand et al., Negotiating Science. We used this to provide a framework for inquiry activities in science.
- 5 Practices for Orchestrating Productive Mathematics Discussions.
That was actually quite a lot of reading for 6 weeks. We only got through Chapter 7 of The Teaching Gap, since that is the point after which the authors mostly just repeat themselves.
I gave each student a giant Post-It and asked him or her to do a concept map using Novak and Gowin’s 1984 procedure and using their scoring scheme. http://www.flaguide.org/cat/conmap/conmapfig5.php
Several students struggled mightily with this format. More about struggling later.
Thinking about the maps in public
I wanted the maps to be public records of thinking, but didn’t want to put anyone on the spot. Therefore each map was displayed on the wall and was only identified with a number. We did a gallery walk during lunch; I asked students to record on index cards what they thought was interesting or new about each map, and what was similar to what they put.
I collected those cards, and a first glance through them shows they didn’t write much. However I still think it was an important focus to help them look at other people’s maps, since they were all quite different.
We then went around to each map and talked about what the students saw in it. The easiest entry point for the students was surface features, how it was organized. Several remarked on people having chosen different starting points for the map.
About halfway through, I started pointing out things that I saw, going back to the earlier maps and comparing. Students stopped contributing much, once they realized I was going to tell them “the right answer.” Of course it wasn’t, but I was trying to get certain ways of thinking on the table. I think they also were at a loss as to what to say. The holistic approach, looking at where the maps went, what concepts had lots of links and what seemed isolated, was new to them. In making a quick instructional decision, I considered briefly that going with a cognitive apprenticeship model, in which I shared my thinking with them, was probably going to be most productive.
This was such a rich discussion, I want to get down as much as I remember and it might be an overly long and boring blog post. But I do want to capture what happened while it is still fresh in my mind.
I was aware that a person got very upset when I pointed out how a particular map showed that this set of ideas was not integrated with the rest of the map. (Someone appearing to get upset or embarrassed actually happened more than once.) I infer that the persons who seemed upset were the authors of the map in question. I was very careful to say, “This person did…” In truth, I knew who authored only 3 of the 13 maps. Because we were pretty much anonymous, so they were not singled out in public. It is interesting to me that several students seemed to feel that their maps were private performances that should not be critiqued in public. I’m an artist accustomed to having my drawings and paintings critiqued by art professors. Critiques are always scary, but they are also very powerful because they give the entire group the benefit of the instructor’s thinking.
I think of Fred Erickson repeating several times in my own grad school classes, “School is the only place where people must publicly display incompetence.” In spite of my repeating often to my own students that the right answer is how you’re thinking, not the content of what you say, the social practices surrounding school being about the right answers is still the dominant cultural model. In spite of my never saying that one of the maps was wrong, some students still interpreted my remarks as showing them up as incompetent.
I ended class saying the maps made me feel really good, that it was formative assessment for me, I can see what people got out of the class, and I’m pleased. I was. Of course the students wanted to know how I was going to grade them. I said, I’m going to write each of you a letter about your map, and I want you to write me back. (Even though class meetings are over, there is still an assignment out there to do a unit plan. Class is officially over in May.)
specific items that interested me
One of the maps had a strand that included “disciplinary language,” that was cross-linked to “writing,” which was also cross-linked to disciplinary practices. There was another independent strand that included “discussion,” that was linked to “teacher,” and not linked to disciplinary language or practice. I didn’t say anything public about this observation; I thought it might seem too critical. I will write to the author about it. I also note that our pre-service teachers have the most difficulty with the section of EdTPA having to do with academic language. That this shows up in at least one map is confirmation to me of the power of concept mapping.
One of the students who was having a really hard time, had chosen “knowledge” for her topic and “teacher” and “student” for the next level. As I walked around, she asked me for help. She couldn’t figure out to where put any of the other labels, and she couldn’t think of what to write as links. I asked her to clarify, what did she define the link between teacher and knowledge to be, and what was the link between student and knowledge. She replied, The teacher has knowledge, and the student has some knowledge. Without saying anything, I thought, This is the traditional transmission model of teaching, slightly updated to include students’ prior knowledge. I replied to her that she might try different concepts instead of student and teacher, maybe that was the problem. She was able to successfully complete the map.
to be continued…