Roughly ten years ago, I was taking one of my first courses as a graduate student — a survey course in the learning sciences. Each week, the readings centered on a particular topic in one of the several realms of learning. One class I remember in particular focused on issues of teacher knowledge.1 The unifying question of the readings was, What kinds of knowledge do teachers need to be effective?
We began the discussion by considering a less precise, but more tractable question: What are some qualities that you think helps make someone a good teacher?2 Some answers my classmates and I offered were more technical: a strong background in the subject, a repertoire of effective classroom management strategies. Others were highly affective or emotional: kind and caring, a good listener, slow to frustration.
The suggestion I remember most clearly, though, is this one: A good teacher makes skillful use of examples.
This was mentioned in at least one of the course readings (Shulman, 1986), so it really shouldn’t have felt new, but it did.3 Over the next few years, I occasionally pondered why that particular response struck me as so interesting and memorable. I eventually landed on three reasons:
- It rang true for me. Some of the teachers I liked the best in high school, for example, were particularly good at providing and contrasting examples to communicate ideas.
- It applied specifically to teaching in a way that many other suggestions did not. Being an attentive listener, for example, probably makes one better at a lot of things. Skillful use of examples seems less widely applicable.
Since then, I have become interested in capturing bits of knowledge and specific skills that satisfied these criteria. Sometimes, I come across them in literature I’m reading, but the really interesting ones are those that come to my attention suddenly and at unexpected moments. I had such an experience this week.
As I answered comments on my last post, which attempts to define the core features of a curriculum, was struck again and again at how slippery those features seem to be. As soon as I dismissed something as non-essential, I would come up with a reason it might be important or how it connects to something else important, and even though I did write about four things I do think are essential, I’m still struggling to unpack what they really mean and how they might be built into a digital curriculum. I thought to myself that what I am trying to create, in essence, is a model of a curriculum — something that captures what’s relevant and strips away what isn’t.
And then I had this thought: This is what mathematical modeling must be like for kids. This is why it is hard!
For me, creating a mathematical model of the sort expected from elementary school children is pretty simple. Picking out the mathematically salient features is straightforward. When I read a problem — again, the kind of problem that we might expect an elementary student to solve — those essential features are pretty easy to locate. To a 6-year-old, however, that problem could be just as murky and ill-defined as the concept of curriculum is for me. In that moment, I had a bit of empathy for kids learning how to model.
That’s how I came to what I think is another characteristic of good teachers: They are able to remember what it’s like to learn something for the first time. It fits all three of my criteria from above: It really struck me as true as it came to me, it’s more specific than a general notion of caring or relating to students, and it’s important for teaching, specifically.
One of the things I find most alarming about our political climate in the United States is the consistent devaluing or dismissal of education as an area of expertise. This isn’t new, but was brought newly to my attention when the U.S. Senate confirmed our current Secretary of Education, who neither possesses any experience with public education nor demonstrated knowledge of it in her confirmation hearing. From a professional and academic perspective, I find these “good teacher qualities” interesting and potentially useful in teacher education. But even setting that aside, I find them useful for explaining to people outside of an education field what expertise in education looks like and how it is different from expertise in the discipline being taught.
What do you think? Do these bits of educational expertise make sense to you? What else makes a good teacher? What makes a good administrator or curriculum coordinator? How can we communicate the value of educational expertise to those outside our field?
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
- In case anyone is interested, here is the reading list from that week of the course:
Shulman (1986) — See reference list above.
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C., & Loef, M. (1989). Using knowledge of children’s mathematical thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499-531.
Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653-689.
Leinhardt, G. (2001). Instructional explanations: A commonplace for teaching and location for contrast. In Handbook of Research on Teaching (4th edition, pp. 333-357). Washington, DC: American Educational Research Association.
- I am a wee bit worried that the tone of this post suggests that I consider myself in some hierarchical order above teachers — that I believe myself to be in a place that allows me to evaluate them and decide what makes them effective or ineffective. Please be assured that is not the case. As I hope you will see by the end of the post, I think teaching is one of the most difficult and highly undervalued professions in the world (or at least the U.S.), and my objective here is to help communicate why education expertise needs to be more highly valued.
- I did not know then, but I know now, that use of examples is also included in the Mathematical Knowledge for Teaching framework. See:
Ball, D. L., Thames, M. H., Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 39(5), 389-407.