Triangles, STEM and Embodied Knowledge
Categories: Fellow Alumni: Dan Lyles
Tags: Dan Lyles, math, seventh grade
When I sit in on the classrooms at a local middle school during math courses in the seventh grade, I’m always struck by how simultaneously useful, and not expressed as useful most given subjects are. For example, the class has been looking at the Pythagorean Theorem for a few weeks now and for many of the students, it is as perplexing and foreign of a concept today as it was the first day they began using it. Part of the difficulty is the normal way that mastery of a concept requires hours of work and practice to gain competency with the idea, but part of the problem comes down to an ability to transfer the knowledge mastered in one area to another application that, while not functionally different, is dissimilar enough for the students to sense the relationship between the two things. This has the effect of making mathematics appear mysterious or for many kids, an activity that separates the ‘smart’ children from everyone else. I started to sense that there was much more going on with the way that triangles were taught than simply differing levels of competency.
In what way, I began to ask, is the ability to make sense of the appropriateness of a thinking tool obvious based on how it is communicated? I think this is an ongoing tension that we as people talking about situated knowledge have to consider and work with. Much of what I see to be the problem is the way in which the functioning of much of math education is meant to impart tacit knowledge to students who are expecting information to be presented to them in a much more explicit format. I think that is where we step in as STS scholars to raise important points about making the tacit explicit, both to the student who requires the ability to pass the immediate course requirements as well as to the teachers who are increasingly put under pressure by an institutional framework that seeks to couple test derived measures of success with their own economic survival. If we are to take the transformation of STEM pedagogy seriously, this is the space that we are forced to operate in- one where stepwise and gradual change is the order of the day.
The most interesting intervention I found was to approach the problem from the perspective that if the knowledge that we’re seeking is tacit, they it might be useful to approach those topics in a lived experience that the student can enact and thus have one of many useful ways of reminding themselves of the knowledge that they already know. In the case of triangles, I drew out a city grid and told the students that what I was trying to do was figure out how far away my friend lived in the city of Albany. Since I didn’t have a measuring tape that went across buildings, streets and parks, I had to estimate, but that I could count six blocks one direction and then another 4 blocks perpendicular to it in order to form the legs of a triangle. Using some estimation (4 blocks squared + 6 blocks squared equals the number of blocks away my friend lives squared) and some average block lengths, I hope to have provided a mental tool in order to attach the idea of the theorem to a lived experience that the kids can enact without needing to be prompted by a particular diagram or unfamiliar example. The flagpole, shadow triangle that seems ubiquitous in this situation comes to mind.
What STS is useful for in this case is suggesting that this intervention should be more successful because what we are relying on is wedding of cultural practice, in this case part of that is living in an urban environment, with the math concepts that we seek to teach. This application of ethnomathmatics on a small scale is a useful orienting tool to the fact that education happens in cultural contexts and that much can be gained for utilized an awareness of the way that learning happens through these repeated and embodied actions. However, ethnomathmatics is not a magic panacea that will solve all problems. With it comes the problematic notion of essentialization that we will have to address whenever we raise the issue of the culture of mathematics in a space that may have advanced the ‘culture of no culture’ in terms of math’s universalist use. In the case of measuring cities by blocks and triangles, the point at which this is no longer universal is hard to spot, but to say that we would not be able to talk about triangles as a tool for measuring distance without the city’s grid has a certain appeal. There might even be space for instilling a sense of empowerment in the student by suggesting that what we are teaching is not merely a cryptic system of signs that has no apparent use, but a system that is directly related to their everyday experience.
To take this further, we might begin by asking a series of questions related to the way embodiment comes into the teaching of STEM subjects. What are the embodied skills that are implied by the way we currently go about talking about STEM subjects to middle school students? It would seem that much of the education is around obvious skills that apply to adults, but what use does a seventh grader have for knowing the area of a circle if they do not have a concrete activity to attach that to? In a world were teachers have some discretion over the examples and activities that are used to communicate these concepts, I see some play in terms of getting alternate examples instituted. The larger question is that if this works, what next? Perhaps it would require setting up STEM curricula very different if it meant that any attempts at national standards would have to take into account that the related activities and examples that teachers would need to pull from would relate closely to their localities. Would that knowledge transfer across to new areas when the students grew up and chose to move? What would have to happen in order to give schools the kinds of autonomy to make radical changes in terms of the way that embodied skills were taught and related to the pedagogy?
In the meantime, there are plenty of students at poorly funded and largely written off schools who might benefit from an opportunity to develop new approaches, especially if they included the recognition that the development of this alternative STEM pedagogy might mean finding ways of getting the students out of the classroom an into the world (within reason, of course) to teach the embodied skill that would relate to the subject that they’re trying to teach. Maybe a STEM approach that focused on teaching gardening as a way to talk about cellular growth and wood working as a way of teaching measurement isn’t as far away as we might think.
