Today our microanalytic research group focused on videos of STEM education.
Watching STEM classes reminds me of a field trip a fellow researcher and I took to observe a physics class that used project based learning. Project based learning is a more hands on and collaborative teaching approach which is gaining popularity among physics educators as an alternative to traditional lecture. We observed an optics lab at a local university, and after the class we spoke about what we had observed. Whereas the other researcher had focused on the optics and math, I had been captivated by the awkwardness of the class. I had never envisioned the PJBL process to be such an awkward one!
The first video that we watched today involved a student interchangeably using the terms chart and graph and softening their use with the term “thing.” There was some debate among the researchers as to whether the student had known the answer but chosen to distance himself from the response or whether the student was hedging because he was uncertain. The teacher responded by telling the student not to talk about things, but rather to talk to her in math terms.
What does it mean to understand something in math? The math educators in the room made it clear that a lack of the correct terminology signaled that the student didn’t necessarily understand the subject matter. There was no way for the teacher to know whether the student knew the difference between a chart and a graph from their use of the terms. The conversation on our end was not about the conceptual competence that the student showed. He was at the board, working through the problem, and he had begun his interaction with a winding description of the process necessary (as he imagined it) to solve the problem. It was clear that he did understand the problem and the necessary steps to solve it on some level (whether correct or not), but that level of understanding was not one that mattered.
I was surprised at the degree to which the use of mathematical language was framed as a choice on the part of the student. The teacher asked the student to use mathematical language with her. One math educator in our group spoke about students “getting away with fudging answers.” One researcher said that the correct terms “must be used,” and another commented about the lack of correct terms as indication that the student did “not have a proper understanding” of the material. All of this talk seems to bely the underlying truth that the student chose to use inexact language for a reason (whether social or epistemic).
The next video we watched showed a math teacher working through a problem. I was really struck by her lack of enthusiasm. I noticed her sighs, her lack of engagement with the students even when directly addressing them, and her tone when reading the problem from the textbook. Despite her apparent lack of enthusiasm, her mood appeared considerably brighter when she finished working through the problem. I found this interesting, because physics teachers usually report that their favorite part of their job is watching the students’ “a-ha!” moments. Maybe the rewards of technical problem solving are a motivator for both students and teachers alike? But the process of technical problem solving itself is rarely as motivating.
All of this leads me to one particularly interesting question. How do people in STEM learning settings distance themselves from the material? What discursive tools do they use? Who uses these discursive tools? And does the use of these tools change over time? I wonder in particular whether discursive distancing, which often parallels female discursive patterns, is more common among females than males as they progress through their education? Is there any kind of quantitative correlate to the use of discursive distancing? Is it more common among people who believe that they aren’t good at STEM? Is discursive distancing less common among people who pursue STEM careers? Is there a correlation between distancing and test scores?
Awkwardness in STEM education is fertile ground for qualitative researchers. To what extent is the learning or solving process emphasized and to what extent is the answer valued above all else? How is mathematical language socialized? The process of solving technical problems is a messy and uncomfortable one. It rarely goes smoothly, and in fact challenges often lead to more challenges. The process of trying and failing or trying and learning is not a sexy or attractive one, and there is rampant concern that focusing on the process of learning robs students of the ability to demonstrate their knowledge in a way that matters to people who speak the traditional languages of math and science.
We spoke a little about the phenomena of connected math. It sounds to me very closely parallel to project based learning initiatives in physics. I was left wondering why such a similar teaching process could be valued as a teaching tool for all students in one field and relegated to a teaching tool for struggling students in another neighboring field. I wonder about the similarities and differences between the outcomes of these methods. Much of this may rest on politics, and I suspect that the politics are rooted in deeply held and less questioned beliefs about STEM education.
STEM education initiatives have grown quite a bit in recent years, and it’s clear that there is quite a bit of interesting research left to be done.
All of this talk seems to bely the underlying truth that the student chose to use inexact language for a reason (whether social or epistemic).
How is mathematical language socialized?
I think you answered your own question. The teacher frames the student’s linguistic choices as intentional because that’s the ideology to which the student is being socialized: doing math means choosing to be precise, linguistically as well as in other ways. Of course the student has reasons for being imprecise, but those reasons run counter to the program of socialization, so the teacher can’t validate them.
We don’t have enough data to know, but it’s possible the student is being imprecise for just this reason, as a display of resistance.
Daniel, would you talk about other language learning this way, too? In what other field could an inexact answer be seen as a potential act of rebellion? Where is the space for learning?
Well that’s why I said we’d need more data. But IMO it could be an act of rebellion in any field. If you’re socialized to an academic discipline, you’ve learned its register, so refusing to use the register is a way of taking an oppositional stance to the process of socialization itself – it indexes an outsider identity.
For example, this actually happened:
Me: Student, why are you not standing during the Pledge of Allegiance? If you’re making some kind of protest or political statement, I respect that and we can talk about it. But if you just can’t be bothered, that’s disrespectful and I’d ask you to stand next time.
Student: Yeah, politics thing.
The teacher was very controlling, and I could imagine that if he knew the answer but wanted to avoid being put in the good student box he may choose to express that through inexact language. BUT in this case he began his answer with a long winded response that was clearly off the target, and then he seemed to have trouble choosing between table or chart. Do you think that these were part of the same concerted rebellion?
I don’t think he was rebelling, actually – just saying that’s within the indexical field of imprecise language in math class. The difference between chart and graph is like the difference between expression and equation: it’s obvious once you know it, but not transparent to newcomers. You’re not explicitly told that there are two distinct types of graphical representation that go by different names. You’re supposed to figure it out on your own.
On the other hand I didn’t think his initial response was off target. Long winded, certainly, and also imprecise, but the teacher seemed to know what he meant by it, and on the third or fourth playback I could see it too. I was intrigued that she let his imprecision go at that point but wouldn’t let him get away with calling a chart a graph.
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