I don’t know how I feel about math

[Adam Ross]

We all do arithmetic constantly, even if we aren’t directly thinking about it. The same goes for Operant Conditioning. And we know how the operators work in arithmetic. Negative + Negative = Negative. Negative – Positive = Negative. Positive – Negative = Positive. Negative * Negative = Positive. Negative * Positive = Negative. But how do they work for operant conditioning?

This past week, I saw lots of examples of Behavioral Reinforcement. I was working with a student who has had a recent history of missing classes, and whose teachers are worried is falling behind. In our discussion in class, we talked about how teachers creating a welcoming environment for students in situations much like this one is so important. In Skinnerian terms, the stimulus in this scenario was the teacher holding class, and every operant has the choice to respond by either attending class or skipping. I don’t know this operant’s exact situation, but let’s say they choose to come to class three quarters of the time it is held. Before report cards come out, there is barely any reinforcement of not coming to class, at worst only the positive punishment of a shameful phone call home. In this scenario, the student was absent from Bio class while his classmates were taking data for a lab. The teacher gave him a lab handout with all of the work he needed to do marked for him, a set of fake data in all of the data tables, and sent him to the academic skills center to get working. I helped him finish his lab, and he needed a review of some of the material but was able to answer most of the questions. I could see a naïve teacher thinking, This student needs to understand that truancy is not okay. I’m going to show them this with positive punishment. If this student is absent during lab day, then he will not have data to answer questions with, so it’s up to him to make up for it by asking for data from his friends, which creates more work for him and is inherently shameful. He needs to pass this class, so I will create more work for him to do in order to pass and this will be a suitable punishment. But this teacher would be totally misusing Skinner’s principles! Unless the teacher sends these materials home, this punishment could only be delivered on the days that the student comes to class, therefore the teacher would be punishing the good behavior of coming to class. This would lead to the extinction of this behavior, the student would stop coming to class. This outcome would be disastrous because aside from preventing him from learning biology, it would have a profound negative impact on the student’s faith in the school system. But the student I worked with had a much better teacher. Instead of leaving him on his own to make up for not having data, they filled in a data table for him, and tried to make it easier for him to make up the work he was missing by sending him to me. This is an example of a negative reinforcement of his coming to class, negative because workload was taken away from him.

In contrast, I had the misfortune of watching the Premack principle be completely misused on a different student. This student loves to talk about video games, I am positive that talking about video games is his highest probability behavior. By listening to this student, this tutor was providing a positive reinforcement for the behavior of putting off work to talk about video games. I could tell that the student enjoyed this reinforcer. Based on past experiences with this student, I can take an informed guess that he was putting off schoolwork that he doesn’t have much intention to put effort into. I think this should be met with some type of punishment; the Academic Support Center is not a space to “hang out” in, even though taking a break is accepted.

I suspect that the tutor was just trying to connect with the student and form a relationship. I think there is a basis for this in Bandura’s theories. On page 356 of the reading for Thursday in Learning and Instruction, it is written “Models that have an impact may appear to be prestigious, appear to deserve trust, portray consensus in a group, offer believable standards to guide others’ aspirations, or provide realistic reference figures for observer comparison” which seems to be the basis for the culture of bonding with students that the ASC promotes. On the surface, this seems like a point of contention between Operant Conditioning and Social Learning, but I don’t fully buy that because I don’t think this is an effective way to promote social learning. One criticism I have of this particular tutor is that he tries too hard to connect with students like a friend would, maybe putting too much emphasis in the “realistic reference figures” part. He might think that when he listens to a student talk about video games, that student will relate to him and this will make him a realistic reference figure. I interpret the reading to mean that ALL of those things must be present to make someone an effective model, not just one of them, and someone who lets you talk their ear off about video games isn’t someone who is prestigious or offers standards of any kind. I think this is a part of social learning that it is easy to misuse, and I’ve seen lots of teachers do this before.

I saw some cognitive approaches to tutoring that I thought were better. I saw vicarious reinforcement when a student told me that the studying we did together prepared him for his chemistry test, and he was happy about the grade he received on it. Students looking at him would see that success is possible and you don’t have to be a typical straight-A student to achieve it. I saw a student studying for her biology test through the rehearsal of labeling the different sections of a leaf.

I would say I am a cognitivist at heart, behaviorism seems to reduce humans absorbing knowledge to the level of other animals learning simple tasks. I think intellectual learning is different from reproduction of tasks, because everyone has different internal streams of consciousness that influence what they will think of different things. Cognitivism is like the General Relativity to Behaviorism’s Time-is-Time, even though they both seem to work, Cognitivism offers a more robust way to analyze processes of learning.

Something new I observed this week was students telling me about their home lifestyles. Having grown up in an east-coast suburb, I was excited to come to Northfield and meet people that live on farms. I realized that teenagers around the country are pretty similar, and the ones I talk to at NHS would still fit in pretty well in my high school. But I was pleased to find out that one of my students is from Waterford! I’ve seen it on the map a lot, but I’ve always been curious what it would be like to live in such a tiny… Municipality. Waterford has Rt 3 on the west, someone’s massive woodlot on the north, and the Railroad and the Cannon River on the hypotenuse, with only a plumbing company and one full block of suburban-looking (from google maps) houses. I have been curious since I got to Carleton what Waterford is like. This student told me about how there is a funny looking sign on the plumbing company, and it’s too far to walk anywhere, but she still feels like it’s close to the Greenvale neighborhood, which is about halfway from Waterford to the high school. I didn’t want to seem judgemental or nosey, so all I said was “that’s awesome! I’ve always been curious about Waterford because it’s so close to Carleton but I’ve never been there” so I didn’t ask about anything. I wonder if she told me “it’s close to Greenvale” because she wanted to believe it in order to fit in more with the rest of Northfield.

I don’t know about the arithmetic of reinforcers with operant conditioning, and how the analogues for arithmetic operators would work. My instinct is that maybe the reinforcement and the behavior are orthogonal bases, if that makes any sense. Maybe I should be a math or philosophy major instead of a physics major?

[Kara Sun]

Hi Adam,

I really enjoyed reading your post! Your observations about behavior  reinforcement and punishment in your tutoring location are really interesting. I especially appreciated your discussion of the tutor who was allowing their student to avoid work by talking about video games. I like that you acknowledged the tendency to do this in order to bond with the student, but also made the point that you need to find a balance between being liked and also being an adult that can guide the student to finish their work well and learn from it. This is a balance that I also find can be tricky to find. I also enjoy your philosophical musings and your interest in Waterford. You might be destined to be a math teacher! You seem to easily incorporate math into the world around you and that’s a really important part of making math feel applicable to real life that I often found was lacking in my own mathematic education. Thanks for sharing!

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