Episode 38: Learning Math
In this final episode of our Core Learning podcast series, our guest Bruce Smith talks about how students at self-directed democratic schools learn math. Bruce has decades of experience as a staff member in self-directed education, and has worked at several different schools around the US. While at Alpine Valley School, he was the resident math teacher and he outlines how the language of numbers shows up in student’s daily lives and how classes, when they happen, are structured. You can listen to the rest of the Core Learning series here.
Also available on YouTube.
Listen to another interview with Bruce Smith on our show
Listen to the rest of the Core Learning series (Reading, Writing and Arithmetic)
Watch video interviews with students and staff at another democratic school all about how they learn math
Read an article about learning math from a sister school of ours in upstate New York
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Marc Gallivan: (00:00)
Hello and welcome to the Alpine Valley School podcast. I'm your host, Marc Gallivan. We are doing an episode of the show coming up that's all about your questions, so we need you to send us questions that you have - if you're a student involved in self-directed democratic education, if you're a parent, if you're somebody who's thought about it for a long time, if you're someone who works in this industry and has a particularly thorny question or issue you'd like us to try and unpack on the show, you are the perfect candidate. You can send us your questions to email@example.com. We'd also love voice memos if you want to record one and email it to that address. We're looking for anything you want to discuss with our graduates, other self-directed democratic schooling experts. Anyone who sends in a question will be entered into a drawing to win a copy of Jim Rietmulder's awesome book "When Kids Rule the School", so make sure you send in those questions right away and we will enter you to win a copy of that great book. This is the final episode of our core learning series which started with learning to read, continued with learning to write and this episode concludes with learning math. This is episode 38 of the show. You can find show notes for this episode at alpinevalleyschool.com/podcast/ep38 for episode 38, which also includes a full transcript of the episode and we are now including a full unedited version of the interview for those who want to listen to the whole thing. So, you can listen to the short version here, but if you go to the show notes page, there'll be an option to listen to the complete audio for this episode without any bits cut out. Before we get into the interview, I just want to do a little bit of quick housekeeping. The first thing is that we have a newsletter that we send out every week where we basically scour the Internet for the best resources in self-directed democratic education. We put those all together for you in a lovely email newsletter and send that out to your inbox every Wednesday. If you want to get on that, you can visit our alpinevalleyschool.com/newsletter and sign up to receive that. You can also view past editions of the newsletter on that website. We are on social media basically everywhere you can go. Uh, if you look for Alpine Valley School, you'll find our page. We're pretty heavy users of Facebook and Instagram in particular so you can definitely find us there if you want to see what we're also sharing on those channels. We also have a meet and greet event coming up soon. That is an opportunity for kind of an informal gathering with current families and graduates and some new faces as well to just get together and spend some time talking. You can RSVP on our Facebook page for that event and there will always be events posted there as well. If you somehow missed this one, you can always come to a future open house. We do all kinds of events all throughout the year, so keep an eye on that Facebook page to stay up to date.
My interview today is with Bruce Smith, who is someone that if you are in the self-directed democratic education sphere, you've certainly heard of, you probably have even met him. He may have come to your school to consult for you. He's got decades of experience in this style of education, has worked at several different schools. He's been on our podcast before so you can find the link to that episode in the show notes. And when I was a student at Alpine Valley School, Bruce was our resident math teacher. So I couldn't think of anyone better to ask about how math unfolds at schools like ours. So I asked him a few questions about how students learn math and this is what he had to say.
Bruce Smith: (03:59)
My name is Bruce Smith. I first started staffing at separate schools in 1997. Uh, came on board at Alpine Valley School for the first time in 1998 and with the exception of a couple of years where I had to work a different job. I've been working at Sudbury schools ever since. So I think four different Sudbury schools, maybe including the one that I helped start in the Chicago area. And currently I work at Clearview Sudbury School in Austin, Texas.
Marc Gallivan: (04:26)
How does math show up in the lives of students at self directed Democratic Schools?
Bruce Smith: (04:32)
Well I'm not sure that I see it taking on a different role necessarily than any number of other skills or things that people might learn. You know that the part of the philosophy of the Sudbury model is that if something is truly basic to success in actual life, then the schools as scaled down models of the real world will inevitably present situations where students run into the need for those skills in a way that's meaningful and, and relevant and something that they want. So in terms of math, the one one of the uniqueness, one of the unique aspects I think of math is that that was, especially at Alpine Valley, the subject that I had the most requests for actual instruction. Um, typically people learn during the day and with math it can be anything from cooking to money to managing their time. In terms of the day to day learning without necessarily even being aware that you're learning something like, like numbers and arithmetic and how to do all that. Um, but math did get the most requests as far as I know for instruction. And the way I explained that to myself or, or my best guess at the time was that it was maybe roughly analogous to when someone seeks out a personal trainer, uh, you know they sign up for a gym membership and they say, all right, here's this thing that I need to get better at. And I just know, I know myself, I know this thing. I'm much less likely to do it unless I get someone to coach me through it. And someone who, where there's a little accountability if I don't show up or if I slack off or whatever. Um, or maybe that it's just for those particular people, it's not simply that they needed someone to nudge them a bit, but that it just wasn't as obvious or implicit in the day to day situations they were encountering. So for whatever reason, I that that did seem to be the most popular request and, but otherwise it was just in many ways it just seemed like one more interesting, useful aspect of the environment for them to explore.
Marc Gallivan: (06:47)
What did the math classes that you taught look like?
Bruce Smith: (06:50)
Well, it could be all kinds of different things. Um, I had, I had one math class, probably the longest running math class was with three girls who were, I'm not sure how they, how old they were at the time, but the class probably went on for three or maybe even four years. Um, so they were probably 11 to 14 ish during that time. And so that was one where it was through three friends who just showed up and they wanted to learn math together and they stayed with it for awhile. Uh, there was an older student who wanted to learn Algebra and then she went on to do sat math prep with me. That was one on one. And, and then there was, I what I'm pretty sure at the time, we call it the many people math class. Um, and it was huge. It must have been eight or nine people, which it's qualifies as huge in terms of my Sudbury teaching experience, formal class teaching experience. Um, and that was kinda crazy actually because they were all doing arithmetic more or less. But I would have pages and pages of worksheets and problems and I would be like this human pinball bouncing back and forth between them. I might start out the class with one five minute lesson. Okay, here's this one type of problem. Here is one way to do it. I will work with each of you individually to make sure that it makes sense for you. Um, but then most of the class time I was just going back and forth and, and working on x specific problems with specific people and trying to basically find the one way that was going to connect, uh, because this is a very common dynamic with me and teaching math in a Sudbury environment is that instead of saying, this is how, this is the way I'm going to teach it, this is, I have, I have studied this. I know this is the best way to teach this particular concept. It was more like I would, I did, we'd look at the type of problem and I would say, okay, here's one possible way of approaching this and it doesn't make sense to you. That's fine. We'll go on to number two. If number two doesn't work, that's fine. It's not a reflection on you. It's more a matter of trying to find what's going to connect with that particular person at that particular moment or stage in their learning. And so eventually more often than not, we would hit upon some way of making it make sense to them. Um, but in terms of what it looks like, yeah, if it was more than three or four people, that was pretty rare. So it's very highly individualized and the highly customized and more about it. Maybe it's the difference between buying a suit off the rack and getting one that that's, um, finely tailored and customized to fit you.
That's kind of how it worked. I, I also wanted to include my favorite math teaching story, which you may have heard, um, a number of times. So I ask for your indulgence on that. It's just, it's just so cool. So the three girls who took the class for three years at a time, um, they, they not only did they always show up, but they tended to be the ones getting me for class. I would be busy with some other administrative thing or what have you. And they would say, Bruce, it's time for class. You're late, come on. And I would show up for class. Well, one day I was, I showed up on time without prompting and they weren't there, which was pretty unusual. I thought, well, I'll, I'll wait for a few minutes because my standing agreement with teaching was that a teaching a Sudbury class was that I will show up on time if you don't show up, I've got other things to do, you know, and if you continue not showing up, we'll maybe need to talk about that. But, so I waited for a few minutes and then they continued to not be there. So I went looking for them. And you know the reason why these three girls missed math class was that maybe 15 or 20 minutes longer than that, I don't know, before class they started working on the material. So they were doing that by themselves and in another part of the school and they lost track of time. So they missed math class because they were working on math and forgot that there was this class that they needed to go to with it.
Marc Gallivan: (11:00)
So what about students who never take a single formal class during their time at the school? How do they learn the language of numbers and incorporate it into their lives?
Bruce Smith: (11:15)
Well, I think one word that you just used jumped out to me and I think is key and that's language. And I would even stress that in the classes I teach that math is a language, it's a tool. It's a way of accessing the world around you. And as for how people who never took a class would access it. I, you know, I think the fact that the schools are run democratically and that part of that includes spending the school's money, as I was saying before, anything that has to do with math in your personal, um, day to day existence, you may not even know that you learning it. So I think it's actually, there's another element to it as well, I would say, which is that depending on how old a student is when they enroll at a Sudbury school and what their history is with formal instruction or math or what have you, I think that there's a lot less reason for them to develop math anxiety, uh, at Alpine Valley or, or other Sudbury schools because they're not, you know, they don't have a teacher sending up in front of them. Not to pick on even a, like a hypothetical straw man teacher here. But I think that it's very easy for people who are good at something to try to explain it to someone else and say, oh, this is simple. This is easy. Like, maybe, maybe that's the last thing that someone who's struggling with it needs to know. So I think that a, in addition to immersing them in a real world, real world environment where quantitative reasoning is just embedded in, in life, I think also that we avoid missing things up and making them seem even more difficult. I think the fact that that kids can grow up at a Sudbury school and not lose their zest for learning and not lose their confidence and just regard math or any other thing that might be difficult and might be notorious just regard it as one more interesting thing to learn. One more game to solve, one more puzzle. Um, I think that with that kind of confidence in themselves and that that removal of additive anxiety about things that might be difficult, that for example, if someone goes out into the world without having taken a math class and they get into a job where they have to learn how to manipulate spreadsheets or do things, statistics, they just, they know how to fill the gaps. They know how to fill the gaps in their learning and they're not afraid to fill the gaps and, and they're confident in their own ability to master things that are completely unusual to them. So I was, uh, I was rereading this blog post that I wrote about math and Sudbury and that reminded me of this other time when this, this I think is a good illustration of how random how or how it randomly instruction can happen. So somebody in some conversation I have, I don't even have any idea how the conversation came up, but they were asking a question about binary numbers and you know, like one zero one zero and all that. And I thought, well Gosh, I don't, I can't answer that as well as I would like. And the student and I just sat down and for the next, I don't know, 30 45 minutes longer than that. We looked things up, we worked out possible problems on the chalkboard and I don't know how much of that stuck with her or if that led to anything useful, but it was just, it was extremely, it was just fun. It was this random thing that randomly came up and I guess that that was math class for that 30 or 45 minute period. Um, and it was, and it was so, it was driven by curiosity and it was permitted by the freedom of the school where I could take the time and she could take the time because we had this mutual interest, we just pursued it together. It was over quickly and we dropped it and we moved on. So I think that's an example of, I think that's a good example of how it, it's not necessarily a formal class situation where we schedule it in advance and there's a curriculum and it goes on for a certain period of time. You can have just random bursts and moments of math learning and math instruction and it's fun and it's not necessarily, it's not a headache for anyone and who knows what use most it has down the road. But I think you can ask what usefulness, any sort of instruction we'll have down the road. I just love that at our schools, this kind of enjoyable, spontaneous, mutually interest driven learning as possible.
Marc Gallivan: (15:53)
Thanks so much to Bruce for coming on the show and talking to us about how students learn math. You can listen to the rest of the core learning series, which includes reading, writing, and arithmetic at alpinevalleyschool.com/podcast. This is episode 38 of the Alpine Valley School podcast. You can find show notes for this episode at alpinevalleyschool.com/podcast/ep38 for episode 38 which includes a full transcript of the episode, a link to the other interview we did with Bruce in the past and a full unedited version of the audio from the episode. Just one final reminder about our question and answer episode that we're going to be doing coming up. If you email us your questions or voice memos to firstname.lastname@example.org your question may be featured on that episode and anyone who sends in a question will be entered to win a copy of Jim Rietmulder's wonderful book "When Kids Rule the School". Thanks so much. I'm Marc Gallivan, this is the Alpine Valley School podcast, and we'll be back again soon with more stories of real learning for real life.