Middle and High School … from a Montessori Point of View
The most productive place to work varies for each student. Some need more rigorous structure–chair and desk; pen and paper–while others can get a lot done while lying in front of the fire. A key here, I think, is that the students have enough space. They’re working on different projects and they don’t need to collaborate, so a meter separation (the same distance they’re required to be apart during personal reflection time) gives everyone space to do their own thing.
My high-school biology class is taking their exam on genetics and evolution. To make the test a little more interesting, and to point out that there may be some relevance for this knowledge in the future, I made the test a questionnaire for the new head of the Mars Colonization Project. It begins like this:
Friday, January 30th, 2054.
Dear Dr. ________________ (insert your name here):
We are excited that you have accepted our offer to head the Biomedical Division of the MCP. As we are engaged in the first ever effort to colonize another planet, we know that we will face many unique challenges. Your expertise in pluripotent stem cell research and oncology will be extremely valuable to us — even though some of us administrators still don’t know what pluripotent stem cells are.
Please fill out the questions in this document to help us with our planning for the colony and to help our Human Resources department assemble your research and medical team.
Because of the sensitivity of some of the personal information included in this document, please write out, and sign, the Honor Code below before turning the page.
Yours truly,
Board of Administrators,
Martian Colonization Project
Then I pose all of the questions in this context. For example, to get their knowledge of vocabulary I ask them to define the scientific words and phrases (which they’ve used in their scientific publications many, many times), in terms that laymen — like the people on the board of administrators — could understand.
To get at more complex concepts, like the molecular process of gene expression and regulation, I phrased the question like this:
Medical Issues Related to Ongoing Colonization Planning
The trip to Mars will take five years, so we will be placing most of the colonists into cryogenic sleep for most of that time. We are still working out some of the bugs in the cryogenic technology, and we need your help.
To put people into cryogenic sleep, we need to stop their digestion of carbohydrates. Your predecessor, Dr. Malign, told us that we could do this using RNA interference, by injecting them with engineered microRNA that would block the production of the enzyme amalyse.
Could you draw a diagram of a cell showing how proteins are expressed from DNA, and how microRNA would interfere with protein production. Are there other methods for preventing protein expression?
We’ll see how the students do on the test, however at least one student glanced at the front page and said, “This is kinda cool,” (actually, she first asked if I’d stolen the idea from the internet somewhere), which is significant praise coming from a teenager.
My biology students are doing an exercise in genetics and heredity that requires them to combine the genes of two parents to see what their offspring might look like. They do the procedure twice — to create two kids — so they can see how the same parents can produce children who look similar but have distinct differences. To actually see what the kids look like, the students have to draw the faces of their “children”.
“I’m not going to claim that child as my own!”
I was walking through the class when I heard that. Apparently one student, who’d had a bit of art training, was paired with another student who had not.
Fortunately, I was able to convince the more practiced artist to give the rest of the class a lesson on how to draw faces. She did an awesome job; first drawing a female face and then adapting it a bit to make it look more male.
If nothing else, I tried to make sure that the other students registered the idea that proportion is important in drawing biological specimens — like faces — from real life. Just getting the proportions right made a huge difference in the quality of their drawings. The forehead region should be the largest (from the top of the head to the eyebrows), then the area between the eyebrows and the bottom of the nose, then the nose to lips, and then, finally, the region from lips to chin should be shortest. You can see the proportion lines in the picture above.
The adaptation stage, where she made the facial features more masculine, was also quite useful. The students had to think about what were typical male features and if there were a genetic basis to things like square chins.
Although all of the other students’ drawings improved markedly, including her simulated spouse’s, I don’t think my art-teaching student was absolutely happy with the end results after the one lesson. She ended up handing in two drawings of her own even though everyone else (including her partner) did one each.
However, having all the students on the same page, working with the same basic drawing methods, helped improve the heredity exercise because it reduced a lot of the variability in the pictures that resulted from different drawing styles and skill levels.
I also think that taking these interludes for art lessons are quite useful in a science class, since it emphasizes the importance of accurate observation, shapes student’s abilities to represent what they see in diagrams, and demonstrates that they can — and should — be applying the skills they learn in other classes to their sciences.
Joshua Davis has a fascinating article on a math teacher who borough collaborative, self-motivated learning to students at a school in a drug-war-torn Mexican city. The results were excellent.
Davis also cites a study by Gopnik and others that showed that:
kids given no instruction were much more likely to come up with novel solutions to a problem.
↬ Ms. Douglass.
“Rarely can a response make something better. What makes something better is connection”
I gave the middle-schoolers twelve containers — cups, bottles, mugs, etc. — that I found around the classroom and asked them to figure out which one would keep in heat the best. In fact, I actually asked them to rank the containers because we’d just talked and read about thermal energy. This project is intended to have them learn about thermal energy and heat transfer, while discovering the advantages of the scientific method through practice.
Day 1: Observation and Deduction: When I asked them to rank that containers based on what they knew, I’d hoped that they’d discuss the thermal properties of the cups and bottles. And they did this to a certain degree, however, part of their reasoning for the numbers one and two containers, were that these were the ones I used. Indeed, since I use the double walled glass mug with the lid (container number 7) almost every day, while I only use the steel thermos-mug (container number 6) on field trips (see here for example), they reasoned that the glass mug must have better thermal properties.
Day 2: Exploratory Science and Project Organization: On day 2, I asked the class to see how good their ranking of the containers was by actually testing them. Ever since the complex machines project where they had to choose their own objective, they’ve been wanting more independence, so I told them to pretend I was not in the room. I was not going to say or do anything to help, except provide them with a hot plate and a boiling kettle, and keep an eye out for safety.
They got to work quickly. Or at least some of them did while the other half of the class wondered around the room having their own, no-doubt important, conversations. I pulled them all back in after about half and hour to talk about what had happened. But before we discussed anything, I had them write down — pop quiz style — what their procedure was and how it could be improved. The vagueness of some of the answers made it obvious to both to me and the ones who had not been paying attention who’d actually been working on the project.
Of the ones who’d been working in the project, I brought to their attention that they’d not really spent any time planning and trying out a procedure, but they’d just jumped right in, with everyone following the instructions of the one student who they usually look to for leadership. Their procedure, while sound in theory would have benefited from a few small changes — which they did recognize themselves — and the involvement of more of the class. In particular, they were trying to check the temperature of the water every 10 seconds, but it would take a few seconds to unscrew lids, and about 5 additional seconds for the thermometer to equilibrate. They also were restricted because they were all sharing one stopwatch while trying to use multiple thermometers.
Day 3: First Iteration: Now that they’ve had a bit of trial by fire, tomorrow they’ll try their testing again. I’m optimistic that they’ve learned a lot from the second day’s experience, but we’ll see how it turns out.
Darkness can conceal identity and encourage moral transgressions.
— Zhong et al., 2010: Good Lamps Are the Best Police: Darkness Increases Dishonesty and Self-Interested Behavior in Psychological Science.
My students asked me today if we could turn off the lights during biology class and just use the natural light from outside. I’m usually not opposed, but it was overcast, so it would have been a little dark.
I put it to a vote and we had just one or two students who were against it. My policy in these cases, where we’re changing the working environment, is to respect the wishes of the minority unless there’s a compelling argument about why we should change things.
One student proposed a compelling argument. At least he proposed to try to find a compelling argument.
“If I can find a study that says lower light is better for learning can we do it?” he asked, with his hands hovering over his iPad.
“Sure,” I replied, “But not today. You can do it on your own time.”
We’ll see what he comes up with tomorrow. I, however, ran into this article that describes a study (Zhong et al., 2010) that found that, “participants in a dimly-lit room cheated more often than those in a lighter one,” (Konnikova, 2013).
While both groups performed equally well on a set of math problems, students in the darker room self-reported that they correctly solved, on average, four more problems than the other group—earning $1.85 more as a result, since they were being paid for each correct answer. The authors suggested that the darkness created an “illusory anonymity”: even though you aren’t actually more anonymous in the dark than in the light, you feel as though you are, making you more likely to engage in behaviors you otherwise wouldn’t.
–Konnikova, 2013: Inside the Cheater’s Mind in The New Yorker.
Konnikova’s New Yorker article is worth the read, because it summarizes other factors that encourage cheating as well as things to prevent it. Things that encourage cheating:
The things that discourage cheating are the things the encourage some self-reflection, like:
And finally, it’s important to note that we will tend to rationalize our cheating, so we’re more likely to do it later.
So, I think it’ll take a lot of convincing to get me to turn off the lights, except perhaps on very sunny days.
Gary Rubinstein argues that we teach too many subjects in math, so we should reduce the number of topics in the curriculum and make math beyond eight grade into electives.
The biggest problem with math education is that there are way too many topics that teachers are required to teach. … When teachers have to teach too many topics, they do not have time to cover them all in a deep way. The teacher, then, has to choose which topics to cover in a meaningful way, and which to cover superficially.
–Rubinstein (2012): The Death of math on Gary Rubinstein’s Blog
And the decision on which subject to cover in-depth is determined by the design of the tests.
I’d certainly support his first suggestion.