This week’s Occupy Math is on a familiar topic, the effective teaching of math, but it was sparked by a number of recent media reports on why students in Occupy Math’s part of Canada are doing worse into the teeth of increased spending and emphasis on math. The problem has two parts. The first is the elementary teachers are not required to learn math themselves and are often afraid of it. The second is they are being handed a teaching strategy that cannot work and then getting no help trying to make it work. This is a big multi-part problem and Occupy Math hopes we can all dive in and help.
Are we properly training the front line math teachers?
Briefly: no, not really. Ontario tests students in third and sixth grade and, in that span, the fraction of students that are performing at grade level goes down. A plausible article in the Globe and Mail suggests that the problem is that the third grade teachers are not trained in math. You might ask yourself how hard it is to teach third grade math, but Occupy Math is pretty sure that it is harder than teaching first year university math. Sure, there is less and simpler content, but the people you are working with are developing the cognitive skills they will use for the rest of their lives. A pretty deep understanding of math, its methods and goals, is needed to get that right!
In fact, the situation is worse than it would be if ignorance of math were the only factor. Many grade school teachers are afraid of math and pass on that fear to their students. Female students are disproportionately impacted — elementary teachers are majority female and so are more likely to be role models for female students. This phenomenon is well documented. It is not often that Occupy Math gets to link to the Proceedings of the National Academy of Sciences! It is also worth saying that Occupy Math is mentioning third grade teachers because that’s when the test is, not because they have extra problems or anything.
What can we do about this?
Occupy Math thinks that a good first step would be to stop blaming the teachers for problems caused by the administrative structure, the ineffective curriculum, and badly designed evaluations. A neccesary second step is that certification as an elementary teacher should require at least four math courses including one on the history, structure, and philosophy of math and one one dealing with math anxiety. Teaching teachers to compensate for math anxiety can help them with their own negative feelings. Finally, since none of this happens instantly, we should create a co-op program where senior math students and graduate students are deployed to schools as teaching aids. Screening and training would be needed, but this would help across the board. For the students who are interested, this would be a much better job than flipping burgers and it might help with the problem of teacher isolation. While in graduate school, Occupy Math worked in a middle school as a “math aide” and was the only adult in the whole 7th grade that actually knew any math. The teacher could not add two digit numbers — distressing, but at least they knew they needed the help.
What about the curriculum?
A good place to start is to note that what we are asking teachers to teach and how we are asking them to teach is broken. Occupy Math has posted on the lack of problem solving skills in high school graduates before. We are currently dumping $60,000,000 into improving math teaching and increasing the amount of time spent on math teaching. The problem is that the money is being spent on trying harder to do something that cannot ever work. The media calls this “doubling down on a failed strategy” but Occupy Math thinks that a shorter phrase like “dumb” might cover it.
A big problem with “education” theory is that the people that work in it are often trapped by magical thinking — they believe there is a “right” way to teach and that if they find it all the problems will go away. This is, of course, complete nonsense. First of all, the good strategy at a particular time is pretty dependent on who the teacher is. Beyond that, the world changes, the student population changes, and you have to pay attention and interact with the front line teachers and parents to keep math education healthy. The current system is a Soviet-style command bureaucracy and it gets results like one. The idea of trying to turn teachers into uniform commodities reminds Occupy Math of the planet Camazotz from A Wrinkle in Time.
The current disaster.
The fad that is currently being over-used is discovery learning, in which students explore and deduce things for themselves. It is easy to find studies — with which Occupy Math wholeheartedly agrees — that show that students remember what they learn by discovery far better than what they are taught by rote or drill. Why then is discovery learning problematic?
- It is experimentally obvious based on the outcomes in the Ontario schools that, when it is the dominant mode of instruction, it does not work. No pile of theoretical tracts can wish that fact out of existence.
- For discovery learning to be effective, the teacher must skillfully guide it. There is no reason the students will necessarily discover the things you need them to learn: discovery is a pretty random process. Remember — these are the teachers we are not training enough, on average.
- Time is finite! Discovery learning is clearly inferior to drill and rote learning when there is not enough time to perform guided discovery. In addition there are many facts where drill can be made like a sporting event while discovery is frustrating or boring.
- Students that have some math can acquire more and solidify their understanding via discovery learning, but there is strong evidence that discovery learning is not an effecive method for learning basic math skills.
A couple hours of discovery on an enrichment topic once a week is about the right level. Using discovery learning as the primary instruction technique is irresponsible and the students of Ontario — including those in Occupy Math’s classroom — are suffering from it.
“Forcing a poor little sixth grader to figure out pi for themselves is just mean!”
The quote in the heading is from Occupy Math’s editor. In sixth grade, she was given the problem of finding the ratio of the distance around a circle to the distance across. This is, of course, the universal constant pi. Occupy Math’s editor came to her parents who made semi-helpful strategic comments and eventually she got a value of just above three. This places her answer between the Biblical value of 3 and the ancient Egyptian value of 256/81. The problem was quite frustrating for the younger version of Occupy Math’s editor and, here’s the topper, most parents just told their kids the approximate value of pi. Done correctly — with teacher supervision — estimating pi can be a cool exercise. Assigning it as homework is exactly not how discovery learning is supposed to work. The fact it was assigned as homework shows that the teacher did not know how discovery learning is supposed to work.
Occupy Math once went to an Easter egg hunt at a public park in Ames, Iowa. The parents, ignoring the instructions from the event’s organizer, ran into the field with their kids helping their kids to “win”. You don’t win an Easter egg hunt! An analogous phenomena is the “Hockey Parent” in Canada and the “Soccer Parent” (or possibly Little League?) in the United States. Assigning discovery learning as homework lets these rule-ignoring, success-obsessed, clueless, irresponsible people be in charge of doing something they don’t know how to do. As you might expect, outcomes are not optimal.
What is needed is a real math curriculum developed by teachers and parents with administrators facilitating and providing resources. The people currently in charge of the curriculum have demonstrated culpable incompetence and should not be permitted to continue. This teachers and parents model is used in the State of Iowa which achieves best-in-the-nation results routinely with middle-of-the-pack budgets. If you have thoughts on this issue — or other ideas for reform — Occupy Math would love to hear from you. Please comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics