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Today's NY Times Magazine has an article titled "Why do Americans stink at math?" It gives a very positive depiction of a set of methods advocated by Magdelene Lampert in her book Teaching Problems and the Problems of Teaching (which I haven't read). As described in the article, what Lampert advocates is changing from the traditional "I, We, You" method (demonstrate how to solve a problem, then do one with the students, then have them try one individually) to what the author of the article describes as "You, Y'all, We." In this method, the teacher starts class by posing a single "problem of the day." Students first try to tackle it individually, then get together in groups, and at the end the whole class discusses it.

Lampert seems to specialize in elementary education, especially grade 5-ish. Is there anyone here who has tried this method at the college level, or who knows of an account of whether it's been tried, or whether it is or is not likely to be appropriate?

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At the undergraduate level, this kind of teaching does is often called "Inquiry-Based Learning". The University of Michigan has a center devoted to IBL mathematics at http://www.math.lsa.umich.edu/ibl/. At that link you can find resources on how IBL is implemented, and some program assessment information. IBL is closely related to the "Moore Method", although that phrase seems to mean different things to different people.

My impression (and I do not have evidence to back this up) is that when IBL is taught well it is far superior to more traditional methods, but it is really, really hard to teach IBL well. In fact Lampert's book is mostly about how hard it is to do it well, even at the elementary level, and the types of problems (in the sense of conflicts between competing imperatives) this type of teaching creates for teachers -- hence the title of her book. Sherwood Botsford in his answer identifies one of those problems (the possibility that some students will freeload off of the efforts of a small minority of productive students). Lampert deals with this problem (and many others) extensively. I think it is a fair summary of her work to say that she does not claim to have any easy solutions to these problems; her goal was to explore and illuminate the complexity of the work.

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  • $\begingroup$ Thanks for the answer. I'm familiar with inquiry-based learning. I was asking about this specific technique. $\endgroup$ – Ben Crowell Sep 19 '14 at 19:08
  • $\begingroup$ In my experience IBL is this technique, more or less. $\endgroup$ – mweiss Sep 19 '14 at 19:14
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Frankly I expect it to fail as an overall technique. There is a place for this sort of thing, but typically in any group one person does it, one might comment, the rest watch. And that is true where the group is two or a class.

The place for this is to keep the class interesting. Show where math comes into play in unexpected places. I would be willing to use 10% of class time for this.

A huge amount of math is chunking. At any given level, you use the stuff you learned last week with some difficulty, the stuff you learned last year with more ease. At a college level you shouldn't have to think about factoring or rationalizing a complex denominator -- you've done enough problems that it is automatic. You don't want to have to think about all the levels of the problem.

Math is a lot like sport that way. You practice one action until you do it right. Then you build that action into a more complex action.

Math is dull for many people. Our choice of what we teach is partially at fault. The way we teach it is partly at fault.

(In the day to day life of a Registed Nurse how likely is she to need to do a definite integral or solve a system of two equations, two unknowns?)

The most useful math course I've taken? Euclidian Geometry. The number of times I've used concepts from EG to do row layout on my tree farm, cutting diagrams for plywood....

If you are a meteorologist, then yes, you have to understand first and second partial differentials. But 90% of college students need little more math than that required for bookkeeping and estimation.

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    $\begingroup$ Do the last four paragraphs here answer any of the questions in the original post? $\endgroup$ – user173 Sep 17 '14 at 7:46
  • $\begingroup$ Perhaps math is dull for some people because of the repetitive way it is taught, similar to practice in sport instead of considering how students might come to form a coherent understanding. And, in fact, this problem is just the thing that work like Dr. Lambert's is intended to address. Something to consider. $\endgroup$ – JPBurke Sep 17 '14 at 18:50
  • $\begingroup$ Out of curiosity, what kind of trees do you grow? I am thinking of starting a nut farm in the near future. $\endgroup$ – Steven Gubkin Sep 17 '14 at 23:43
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    $\begingroup$ @StevenGubkin sherwoods-forests.com $\endgroup$ – Sherwood Botsford Sep 19 '14 at 18:52
  • $\begingroup$ @JPBurke: There are rare individuals who can be shown something once or twice, do one or two problems, and instantly internalize them. I knew one individual who read "Freedom of the Hills" one of the standard texts for mountaineering, and led a class 5.10 climb flawlessly. Both in mountaineering and in mathematics such people are rare. There are musicians who hear a piece and can play it. But most musicians have to spend boring hours playing scales and do exercises. So too with math. $\endgroup$ – Sherwood Botsford Sep 19 '14 at 18:55

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