Wednesday, January 31, 2007

Amateur survey of mathematics teachers

There is a lot of talk about what kind of knowledge mathematics teachers need in order to teach well. I am curious as to what practicing teachers think about this. Here are few questions for those of you who may stumble upon this page:

  1. Do you think that mathematics courses you took as part of your preparation program (whether it be undergraduate, or certification, or anything else) are relevant to what you do in the classroom? In other words, do you think that what you learned there is directly or indirectly applicable to your profession?

  2. Same questions about methods courses you my have taken.

  3. In light of your experience in the classroom, if you had a say in what should be taught to future teachers as a part of their preparation, what would it be? Or, what do you wish you learned before you started teaching?

It is possible that I am asking wrong questions. If you think that is the case, then offer your own questions. And answers :)


Mr. Kuropatwa said...

Mathematics content courses are definitely relevant. The more content that teachers are familiar with the better they can teach for understanding. For example, knowing polynomial division informs elementary teachers when teaching the long division algorithm.

Methods courses weren't so great. Classroom management is a big issue. I was blessed with prof. who tackled this issue head on in my Mathematics methods class. However, she did so only after the entire class complained loudly that this was something that wasn't being addressed in any other course.

What would be valuable are specific strategies for teaching specific content followed by a discussion of the principles underlying the pedagogy. It can then be extended and generalized to other specific content. For example, begin teaching new content by tying it to to older previously learned content.

Synthetic division, remainder theorem and factor theorem. I always begin by having students do some arithmetic using the long division algorithm they way they did in grade 5. e.g. 215/3 = 71 R2. We then go through a polynomial long division such as 2x^2 - 3x^2 + 5x +4 divided by x+3 showing how similar it is to long division. This also informs a discussion of the remainder and factor theorems. Synthetic division comes next in the context of simplifying the process of long division and cutting down on the number of times the same digit is written. The big ideas here are linking new learning to old by identifying the same algorithm used in different contexts and motivating new procedures by illustrating that they same underlying concepts are being used.

Another thing that would have been really helpful but was absent from my methods courses was the connection between research and practice. How do we learn? What does brain research tell us about this? (New information generally needs to be "input" six times, on average, in order to move from short to long term memory.) Stuff like this would also have been helpful. I can't get enough of this sort of stuff.

And of course, the continually changing role of technology in education.

e said...


Thanks much! This

"What would be valuable are specific strategies for teaching specific content followed by a discussion of the principles underlying the pedagogy."

is something I kept thinking about as I sat through math methods course this past semester. There is everlasting struggle as to where to put this type of material: into content or methods courses. I'll work on it.

Jonathan said...

For classroom issues, the best would have been some sort of internship (I began with no student teaching). If they started me with a 60% classload, and had me assigned to watch, plan with, discuss with, etc, experienced teachers, then the learning curve would have been far steeper.

In the end, all of my math content courses matter. About half of my methods courses did.


e said...


This is really surprising. All the preparation programs I know of have student teaching. Did you do it as an undergraduate or was it only a certification program?

Jonathan said...

Alternate certification... worked on it when I began teaching, not before. Increasingly common in many states, but this was 10 years ago, in NY.

Jonathan this is the real link; ignore the one up top

Jackie said...

Not sure if you're still interested, but...

I just finished my student teaching and a traditional certification program (after an almost 18 year "break").

Mathematics courses were worthwhile and interesting. Not sure when Real Analysis will apply but...

I had one methods course which was somewhat helpful. The fact that it was combined elem. ed/secondary ed detracted from its value. I agree that specific topics and methods would be VERY helpful. As would use of sketchpad and various other programs.

Secondary Education courses were, uhm, useless. Interesting, but not at all applicable to the reality of today's classrooms.

One comment: sadly many of my classmates in my math courses were not prepared for advanced mathematical work. They lacked fundemental understanding of Algebra II/Pre-Calc. Once they were "shown" how to do a problem, they could copy it - not sure they ever understood it. I'm scared to think of how they will teach these concepts. I think more emphasis on understanding the concepts of the math we'll be teaching would be more helpful than "advanced" mathematics.

e said...

Hi Jackie,

Thanks, I certainly am still interested. I am packing for my move, so I'm little slower to respond than usual. I find it really surprising that elementary and secondary had the same methods course. That does seem little strange, as one would think that methods for K-5 are different from those for 6-12. A lot different. As for analysis, I am fairly certain you will find it very helpful, especially if you teach precalc or calc. But even if you don't, I'm sure there'll be times when better and broader understanding of functions, continuity, limits and such will come in handy.

And finally about your last comment: I, too, am afraid about mathematics some teachers (don't) know.