Building a better math teacher: Math professor considers new ways to use what we already know

For years, it has been assumed that teachers -- specifically math teachers -- need to master the content they intend to teach. And the best way to do this is to take courses beyond that content.

Yet in a paper published today in the Education Forum of the journal Science, Dr. Brent Davis of the University of Calgary says research does not support this common belief. There is little evidence that advanced courses in mathematics contribute to more effective teaching.

"You know that feeling, when you try to explain to a child how to add multi-digit numbers, and you realize that it has become so obvious and sensible that you wondered why it ever seemed difficult?" asks Davis, a professor and Chair of in the Faculty of Education.

"That's what you want to be an expert, and that's what you want to guard against to be an effective teacher. WIth years of practice and experience, it's easy to forget the difficulty involved for novices in coming to an understanding."

In his paper, "Mathematics Teachers' Subtle, Complex Disciplinary Knowledge," Davis argues that while recent studies stress the importance of teachers' explicit knowledge of mathematics course content, it is equally valuable for to be comfortable with the less clear, or tacit, knowledge inherent in mathematics as well. The challenge, says Davis, is to find a way to identify that knowledge.

Davis uses the example of multiplication to illustrate how can apply implicit knowledge by using different approaches to explain the subtleties of mathematics to their students. When introduced to multiplication, the straightforward concept of repeated addition becomes more confounding with the incorporation more complex applications, such as multiplying by fractions or multiplying by negative numbers.

Davis believes if teachers are able to develop a deeper understanding of with their students, however, it may prevent student frustration in later coursework and prepare them to contribute within a knowledge-based economy.

"We can build a better math teache,r" says Davis. "But it's more about engaging with one another to deconstruct concepts than about learning more advanced math or engaging in problem solving."

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Jun 23, 2011
Understanding the fundamentals from multiple viewpoints and being able to apply them to material beyond what one is currently teaching are both important. The former is needed to allow understanding of what the math is about, the latter to give students a reason to want to know it. Too often math becomes empty symbol shuffling - I recall a trigonometry course which was nothing but memorizing formulas and doing identities, and it wasn't until the last week of the course that the teacher bothered to point out the relationship between the helix, the circle, the sine and the cosine. That should have been the first thing taught, not the last - without a good visualization one is groping in the dark. On the other hand, I remember how dull and pointless factoring equations was. If the teacher had taken a class to do a hand-waving preview of calculus and the application of factoring to finding maxima, minima and inflection points, I would have seen a lot more reason to work on factoring.

Jun 23, 2011
Basic math should be simply taught. This year one of my kids in elementry had to solve problems so strange that they stumped Jr High, High Schooler, and Physics Major students. We had to google how to solve the problem.

It seems that those who are designing the math curiculum are doing everything they can to HURT and HINDER students from learning math. We teach our kids how to math the old fashoned way, and all my kids are top of their class when it comes to math. I tell my kids that is how the teacher wants you to do it, but do it this way.

I feel sorry for kids who don't have parents involved in their schooling.

Jun 23, 2011
Always use manipulatives when teaching basic math. Symbolic numbers are still to abstract for most children when they are learning multiplication and so on. You can even teach abstract concepts like fractions.
Also in many ways it is easier to go straight from a manipulative hands on example to abstract variables than it is to go from written numbers (an abstract concept) to variables (another abstract concept). Written numbers are merely a visual tool. They have no actual mathematical meaning.

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