Math teachers, math specialists and what makes a good math teacher

As many groups do, the ASCD SmartBrief for this week listed some of the top stories of 2008. One story, published in April, asked "what makes an effective math teacher?"

The answer is - we don't really know. But, at least in the early grades teaching skills need to be coupled with strong math foundations.

One of the interesting points made in the article was about the growing use of math specialists at the early grades. The observation that younger students may benefit from the nurturing provided by having one teacher for all subject areas does not necessarily diminish the value of having content specific teachers in certain subjects. Surely the benefits of greater competency in delivering the subject matter is as important as the nurturing of the generalist teacher. And is there an assumption that a specialist cannot be nurturing? Besides young children are somewhat familiar with other teachers... art, music, PE are usually specialists.

TO PONDER
Based on the reading and work I have done this year it seems clear to me that despite some overlap, there are significant differences in strategies needed to convey math concepts to younger as well as to struggling students. Just what they are is not easy to define.

What can they see

So today we were doing problems involving finding the area of composite figures. My students know the area formulas and they know how to find the area of given polygons.

But what they cannot do, it seems, is see regular polygons in composite figures. They are unable to break up an L shaped figure into 2 rectangles.
They also have difficulty using corresponding sides to figure incomplete lengths.

So while they can use the numbers in formulas, they clearly are not relating them to the real world.

TO PONDER:
Why do they have so much trouble visualizing the parts and breaking down the whole?

What can be done in math to help with this visualization deficit? Certainly lots of visual examples and perhaps manipulatives that can be taken apart and put together to form composites and regular figures. And maybe it is not what can be done in math but what can be done in other areas including art and science to attach math to the real world.

How To Teach and Manage 'Generation Net

In this article  from Science Tech Today by Dan Tapscott suggests that today's kids, Generation Net have " different mental habits than their Boomer parents" and their Boomer teachers. He points out that:

They expect a conversation, rather than a lecture, and they're used to working in groups, rather than toiling alone. Digital immersion has even affected the way they absorb information. They don't necessarily read a page from left to right and from top to bottom. They might instead skip around, scanning for pertinent information of interest.

He concludes that

The old model, the sage on the stage, needs to be abandoned, and schools and employers need to look at education as an interactive, collaborative venture that lasts a lifetime.

The call to change pedagogy from the sage on the sage model is hardly new. Collaborative (or the older term cooperative) learning has an established research base. Learning to learn as opposed to learning facts has been a goal for some time. 

The Ponderable:

My reaction to this article was at first glance very positive. At second glance I was struck with the DUH syndrome - haven't we been talking about this for a long time, at least since the introduction of the SCANS skills. Why is this being treated as a novel approach....... 

Seven skills students desperately need

"We are making [Adequate Yearly Progress] at the expense of failing our kids at life"

This is one of the best comments I have heard about our rush to rely on tests. Tony Wagner has published an essay for eSchool News describing the seven skills students desperately need. Please note that none of these skills can be adequately tested in a snapshot or multiple choice format. And.... all of these skills should be playing a large role in any educational activity. Can you predict what they might be? The skills are listed below.

To Ponder: If we are moving from an information aquisition climate to an information use climate, how must schooling change to insure survival let alone success in this habitat?



1. Problem-solving and critical thinking;
2. Collaboration across networks and leading by influence;
3. Agility and adaptability;
4. Initiative and entrepreneurship;
5. Effective written and oral communication;
6. Accessing and analyzing information; and
7. Curiosity and imagination.

What do they know?

I was helping in a 7th grade math class. This teacher is well organized and puts process charts with step by step directions on the walls.

So yesterday students were figuring slopes and having trouble subtracting negative numbers. The charts were on the wall. She even pointed them out. A student asked about a problem and the teacher referred to the chart and asked the student to read the steps. The student did..... and then asked the same question..... as though she could not apply the steps to her problem......

I have noticed in my intensive a similar thing. We keep notebooks with definitions and model problems. Some students seem to have a difficult time recognizing similar problems. Some will not take the time to look?

To Ponder: How do you get students to use resources they have? How do you "force" them to think about a problem and not immediately ask the question? And how much help is too much?