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?

Grades - but he earned a 40

As a special education teacher I have long pondered over the conundrum of grades particularly for those students whose disabilities make it extra hard for them to learn at a pace somewhat close to their peers. Modified materials, and all kinds of testing accommodations can be put in place but at some point, some students take a test and the score is very low.

We had a discussion today about first trimester grades. One student, not an IEP student has a grade of 30 indicative of the fact that he has done NO work. Another, struggling learner has a grade of 49 --- everything is just so very hard for him.

In our district 60 is passing. So the first student will have to get a 90 to get a passing average next trimester. My student will have to get a 71.

An educational psychology course I once took talked alot about efficacy theory - the idea that if you think you can succeed you will be willing to put some effort into a task. The corollary is that if you think there is no hope, you will not even try and in effect dig yourself into a deeper hole.

For many kids a very low grade is a signal that they need not bother to try --- there is no way they can bring that up to passing.

Some schools adopt a circle 55 grade. The circle indicated that the actual grade is much lower but that the school is giving a reasonable chance to get a passing average. A second chance as it were....but a realistic one. And some hope for success. A grade of 30 in the first semester gives no real hope.

Yes they earned a 30 or a 49.....
But what is the purpose of a grade? And if a student starts out with so low a grade should he just drop out....since there is no hope for passing?
But the student knew that he was failing and still did nothing.....he should take responsibility for what he did or did not do.

And does this argument change for 3rd trimester?

To Ponder : when is a grade a informative and when is it punitive?

Motivation vs confidence

Motivation vs confidence - or do I feel the way I should?
Students were given a Math Attitude Survey. While there were no outstanding trends it was interesting to see how many students said they believed that math was important, would be important in their future and that they should be taking more math classes while at the same time admitting that they found math confusing, or hard, that they felt nervous about taking math classes, that they felt they could not solve problems easily.

To consider: what can be done in Middle School to play on their apparant motivation in order to build confidence.

Repetition or novelty

Traditional pedagogy says that most students need to practice a skill many times to master it. With raw computation this seems to make some sense.

In looking over materials about story/ word problems, it seems that that policy is followed as well.

However, there seems to be a glitch in that students often realize... oh this is an addtion problem and so add the numbers. They get into the habit of combining numbers without thinking about how the numbers relate to each other.

Even within a category type of problem it may be necessary to introduce some novelty to insure that the problem is read as a story and not as a series of numbers. Introducing irrelevent number facts and numerical terms that are not part of a computation (the 2nd boy, grade 8) is one way to maintain alertness but for some of my students, recognizing this fact is difficult.

Some students seem to need many opportunities to talk aloud about what they are doing and why,

To think about..... what is the story telling me? What is going on? What is important?

Do students with ADD who by definition have trouble organizing and prioritizing have greater difficulty filtering the relevant facts from the story?

Half a bus in the real world

We have been working on story problems for a month.
We have been using combine and compare schemas and there seems to be some improvement with basic questions.

So today there was a trick question.

5 classes are going on a field trip. Each class has 23 students. 2 adults will go with each class.
The buses hold 40 people. How many buses will be needed?

4/5 kids gave the answer as 3 and 5 left over. One student said the answer was 3.12 buses.


There are a lot of numbers in this problem. Small numbers but lots of them.
Students had a hard time telling about the relationships between the numbers.


To think about.
How do you get students to see the relationships between numbers in a problem.... and to decide which numbers go with which?

Sense and nonsense

These are revelations I had at the beginning of the year when I first started the Math Intensive with 6th graders.


You cannot combine unlike categories
Apples plus oranges can be fruit
Apples plus oranges cannot be applanges
You cannot add money + people
(dated 10/7/07)

Today (Nov 4) I gave students a problem about students and buses and tickets to a play.
(3 busloads of students; 23 students and 3 adults per bus --- how many tickets are needed?)

Two students attempted to add buses + students to get to the number of tickets.

To think about:
What does "per" mean as a math operation?

Common Words - uncommon ideas

I have been working with students struggling to figure out word problems.

For the most part, the "math" in terms of computation is not the problem. Their problem seems to be making sense of the problem, seeing the relationships between the numbers, and looking at a real world model.

These are kids who can give you 1/2 a dollar and cut a pie in half. They readily distribute half the papers to each group.

They can even tell you that Joe has twice as many pencils as Mary.

But they draw a blank when confronted with a problem of the form x is twice as large as y or even worse x is twice a number.

To think about... what is there in the wording that makes this translation difficult?

THe margin of victory

So many of the kids were excited about the election.
They all knew Obama won.
So I presented the numbers for the popular vote on the board
55542743
62680702

First I asked them to read the numbers.... no problem although two students said "You forgot to put the commas in."
OkThen we talked about the margin of victory and one student then figured that was the difference.
OKThen I asked them to estimate the margin of victory.
And they froze!
What number do we round to? Some thought hundred place...some decided hundred thousand. No one picked million or lead digit. When I asked why they had made the choice they did, they did not have a clear answer.
One said he rounded to the first big number.... hundred place.

One said hundred thousand place because that is what most of our problems had looked like.

To think about.... how to tell what is the best place to round to? How is estimation used in the real world?

ADD Knowing and Doing

Another insight from the Learning and the Brain conference at Towson on Nov 1, 2008.

One of the speakers, Dr. Baumgardner, made a point the ADD was a problem of DOING not KNOWING.  

Often the student does know the information or process, but at a given time cannot perform, or get that information into the world. He describes the dilemma as being "at the interface between what information we have acquired and the demands of the outside world. "

Something to ponder:

Stress certainly impedes answering the needs of the outside world. But so does difficulties in organization, prioritizing and making the connections. 

Add and meds

At the Conference, Learning and the Brain, a Dr. Baumgardner spoke on the issue of the teenage brain.... a risky business.

I am sure everyone will agree that the teenage brain is a scary place to visit.

A member of the audience asked about the use of meds as an intervention for students with ADD.  She mentioned that many parents balk at the idea - out of hand... fearful that it will turn their child into a zombie or more charitably change the personality significantly. 

The Doctor pointed out that many of these "scare" stories are based on anecdotes that happened to children when these drugs were first formulated. Current research has led to new meds as well as better ways to monitor meds and he suggested that such effects are far less likely to happen.

Then he framed a question that I suspect more parents and teachers should reflect on:

It is well to consider the negative side effects such meds may induce. BUT there should be equal thought to the possibility of the positive effects. 

If a parent decides not to medicate, and other interventions do not work, then the child is being condemned to a life or struggle when there might have been a solution. The decision not to medicate forces the child along a different life path than he could take had the meds been tried and succeeded.  He suggests that parents suspend their fear of meds long enough to see if they might work. --- The meds can always be stopped. 

Something to ponder. 

A parent could say I don't want my visually impaired son to wear glasses because they will impair his good looks... even if it means I am condemning him to a youth of clumsiness.....

What are the long term consequences of these meds?

What are the long term consequences of not taking the meds?

Catching up

There will be a flurry of entries to this blog over the next few days. I am reposting other blog entries here to keep one record of my thoughts on the subjects of teaching, teaching math, brain and learning and executive function disorder. 

Stressful warmups?

Yesterday I attended a workshop on Learning and the Brain at Towson University in Baltimore. 

The main speaker was Judy Willis, a woman who has an MD as well as a MSED --- a doctor in the classroom!

At one point she summed her talk by saying that the key to brain based learning was "less stress, more novelty" - if you feel pressure, those brain areas that facilitate concentration and attention are engaged in the flight, fright or freeze mode and not available to learning.

It sometimes happen to me that a comment will suddenly enlighten a consideration in a way best described as an AHA moment. 

I had come to the conference in search of ways to support the students I work with. One, in particular, is diagnosed as ADD- Inattentive type. He is having particular problems in math and of lately has been avoiding even copying the warm ups that are put on the board to start class. 

He often does not understand or remember how to do the warm up problems. He well then seem to become even more lethargic and unfocussed.  

What if the warm up itself were the trigger to this behavior? What if, subconsciously, he perceives the warm up itself as a highly stressful activity, one he cannot succeed at, and his brain is engaged in the stress mode rather than the learning mode?

At the very least, starting each class in a stressful mode....... and then anticipating that the start of every class will be  stressful,   hmmm  hardly sets up the conditions for learning.

Something to ponder.

Introduction

This is a blog I am creating in order to have a place to pose questions and record snippets of ideas I that occur to me as I go through my teaching experiences. Many of the snippets are based on comments from the variety of podcasts I subscribe to. Others will be based on other readings. 

I doubt there will be many answers, but I thought it would be interesting to keep a journal like this. The advantage of having it on line is that I can add to it from where ever I am. 

If something piques your interest, please let me know your thoughts

Alida