Modeling

This is a great video that tells about the strategy I'm trying to use in physics:

Notice how the modeling concept works through these phases:

• Model Development 
• Model Deployment 
• Model Failure 

He talks about how modeling goes from the concrete to abstraction. I once tutored a student in Physics who had been a straight A student until Physics Senior Year. It turned out his teacher showed them how to derive equation after equation to define physics concepts, but the only labs they did were after the test, as a reward. The student and I figured out together how the concepts worked, and he started getting A's again!

For more information, look at the American Modeling Teachers' Association (AMTA), where members can find a full curriculum for Physics, Chemistry, Physical Science, and now also Biology. The speaker also mentions the Modeling website at Arizona State University, where the strategy originated.

Solving Difficult Problems

Don't Panic!

My students have been brought up in the math tradition of fast is best, and there's only one way to solve problems, using tried and "true" procedures. Their previous physics teacher had selected a college textbook for them (thinking they were all AP-Physics students, which they were not, even though they were all very intelligent in their own ways.) The textbook took great pride in generating formulas for every conceivable situation, so my students had great difficulty accepting my collection of 4 formulas on the board, which I said would cover any situation they could think of that applied to Newton's 3 Laws. Time and again one of the students (usually the ones who had gotten high grades from the previous teacher) would bring that textbook to me and ask if some version of a formula was the right one to use for a particular problem. I always said, "No, use one of the four on the board." This was very difficult for them to accept until I discovered a wonderful video clip, which I show below.

I have been auditing a MOOC with Stanford Professor Keith Devlin, based on his book Introduction to Mathematical Thinking. ("Auditing" means, I'm not taking it in the allotted time, nor submitting assignments, but I'm at least watching all the video lectures.) In the very first week, he offered a video, which I called How to Solve Difficult Problems.

Techniques the Pros Use to Solve Hard Math Problems from Keith Devlin on Vimeo.

I think showing a clip from this (about half) was the turning point in getting students to understand what I was talking about.The course is intended to introduce HS students to what college math (beyond calculus) will be like, and I am auditing it, so I can mentor my students in what they need to know to succeed in college. One important thing is problem solving - not just math and physics, but everyday life away from home. So we talked about his recommendations

• Don't panic
• take your time
• take a break
• draw a picture or diagram
• write down everything you know
• learn from your mistakes, etc. 

in connection with problem solving in everyday life - deciding which college to apply for or accept, whether to buy a car, and which one, whether to date someone, etc. 
And then we applied these concepts when solving physics problems. After the video they had a much better understanding of how to solve problems. Interestingly enough, on the last test I gave them, they were very good at solving problems where they were expected to model the problem in 6 different ways, but they did poorly on multiple-choice, where I figure many rushed through in their usual manner, bringing in all their physics misconceptions.

A Blessing For One Who Is Exhausted

Sometime Doing the Impossible can leave you exhausted. This poem that a friend had posted on Facebook has been very helpful:

A Blessing For One Who Is Exhausted, by John ODonahue

From To Bless the Space Between Us: A Book of Blessings

When the rhythm of the heart becomes hectic,
Time takes on the strain until it breaks;
Then all the unattended stress falls in
On the mind like an endless, increasing weight,

The light in the mind becomes dim.
Things you could take in your stride before
Now become laborsome events of will.

Weariness invades your spirit.
Gravity begins falling inside you,
Dragging down every bone.

The time you never valued has gone out.
And you are marooned on unsure ground.
Something within you has closed down;
And you cannot push yourself back to life.

You have been forced to enter empty time.
The desire that drove you has relinquished.
There is nothing else to do now but rest
And patiently learn to receive the self
You have forsaken for the race of days.

At first your thinking will darken
And sadness take over like listless weather.
The flow of unwept tears will frighten you.
You have traveled too fast over false ground;
Now your soul has come to take you back.

Take refuge in your senses, open up
To all the small miracles you rushed through.

Become inclined to watch the way of the rain
When it falls slow and free.

Imitate the habit of twilight,
Taking time to open the well of color
That fostered the brightness of day.

Draw alongside the silence of stone
Until its calmness can claim you.
Be excessively gentle with yourself.

Stay clear of those vexed in spirit.
Learn to linger around someone of ease
Who feels they have all the time in the world.

Gradually, you will return to yourself,
Having learned a new respect for your heart
And the joy that dwells far within slow time.

At least the students learned something!

I got three delightful letters today from former students. Even though I had some difficulties with my most recent administration, who didn't like students to feel confused, this article corroborates how I teach, and my students thoroughly understood what I was getting at once they became comfortable with not always knowing: Eric Mazur: ...Confusion is a sign of understanding

At any rate, here are the letters my students sent:

Another student sent this email:

Thank you mrs.yelverton, 

You are an awesome person. And I'm glad I got to meet you. I'll stay in touch and if I need any help I will message you.

Thank you, all my students! I learned a lot from you, and got the opportunity to try out new ideas and strategies. 

It's been nearly a year since I wrote here

I've thought of many posts I wanted to write, but I've been busy learning things, traveling and working. Can't do everything I guess.

Modeling

Last summer I participated in a workshop about Modeling Physics Mechanics. All of the physics teachers in Whittier USD participated, while about half of the students came from other districts. I had heard a lot about how modeling is a tried-and-true way to teach science to pretty much everyone, but I wanted to try it out for myself.

Learning how to use Vernier data

We acted as if we were students, with time out every once in a while to put on our teacher hats. A modeling lesson usually starts with a short demonstration, video, or possibly a min-lecture introduction, but mostly there were demonstrations to wake our curiosity. For example, the first demo was a few washers swinging at the end of a long string hanging from the ceiling. The class discussed what we saw and suggested which variables could be changed to find out more about what we were seeing. Then we split up into groups, which changed for every new topic. Each group picked one of the variables to change, as the independent variable, (number of washers, length of string, distance pulled to the side), and which dependent variable and then did 10 trials. We had to figure out how to do what we planned and measure the dependent variable. In some labs we measured things using Vernier equipment, which was my first introduction to that. In our notebooks, we drew the set-up, wrote about what we were doing, made tables and graphs, and attempted to make some sort of mathematical equation. All of these things are part of the model of the pendulum.

Preparing a white board

Then each group presented a white-board of their experiments in a "Board Meeting". Sometimes we got similar answers, sometimes something went wrong. Often there were various ways to get to the same conclusion. We learned that getting something wrong can be a better way to learn that getting it right. The other students were expected to comment respectfully on the others' white-boards, preferably by asking questions. In that way we all learned from the various approaches.
I am planning on taking either the follow-up course this summer. - on waves - or a first modeling course in chemistry.

Traveling

We had long wanted to take my grandchildren to the wonderful Danish island of Bornholm, where I taught English and German at the island's high school for 7 years in the 1980's. 

My daughter's plans, though, were to visit us in California first, so we met at Yosemite and then had several days at home in Fontana where my youngest grandchild particularly enjoyed our pool. My son even managed to come by with his new fiancee, so we did have a short reunion here.

But we also managed to bring my older grandchildren to Bornholm, which they loved as much as we do. We hiked on the cliffs, rode bicycles and went swimming off the rocky shore. We found some old friends living near our summer cottage, and wandered through the halls of the school where I taught, and even found a group picture of the faculty, including me!

And since the grandchildren live in England, John and I also took a few days both in the countryside and in London before picking them up (since their school ends in late July) and taking them home again.

Studying

I took a very interesting distance course called Matter & Interactions last fall, which used a Momentum first approach, which seemed like an excellent way to structure physics curriculum. We also learned to use the VPython programming language to make small simulations of what we were learning. I wish the modeling curriculum were based on this structure, because it is a very intuitive way to present Newton's 3 Laws. I am continuing with the material of the second semester on my own, since there are videos of all the lectures online.

I'm now taking a MOOC through Stanford on Reading to Learn in Science, since so many of my students seem to have trouble comprehending content in what they read for science classes.

Teaching

Of course all this learning was to give me a good basis for teaching science. I was offered a job as science teacher at a school for Independent Study, which unfortunately, turned out to be mostly desk-work, where students came in to take multiple-choice tests and then moved on to the next. The charter had developed an innovative NGSS-inspired Integrated Science curriculum, which would have involved teaching classes, but there were no available classrooms, and the teachers were very skeptical about it, so very few students were starting it.
Luckily, before Christmas I was offered a classroom job teaching General Physics, which I entered very enthusiastically. Starting to teach in the middle of the school year turned out to be an impossible situation, because the students already have expectations about the course that can be hard to change. The students had been taught science up to that point very traditionally, so it was a struggle to convince them that

1. science can be fun and you can learn something at the same time. 
2. making mistakes is a good way to learn, if you try to learn from the mistakes. 
3. you can help your fellow students by giving them constructive criticism (which is why Modeling teaches to ask respectful questions) 
4. you don't have to learn many different formulas if you understand where the formulas come from. 

I used the Modeling curriculum, starting with Momentum to teach Newton's Laws, and supplementing with the VPython programs I'd done for my online course. We had a nice collection of Vernier equipment to use, so they got to play with some very advanced toys as well. Unfortunately, the District needed a definitive observation about a month after Christmas, when I was still in the process of convincing students all of the above, and the results (in district minds) were not up to par. So I left my students with the curriculum I'd planned for them in the hands of the best subs I could hope for, and now have time for my blog and courses again.
Some day I will find the school that is convinced that the NGSS is the future and that we need to prepare for it, and that hopefully will allow experimentation in methodology to find the best ways to encourage students to love science.