Thursday, April 30, 2009


This quote appeared today in the Sierra Club Daily Ray of Hope:
Don't be too timid and squeamish about your actions.
All life is an experiment.
The more experiments you make the better.
-- Ralph Waldo Emerson

I think that curiosity has been a driving power in my live, and although I've been singed a few times, I still have a few lives left. Curiosity is what leads to experimentation. If you get caught in the same rut, you need to experiment with some aspects of what you're doing, even though it might be hard not to be squeamish!

You can start in the kitchen. Try using a cookbook instead of a prepared meal or package mix. And then see what happens if you vary an ingredient.

(I admit that not all ingredients can be experimented with! When I lived in Denmark, and American friend was trying to bake some traditional Danish cookies using a recipe in Danish. She came across a word she didn't know (which happened to be for baking powder) so she substituted a spice for it. Turned into very aromatic rocks!)

My son got sent to what they called the "Observation Clinic" in Danish schools after making a little experiment in science class, which the teacher caught just before it exploded. One of my colleagues figured he'd end up a great scientist! At least he's ended up a very good computer developer with a lot of good ideas.

When I had been teaching English and German in Denmark for about 6 years, I started to think that I knew pretty much what my life would be like the next 25 years or so. That didn't leave much room for experiments - even though being a teacher in Denmark provided a lot more room for experimenting with curriculum than it appears to be possible here. So I quit teaching and have been experimenting with careers ever since: translator, diaper-service owner/manager/designer..., environmental manager, technical writer, web designer, graphic designer - and now back to teaching, but this time Math. Not all of these experiments were financially successful, but every one of them has developed my knowledge and skills in many different ways. Now I am looking at a career that could last another 5-10 years. That seems like a reasonable length for this experiment.

Encourage students to experiment

I think one of the important things a teacher should do is to encourage students to attack problems in their own way. We can be helpful to show them a few different ways to do things, and then let them do it their way after that. Or let them experiment to find their own way to attack a problem.

I'm mostly thinking Math, now, of course, but this fits for many subjects. When I taught languages in Denmark, I usually only had a very short lesson plan for how to deal with the texts we were reading, including a point or two I wanted to get across. But it was wonderful when the student discussion went its own direction, so that they were expressing their own thoughts. I was dismayed when I did some subbing at a different school once, where the students expected me to write the "right" analysis on the blackboard so they could copy it into their notes. I told my students that the best way to get a good grade in my classes was for them to introduce me some new way of looking at a text!

Sunday, April 19, 2009

Math exercise

I thought this was a great way to start a math class!

Saturday, April 18, 2009


Fledgeling Originally uploaded by J Gilbert
From time to time I am inspired by the little daily quotes I get from the Sierra Club's Daily Ray of Hope.

This was the quote last Wednesday:

and you will find out how to unfold your wings as you fall.
-- Ray Bradbury

So I am jumping into teaching a little unsure of myself, but I expect my wings will unfold! At least I am given a long time to get them unfolded through my Internship program (if there are high schools in my area actually hiring by Fall!) I will be observing classes and taking concentrated coursework this summer before I jump, so I hope that they will give me an inkling about how to get those wings out!

By the way, the lovely picture is captioned on the Flickr site as "Just out of the Phoebe nest." But several of the commenters say it is a cowbird, not a phoebe. I sometimes think of myself as something like a cowbird nurtured in a phoebe's nest. I recall happily my grandfather's a pair of cowbird friends, who would come back to his (organic) garden in New Jersey every summer and eat raisins from the arm of his lawn chair.
But I'm not going to analyze that any further!

Wednesday, April 15, 2009

A Mathematician's Lament

I just read this lovely book in one sitting and then wrote a review about it on a website I just discovered, called Goodreads, which follows here slightly edited. (Note that all links go to the Goodreads site.)

A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart

This brand new book, an expanded essay about why math is taught all wrong in schools, is delightfully short, but a great inspiration while I'm studying for my last CSET Math exam in Trig & Calculus. When I started studying for the CSET a college classmate who has has a long career as a chemist was helping me get my mind around some of the new math concepts. He told me that someone had told him that math was all about definitions. Paul Lockhart couldn't disagree more. It's about solving wonderful, fascinating problems, he says.

The author's thesis is that math is an art - the art of solving problems - and we are teaching the grunt work of math, but not the enjoyment of the art.

He starts with a "Lamentation" about how terrible school math is, as if we were teaching kids to read music notes on paper, without ever letting them listen to, play or compose music. Or an art teacher who teaches color theory and paintbrush techniques so that high school art students can do paint-by-numbers pictures.

He understands that is may be necessary for students to understand the things being taught in school, but he'd prefer it if they figured things out by themselves. The role of the teacher would be to give them the space to discover these things.

But then he concludes with "Exultation" explaining (with a few examples) about how delightful math is. It got me all inspired, since I'm in the process of becoming a math teacher!

I find that math is like a game that needs solving, which fits in to his idea of math as art. The way I have taught before (English and German in Danish high schools) is to get the students figure things out as much as possible. I've rarely had much of a lesson plan, other than the requirements of topics that had to be covered (which was quite free in Denmark.) I don't know possible it will be to teach math (rather than train formulas and definitions) when the students have tests to be taken. But I'm inspired now!

Monday, April 13, 2009

I did a little of the impossible!

I just got back the unofficial results that I have passed the 2 CSET tests I took in March (qualification exams for teaching Algebra and Geometry in California - and elsewhere.) What a relief! Now I still have one more - in Calculus and Trig - in May, and more than a year of Internship training. But at least now I am qualified to start the training!

I also took the Graduate Record General Exam and scored almost the same on the Verbal and Quantitative parts as I did 44 years ago. I guess at least my mind isn't going downhill. But all the math studying did come in helpful for that exam. It had gotten a little rusty. I'm assuming all this blogging is giving me practice for the essay parts.

I also observed a couple of math teachers at a continuation high school this week. That was quite an experience that I haven't digested yet. I want to visit a few regular schools as well.