Tuesday, September 29, 2009

The Possible's slow fuse is lit by the Imagination.

The title of this post is a quote I just read in my Daily Ray of Hope email from the Sierra Club.
The gleam of an heroic Act
Such strange illumination
The Possible's slow fuse is lit
By the Imagination.
Emily Dickenson
When I Googled to find the original poem, one of the sources included this rather depressing quote:
But so few have imagination that there are ten thousand fiddlers to one composer.
Charles F. Kettering
But of course imagination is only the light that illuminates all the hard work we have to do to get the impossible to become a reality.
Genius is one percent inspiration and 99 percent perspiration.
I never did anything worth doing by accident, nor did any of my inventions come by accident. They came by work.
Thomas Alva Edison
So, what does this mean for me in my search for this "impossible" job teaching high school mathematics? I must admit that I haven't been using my imagination (or producing perspiration) enough. I've been applying for jobs through EdJoin, which supposedly lists all the school jobs in California. But most of the jobs apparently "disappear" (to someone the principal already knew) before the District gets to my application.

In between I admit that I've been moping - as well as reading about the pedagogy I hope to use in my very own classroom, and even writing about my readings and reflections here and in Negotiated Identity. But that doesn't seem to be getting me anywhere.

People were telling me that doing Secondary Math would have principals begging me to teach at their schools! Now that's imagination! So I have to use my imagination to light the work needed to be known in the schools.

At least I have finally pulled myself together to find school contacts for the required minimum 25 hours of observation in a variety of different schools and class types, from kindergarten through high school, including classes for English Language Learners and various special ed students. I guess that is the difficult "perspiration" part of doing the impossible.

Tomorrow will be my first observations - in a middle school special ed class. I plan to report on my experiences here. Years ago, soon after moving to Denmark, I tried to work as a substitute teacher. One of the jobs was in a special ed class, which was devastating (and probably the reason I decided to get a Danish university degree that would qualify me for teaching in high school!) I had absolutely no pedagogical training at the time, and certainly not in special ed! I really admire teachers who can work so well with these kids!

I am also lining up observations at an elementary school that does "Dual Immersion" in Spanish and English with the goal to make the students academically fluent in both languages. This will be a challenge to my Spanish. I'm considering offering to volunteer in math classes there once I've completed the rest of the 25 hours!

Sunday, September 27, 2009

How to Remake Education

The New York Times Magazine today is devoted to education. I have already written about one article on my other active blog: Inner City Boarding School. A short collection of entries called How to Remake Education caught my eye as well, but only one entry really made immediate sense to me. Since it is so short, I quote it in full:
Beyond Testing
The single biggest problem in American education is that no one agrees on why we educate. Faced with this lack of consensus, policy makers define good education as higher test scores. But higher test scores are not a definition of good education. Students can get higher scores in reading and mathematics yet remain completely ignorant of science, the arts, civics, history, literature and foreign languages.

Why do we educate? We educate because we want citizens who are capable of taking responsibility for their lives and for our democracy. We want citizens who understand how their government works, who are knowledgeable about the history of their nation and other nations. We need citizens who are thoroughly educated in science. We need people who can communicate in other languages. We must ensure that every young person has the chance to engage in the arts. [My italics]

But because of our narrow-minded utilitarianism, we have forgotten what good education is.

Ravitch is a historian. Her book ‘‘The Death and Life of the Great American School System’’ will be published in February.
Ms Ravitch is participating in an alternating blog with Deborah Meier called Bridging Differences on the Education Week Website, where they are trying to find what they have in common in their otherwise divergent messages about what matters most in education.

One of the other commentators goes on against BA degrees, ranting that they are not worth the paper they are printed on. I think he should read Ms Ravitch little piece - and her coming book - because I don't think he really understands why we educate our children. We are not educating them for that first job they get out of college, but to make them participating citizens in this country and the world.
Another touching story in the magazine is The Lost Student by Michelle Kuo, a Teach for America teacher in the Mississippi Delta for a year.

Wednesday, September 23, 2009

Making Math Problematical

Since I don't have a job yet, I've been doing a lot of extra reading about math pedagogy, wishing I had a class to practice things on. The most exciting I've found so far is Teaching Mathematics through Problem Solving, which unfortunately is out of print (but available used from Amazon). There is a version for PreK-6 and one for 6-12. My first attempt to buy it brought me the PreK-6 book, which I read until the 6-12 arrived today, so I have a head-start on the concepts I'll be reading about. But I thought I'd write a little about my ideas about problematizing math before I get into the book.
My father studied mechanical engineering in the 1930's at Stevens Institute of Technology in Hoboken, NJ, which he always felt was an excellent education. He used to tell me that they had not tried to teach him a lot of facts and formulas (which of course would often be out of date before he had a chance to use them) but how to find the facts and derive the formulas. My college physics professor 30 years later also impressed upon us that we shouldn't learn a bunch of formulas, but instead understand the concepts so we could set up the problems without formulas. With a formula you just have to plug in a few numbers and get answers, but if you don't understand what you're doing you have no way to know if the result it reasonable, or if you, for example, used the wrong units.

From the experience of watching my children grow up, I know that they were more willing to accept facts, rules, whatever, if they had discovered them themselves. In fact, I wrote in my "Mission Statement" for a class this summer:

Through experience with my own children, I know that the younger generation does not want to be fed with my knowledge and experience. Young people learn only what they think they need to learn. Furthermore, they want to experience life themselves, not vicariously through their elders. Any other “learning” remains in short-term memory and can rarely be utilized in their explorations of life. I believe that I can best help young people select what to learn by exposing them to own my passion for learning and exploring; I want to encourage them to maintain their childhood curiosity, rather than to suppress it.
I recall that my son usually wanted to do things his own way, even if that way was much more difficult, including climbing up a steep incline instead of taking the stairs. (Of course there were other times when he was feeling lazy that he wanted me to do things for him...)

We get stronger when we do things, we get better at things when we do them often, particularly if we think about how we are doing them. That's how we learn skills. Kids know all about understanding. That's what they spent the first 5 years of their lives doing, mostly without our help, because they had to figure it out on their own. We don't want them to stop trying to understand when they get to school. Skills aren't enough, and can be forgotten. Understanding can be recalled when needed.

Education has had a variety of methods through the years. Socrates had figured out that people needed to figure things out themselves, way back then! But somewhere along the line there's always some know-it-all who figures s/he knows the best way how to do something and wants to save others the difficulty of having to figure it out themselves, or maybe the tragedy of never figuring it out. We all have been know-it-alls at some point or other. (Like when talking with someone who has an opposing view on some topic dear to our heart. Of course they're wrong and we need to make them understand why!) I remember my (then-)husband trying to teach my son how to crawl(!) Why couldn't he figure out how to move one arm forward, not backwards?

I read a really telling example in another book recently about famous environmentalists. One of them as a child had found a couple of caterpillars and followed their life-cycle. After watching the first pupa open to reveal a butterfly struggling to get out, he decided to help the other butterfly, so it didn't have to struggle. But that one never learned how to fly. It was too weak, because it didn't have to struggle.

So by problematizing math, we make students struggle (a little) to figure things out rather than telling them how to do things. We give them a new problem based on knowledge they have already figured out and understood, and let them figure out how to solve it. If different students come up with different methods (resulting in both correct and incorrect answers) we let the students reflect on the methods so that they can decide which ones are most elegant (I love that mathematical term!) are easiest to understand and can be varied to solve other problems, as well as how not to fall into pitfalls that produce the incorrect answer. Then the students can own the methods they understand rather than the steps and skills we present to them. They learn how to understand, rather than formulas to plug numbers into.

Unfortunately there are many who think we should be taking the problem out of math, to make it easier some how. (In my practice teaching this summer we never presented a single word problem, much less have the students figure things out themselves. It ended up being a lot more difficult getting them to remember stuff than if we'd taken the time to help them understand.) There are others who think we should make math "fun." But isn't it more fun to figure things out yourself? Isn't it more inspiring. Don't you remember those things better, and can't you use them in other situations?

I just noticed that one of the editors of this book is an author in a new series Core-Plus Mathematics for which I just bought the (relatively inexpensive) teachers' guide,

  • ... a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence.
  • Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations.
  • Developed by the CORE-Plus Math Project at Western Michigan University with funding from the National Science Foundation (NSF), Core-Plus Mathematics is written for all students to be successful in mathematics.
My mind is already working out ways to used problematical math in the classroom. I hope I have a classroom where I can use my ideas soon!

Saturday, September 12, 2009

Waiting with a Passion

First Passion flower
Originally uploaded by Hornplayer

Many of my friends are teaching their first classes in their own classrooms now. A new math teacher friend in Denmark comes regularly to FaceBook to tell how much she's enjoying her classes, including baking brownies for fellow teachers and playing a student/teacher soccer game (students won, my friend was very sore the next day!)

And I am applying for jobs, and reading and writing homework assignments, most vigorously my blog Negotiated Identity, about helping ELL students negotiate their identity in this new confusing world while trying to get them up to speed in math as well. The research and personal reflection I've done for the blog (as well as the required book) have been very inspiring. I just wish I had students to try everything out with!

I was asked at an interview recently what my passion is. I immediately said "The Environment" and left it at that. The Environment has been my passion for so long (witness my blog Sustainable Rays), so that was an understandable automatic answer.

But I know that this past year has brought me through months of fun studying math, and inspiring classes at CGU as well as preteaching at summer school, getting to work with real students.

I think the best thing that happened all summer was when a student told me "I used to hate math, but now I'm kinda sorta beginning to like it." I think that inspired my new passion.

I want to inspire other kids with my love of math; inspire them to use the thinking, logic and problem-solving skills of math to gain the personal power to discover and achieve their potential, whatever that may be.

Since I have taught English Learners before (in Denmark) and I have been a second language learner myself, my particular passion is to help ELL students become productive and creative members of their new communities and country.