Ruminations on teaching

How often do we think about what students will do with what we teach them? I mean besides needing it for the next test, or the next class. It seems that most of the math that we teach is not needed by the vast majority of people that are required to learn it. In addition, I recently read that given a problem in their field that requires mathematics a high percentage (I believe over 90%) of people are capable of doing what is required whereas when presented with the same concept in a more traditional way (as it is taught in classrooms) the percentage is criminally lower.

What does this suggest? Teaching math out of context is a bad idea.

Yet I’m also reminded of a quote by textbook author and teacher extraordinaire, Paul Foerster, that “what I know I may never use, but what I don’t know I will definitely never use.” While true, this could be said about anything and suggests, taken to an extreme of course, that we should pack as much into our students brains as possible. Out of context, though, means much of it would be inaccessible.

So I sit here trying to reconcile the fact that most of the material I teach my students they will never use. So what do I really want my students to take with them?

I want them to make mistakes and be okay with it. Or better yet, learn from them.

I want them to learn how to ask good questions, and how to figure out the answers.

I want them to learn that they are the masters of their lives. Their choices determine their happiness in life.

It’s a start at least.

No grades?

I would love to join the revolution to stop giving grades. My students are doing well this year as they struggle with complex ideas and methods of reasoning, but because there is a connection between “a grade” and how well one is doing there is a chance they will see themselves as failures. I don’t have one failure in my classes.

That is not to say nobody makes mistakes, but in my opinion the more mistakes you make, are willing to take ownership of, and ultimately struggle through the more successful you are.

So I want to stop giving grades. It’s not about that anyway, and they mean nothing really (see a previous post I made about them here). They are arbitrary designations of someone’s progress. Even when they are correlated with specific learning goals, they lose the message. Let’s focus on what is important – a students progress toward becoming a productive, healthy, intelligent individual.

Teaching is a liberal activity.

I’m thinking that perhaps part of the reason conservatives are upset with liberal teachers is because we failed them. We did not do a good enough job showing them that life is change. Once we stop growing, learning, and changing, we might as well put our feet up and pile six feet of dirt on top of us.

There is now, and now is different than the past as well as the future. Helping student adjust to the fact that there are few true constants in life, and more importantly how to live a happy and productive life despite – or perhaps because of – that is one of the key things teachers should be focusing on.

Fish or cut bait.

After reading about the response of christian fundamentalists (and others) to the fact that Obama did not make mention of God in his Thanksgiving speech it makes me realize something fundamental about myself that has been a long time in coming. I am an atheist.

I was raised in the Roman Catholic faith, and I fully took part in it all. I was an altar boy, took CCD classes, was a member of the CYO, a member of my parish’s Parish Council, a member of my college retreat team, and even toyed with the idea of becoming a priest. The point is I was not an “Easter/Christmas” catholic. I was in it full speed ahead. I even went to an all boys Catholic high school and a Catholic run university.

I had the usual confusion during high school, but I convinced myself to hang on, but after several things occurred over the course of high school and college, I started to drift from the faith by the time I graduated from college. I sporadically attended church for several years after leaving college, but I had definitely turned into the Easter/Christmas catholic. But there were so many questions that I could never get satisfactory answers about from anyone in the church that I eventually drifted away, disappointed that so often the answer was, “you have to take it on faith.” I am rationalist at my core. This never sat well with me.

Yet I still felt like there was more to life than what I saw around me. I began reading and soul-searching until I found Buddhism. The non-evangelical bent and emphasis on no deity rung true to me. The idea that what I had could be found right in front of me, and the entire notion of mindfulness really clicked with the ideas I had in my mind. Yes, there are spiritual aspects to Buddhism, and yet it was the connection with the world that my teacher taught that made the most sense to me.

While my ex-wife was initially interested in Buddhism as well, she eventually drifted away from it and into magic – as in witchcraft. In the beginning she told me that her beliefs were similar to Buddhism, but the truth is they quickly moved away from that. Mind-reading, spirit entities, and not just one God, but many gods and deities became the norm. She said she liked the more active aspects of magic. In the end, I think it was her way of trying to take control of her life in a way she did not feel she had. Although I went along with her beliefs while we were married, they made me uncomfortable, particularly for our children. But, in truth, it is water under the bridge. She is now married to someone who buys into that. I didn’t. And, I suppose it was living with her that eventually pushed my own thinking to where it is now.

When my divorce happened, it wasn’t Jesus, Buddha, or the Flying Spaghetti Monster that got me through it. It was my own belief in myself and my willingness to not only take a long hard look at who I had allowed myself to become in my marriage, but to take responsibility for my own actions and realize that it would be by my own actions that I could make changes. I realized that I could use the teachings I had learned being a Buddhist, about being aware of the world around me, about karma – the law of cause and effect, and mindfulness, to find myself again. Find the person I had been on a path to become.

More recently I read a book called A Guide to the Good Life, by William B. Irvine. It talked about the philosophy of Stoicism as it was likely practiced by ancient stoics, and more importantly, how it could be used now. It has many similarities to Buddhism, but is truly more of a philosophy than Buddhism is in that there is no spiritual component necessary. I continue to think about how to apply these things to my life.

So I think it is finally time that I acknowledge that I believe in no God, god, or deity of any type. I believe in living a good life because it is the right thing to do, not because of some afterlife punishment. I do not need to do things in this life because I am worried about will happen in the next life. I will, instead, appreciate my loved ones and my life for what it is right now. My goal is that I can impart this to my children, although I do believe that ultimately they will choose their own paths – and with their mother’s beliefs I know that they will have different messages to sift through. But I will strive to show them that this life can be lived and accepted on its own merits and does not need the embellishments that religions place on the world.

And that is why I am an atheist.

What are we teaching?

Having had numerous parents do the following over the years I have started to think about what exactly is the goal in math classrooms. What I have seen parents do, both as a teacher and in my roles as department chair (at two different schools), is call up and tell me that Johnny or Janey have already had the content we teach in *name your math class here* and so can they go to the next class up the line?

The problem is that often said content is either taught piecemeal by the parents or a tutor, or is from a 4-6 week summer course whose primary goal is an information dump of content – there is little time for anything else. Yet, if the math courses that we put forth in our schools are nothing more than transmitters of content, then perhaps these parents “get it” better than we do. If all that matters is the child can check another topic off their list, Trig? Check! Proof? Check! Derivatives? Check!, then perhaps we should get out of the way.

But I don’t feel that way. This would be like a student walking into an English class, hearing that they are doing Macbeth and deciding that because they have read that play they are ready to move on. As if there is nothing else to be learned from the text, or that there are not other, perhaps more important, things to learn in an English class such as communication through writing or speaking. English classes seem to focus heavily on process, recognizing that the content they teach is in service to the process.

Not so in many math classes, it seems. Content is king, and process is too messy in a math classroom, where we are only interested in right answers. Don’t get me wrong, there are many math teachers who know this is not the way to do it, but I don’t see it being articulated. Ask a math teacher what they teach in class and it is very likely you will hear about the topics they are covering. It is not because they do not think there are other important things to learn, but they don’t know how to address these other essential pieces.

When asked, I like to say that what I teach is how to think about mathematics. How to see and make connections. How to approach and attack new problems. For me, the content is in service to the process. Yet, I have to still work to fit in the content that the teacher of the next course will expect of me. How can I teach an “Algebra 2″ class if I don’t manage to fit in all of the content? But if they can’t apply the information, if they don’t know how to connect what they know to new information, then has “making sure all the content is covered” really served them.

It is time for math teachers to begin defining their course based on the procedures, strategies, and processes that are developmentally appropriate for their students, and then filling in the content that will support that.