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.

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.

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.

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.

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.

Of course, it is possible to recognize this tendency and recognize that one’s own perception of a situation may not be what others see or understand. Often times communication is key to resolving the problems that different perspectives can create. Of course, one thing that is required is that there is trust between the parties communicating. If there is not, then there is no willingness to acknowledge that the perception of the other person has is equally valid, even if it comes in direct conflict with our perception of an event. Secondly, communication must not be about “winning,” in other words whose perception is right and whose is wrong, but rather about coming to a new understanding of the event that incorporates both (or more) perspectives on what occurred. It may mean having to give up something we were certain was true in favor of something that is probably closer to the truth, but not quite there.

I was reminded of all of this both because of events at work and in my personal life over the last week. As a teacher it goes without saying that my classroom generally has many people with different perspectives of what is occurring, and each student is picking up different pieces of the action. Helping them recognize this and try to be more open to hearing other perspectives is part of the process of being a good teacher. Yet it goes without saying that often there will be students who do not see events the way you perceive them, much less intend them. What can be hard, particularly with the latter, is when students feel that you have wronged them in some way and you really do not see how that could be. The teacher can become very defensive and instead of just trying to understand where the student is coming from, they make the comment that kids just lie. While no doubt there are students who do lie (just as there are adults who do) I think the reality is that a student has less life experience to understand what occurred, and they are more certain that the way they perceived things must be the only way it occurred. They lack the perspective that a longer life can give them to know that people often see the same thing differently.

As a department chair, I am sometimes called on to navigate relationships between teachers, or teachers and parents. I see my role in these situations often as trying to help people see the situation from the others perspective. This can be hard when one person feels offended by the situation, and doubly hard when the other person does not see how any offense could have occurred. Compound this by the fact that, in the case of teachers and parents, there is often a child involved as well. As a parent myself, I know the desire to believe everything my children say, but it is possible to validate their feelings about the situations and yet recognize that it probably does not represent the entire truth about what occurred. Many years ago I had an incident with a parent where he came in to a parent conference angry with me and, by the end of the conference he was actually yelling at the top of his lungs. In the middle of the library where there were at least 5 other teachers trying to have conferences. Needless to say, I was mortified and my first reaction was to become very defensive. The situation proceeded with additional meetings and conversation until I finally realized that the source of his anger was a meeting we had earlier in the year with all of his son’s teachers in which this parent had walked out thinking that I had agreed to something to which I felt I had not.

As a divorced parent this also rears its head on occasion. It probably goes without saying that had my ex-wife and I spent more time communicating our perceptions of events we may not have divorced… or it would have happened sooner and less acrimoniously. Even now I am reminded that there remains differing perceptions of the events surrounding our divorce that we cannot seem to resolve, particularly where it involves the custody of our children. Unfortunately there is little communication and less trust between us, which suggests it may never be resolved.

There are very few black and white situations in this world. Even the “evil” among us rarely see themselves that way. I’m not suggesting that there should be no consequences for choices or that intentions are all that matters. However, I do believe that it is important to understand people’s motivations and try to see their actions through their lenses, even if ultimately they must face very negative consequences for them. I am thinking, on a lesser scale, of a great student I knew who got caught cheating, which ultimately affected his college prospects. He really was a good kid and not a naturally dishonest one. But he got caught in a pressure cooker of a situation, and he made a bad choice in order to help himself get out of it. Is he a bad kid? No, but if all we looked at were his actions – the cheating – then we might be content to label him that way and move on. However, by focusing on his perceptions of the event, while not excusing him from the consequences, we can help him learn what the right choices are. Fortunately for him, the school this happened at takes this view, and I like to think that this student has gone on to be the honest and upstanding young man he had the potential to be, all because the administration did not just focus on punishing and vilifying him.

When approaching situations it becomes hard to create the dialogue that can bring a better understanding of the situation when one, or both, persons is committed to the “rightness” of their perspective. I have known people who prided themselves on their open-mindedness, but what they really meant is they like to be different and try different things. They are not open-minded enough to accept that the other person might have a valid point. Last summer I was actually physically threatened by a person who thought they knew everything about a situation I was involved in, but the truth is they only knew what the other person told them. Needless to say it is hard to develop trust and foster communication when things like this occur.

I remain committed to seeing each situation as fully as I can, recognizing that I will never see it from every possible perspective. I remain committed to hearing others and trying to see situations through their eyes, even if ultimately I cannot agree with them. Even when people are willing to approach a situation from an open-minded situation, they may have other reasons to ultimately disagree. I don’t advocate giving up your own beliefs or perceptions (as I did often in my first marriage) just to keep the peace. Just take a minute and ask yourself if you really are seeing the whole picture… and recognize that no matter what you think, you aren’t.

One of the things that Wolfram has said is that we can even embed these documents into a WordPress blog. Sadly, that’s only true if you are hosting your own WordPress blog. Those of us without the resources to do so, who have to sign up through wordpress.com do not have that functionality.

Rats, foiled again.

My wife suggested that the theme of my life is being different. The funny thing is that I think I have known this since at least middle school, if not earlier. Through no real fault of my parents I was unable to have the same things as other kids. We did not have a lot of money (although this was a fact I was not totally aware of until I was older), and I was often several steps behind the “popular” trends and thus feeling left out. Instead of feeling victimized because of it, I started to identify myself as being someone who did not follow the mainstream. In fact, I would start to follow a trend only six months to a year after it had started – as if pulling up the rear was some act of defiance. I said I was someone who only did something popular because I liked it not because it was a trend. The reality is I was looking for a way to rationalize not being able to have what others did. But the theme definitely stuck.

Eventually this came to be me looking for ways to step outside the norm. From taking my college newspaper in a direction that was opposed to the school administration to getting married and moving away from home immediately after college despite my family wishing I would stay. From getting my ear pierced and riding a motorcycle to trying new methods of teaching in a school that still approved of lecture. I prided myself as being identified in a newspaper article in my second year of teaching as the “teacher with the pony tail.” One thing after another led to my “being different,” at least in my own eyes, from the mainstream.

I always recognized that, yet at the same time I find that I have a traditional sense of family, of personal respect, that is definitely not of the rebellious type. I swear rarely, and usually only with great provocation. I hold doors for people, I say “please” and “thank you.” So I do not feel that I am rebellious for the sake of rebellion.

As I think more about what this means for me, I also know that there are many nuances and mini-themes that run both parallel and counter to this push-pull of traditional-rebellious themes in my life.

I also cannot help but wonder, as I look at the students in my classes, what themes are they developing and running through their lives? To what extent can I help them recognize and acknowledge those themes, and to what extent can I help them change them? They are more than just a group of students taking math to me. They are young people trying to find their place in the world.

What is your theme?

Goals are, in and of themselves, not bad. But when they become the sole arbiter of success then we have a problem. I watch students year after year who look at what they do in my class (or many others for that matter) as nothing more than a notch in the belt that will help them attain the goal of getting into college. I see politicians, many of whom know nothing about education other than their backsides darkened a school desk chair at one point, who hold up test scores as the only way to know if a school is passing or failing. I see businessman who try to convince us that the only thing we should worry about is the bottom line, and it’s usually their bottom line they want us to be concerned with.

This has made me think a lot about my teaching of mathematics. I think we lose something when we teach math as nothing more than a list of skills and content to be mastered. That’s like taking English for the sole purpose of diagramming sentences and writing technically perfect paragraphs with no substance. Or taking History in order to rattle off the presidents in order or list the important dates leading up to WWI. There is important information, facts, and skills to know in every discipline. But that is not the goal of learning the discipline. English is about communication – both communicating clearly as well as understanding what others say. History teaches us that there are ebbs and flows to humanities march through time. Mathematics can teach us how to think logically and reason through problems.

Process is at least as important as product. I teach the process of mathematics while teaching the content. Problem solving and transfer cannot be taught as separate units. They must be embedded in everything we do in mathematics. Asking questions should not be done once in awhile, but every single day. In my opinion, every day you do not ask a question is a day you have not learned anything.

So my question for the day? What will it take?

A year ago I was new to Portland, Oregon, and I was facing a new job and a new life as a single dad with my kids. I looked forward to the challenges I would be facing during the new year. Of course, as a teacher I see every year that way. I don’t think I could keep doing this job if I thought it would be the same year in and year out.

So what has changed? Life, as always, presents itself to us and we can choose to acknowledge and embrace it, or we can ignore and deny it. Last fall I met an extraordinary woman who, at every turn, showed me what a true partner can be. Fully determined to learn from the mistakes I made in my previous marriage, I moved forward with Shari and, on July 23rd, we were married in a beautiful ceremony in front of our parents and our children and a few friends. I am excited about the life we are building together.

In addition, my ex-wife has decided she wants more time with the children so, without too much drama, we worked out a schedule that gives her about twice as much scheduled time than this past year. I’ll confess that I am not excited about seeing my children less, but I also cannot deny that their mother loves them and that time with her is good for them. But it is a change I am not looking forward to.

Finally, at work I will be taking over the role of department chair. I have done this at my previous school, and while it has not always been my favorite activity, I cannot deny that I am excited about the possibilities.

But what is the same? I love my job. I love teaching students and trying to infect them with my enthusiasm not just for math, but with learning. I look forward to another year of trying new things, getting to know new students, and meeting new and energetic colleagues.

I’d like to say I will write more in my blog. I do mean to. We’ll see.