Since I started at teacher's college, I was told by my mentors not to 'reinvent the wheel'. Everything has been done, just go with it.
I have a serious problem with this attitude and completely disagree with its sentiments.
I understand that they were trying to help me to keep my sanity throughout my teaching career, that if I work too hard I will burn out. Their thoughts were completely acceptable. I understand what it's like to work so hard that a mental breakdown is imminent. Last year, it occurred to me towards the end of the year. I lost my temper at a student after he didn't attempt any work during the class period. I got reprimanded. I was extremely disappointed with myself. After years of mental training, of trying to leave behind my angry side, of trying to be a positive role model for these young people, it took one flash of anger to break down all that work.
Since then, I have had to really reflect on my anger. Most people in my life only know me as a calm, relaxed person. That is how I want to be remembered. That is the life I want to live.
So, is the advice to not reinvent the wheel worth the stress relief?
I argue that it isn't.
My job is to help students improve their mathematical ability to a satisfactory level, according to the government of New Zealand. As a person who cares about the future of our planet and the people that inhabit it, I want to do much more than that.
Looking at the results of the students over the last few years, it is easy to see that mathematical ability is changing. I am not going to say that people are getting worse at mathematics because the definition of what it means to be 'good' at math is ambiguous. It reminds me of a meme that was posted online the other day:
While I don't completely agree with this image, there is some truth to it: Mathematics is being dumbed down (as evidenced not only by the students' math scores, but also in the comments for this picture by math teachers - Yes, surface area can be a 2-Dimensional attribute, it just maps directly onto area of a 2-Dimensional shape!)
The point is that education is changing. The skills required 50 years ago aren't the same as they are today. We don't need every student to understand every algebraic proof in the old curriculum. We don't need them to understand each formal word in geometric calculus. I'd argue that even 50 years ago we didn't need our students to understand everything they were tested on.
What we do need is students that can think outside the box. Students that can take some situation and figure out an efficient method of solving a problem.
Need to take a door frame apart for your job as a labourer? You need to understand which order to take it apart in.
Got a conveyor belt that won't stop moving in your job as an airport employee? You need to understand why it's doing it before you can fix it.
Got a job as a deli-operator at your local supermarket? You need to understand the safety issues of placing sharp knives in the sink when working with others.
You might be thinking "These aren't math problems! You're a math teacher! Stick to your expertise!". I have to disagree in today's world. As I've stated many-a-time, mathematics is not about numbers any more. It's not about calculations or manipulating equations. Mathematics is about pattern recognition and making connections. Those are the important skills (amongst a whole bunch of others) for a mathematician in the 21st century.
So, will I continue to reinvent the wheel? Hell yes! Sure, it takes a heck of a lot of time. I am always working when many other teachers are off having their lunch. I'm working when I get home from school. I work on the weekends. But that's because it is in my goals.
As long as I make time for all my other goals (keeping a positive relationship with my family members, taking care of my house, giving myself time to just get away from it all, donating blood every two weeks, making these posts, keeping my YouTube brand going, and so on..), then I don't have a problem.
My biggest goal is to take care of my own health, physical and mental. I've gotten some flack about that before - that my primary goal should be taking care of my wife and child - but before I can take care of them I need to take care of me. So if I feel myself getting to that state of being run-down or need some time off, then I will do that. My goals will change. My priorities will change. I will happily sacrifice parts of my goals to improve my personal happiness.
Reinventing the wheel is important to my students. They deserve to have a better understanding than what is prescribed. I believe I can help them with that, but not by throwing textbook questions at them. Those days are over. We don't live in a world of static problems that hold their hand to get to an answer. They need strategies to cope in the real world. They need to understand that the real world doesn't work like a textbook problem. They need my newly invented wheels. They need your newly invented wheels.
It's okay to be lazy sometimes, when you need it. But you can do better. Reinvent the wheel and share it! You might have something amazing that the rest of us haven't thought of yet!