The art of relationships in Mathematics
Mathematics can be considered both an Art and a Science, don't you agree?
The words on this post are appearing because somewhere inside a CPU there lies a bit of functionality that's tied between systematically placed buttons on a keyboard and what our driver display adapters can adapt to make this happen. It all looks so seamless, but realistically, the computer is doing a fraction of what the human brain is capable of in order to make it happen, even if we don't understand it (the computer and the brain).
But this isn't a post about the inner workings of Mathematics, as beautiful as they may be (that will come later).
I'd say that as much as Mathematics is both an Art and a Science, I also truly believe that the teaching of Mathematics is both an Art and a Science.
Teaching of Mathematics, and the particulars of working with students, is all about a set of relationships that take place. x & y are just variables which can mean anything, so in this instance, let's consider them Pupil (x) and Teacher (y) .
There is a 3rd variable at play though, and that one is about trust (we'll call it z).
See, teaching has to involve trust. Teachers sometimes have to work very hard to get the trust of their students. The trust that what the teacher is trying to get them to learn is valuable. The trust that teachers can show that they know what they are talking about. The trust that teachers can help guide students to levels that are higher than before.
How does one achieve trust? Well, it helps by developing a relationship with students where they come in as ones who can get power, find new abilities within themselves. Teachers have to make sure that students can believe in them to help them achieve that. Teachers also have to believe in themselves that they can do that as well. How do you know that a teacher believes in themselves? Who hasn't seen a teacher that looks defeated? How many of us educators out there have felt that way before? How many of us feel like we walk in, day in, day out, try to teach students stuff without actually believing they can do anything?
There is a bit of an art to this, and it can come down to basic teaching strategies.
Now, I could go all Jaime Escalante about this, but this was something that he figured out in his teaching practice very quickly (I believe even before he started teaching in America). He had a belief that almost no matter what the background was of a student, after time, he could get them to really high places. He'd be with a similar group of students for maybe 3 years, and BOOM! They'd really skyrocket. He could really build up that trust!
Teachers, do you feel like you have a good relationship with your class? Do you think that your students trust you to help them succeed? If not, what can you do to change that? What can be put in place?
Students, do you think that you can get to a point where you have good learning experiences in your classes where you trust that teachers know what they are talking about and that they can get you further than you can on your own?
so, in short:
y > x (in terms of mathematical understanding, most likely)
x + y - z < x as well as x + y - z < y
x + y + z = positive learning and trust that you can get farther than you could before
Let's get x, y, and z all on the same side of the equation. It makes for the best relationship, and becomes complex and beautiful.
