(If you are reading this blog first, you might want to stop and read the one published before this one. Also, I have a disclaimer to add to yesterday’s blog. Although God provided for the Israelite children when they whined and complained, we know from later chapters that this was not always his response.)
My experience has been that most teachers go into education because they want to help students learn. Yet, as stated in the previous blog, we live in a society where we avoid making others uncomfortable at all costs.
The ‘best’ math class I ever had in college was Introduction to Higher Mathematics – a proof class. We had no homework, no tests and no final. As long as you participated in class adequately you got an A. We all loved it…until I discovered that I was actually supposed to learn how to mathematically prove something and I would be expected to do so in every math class that followed. I liked the easy path and did not complain about it while I was in the class. But you can bet I complained in each of the subsequent mathematics classes. I did not have the necessary foundation upon which to build future understanding.
I am quite sure that many of you can relate to “lacking the necessary foundation upon which to build future understanding” when it comes to mathematics. It is my belief that everyone will hit a wall at some point when it comes to understanding mathematics. The only question is when the wall will show up. Even full time mathematicians may spend years trying to understand a piece of mathematics that’s just beyond their reach.
When faced with the mathematical wall you have 3 choices – stop, go around it, or climb over it. Those who stop are the ones who develop self-helplessness, fear math, hate math, and/or avoid lifelong dreams because of math. Those who go around the wall are those who choose the easy way out – either intentionally or unintentionally. These are the people who seem to do well in mathematics. They are not afraid of it; as a matter of fact, they might even like it because they feel successful. I was this type of person. When I hit a wall I found success at just paying close attention to the rules that the teacher was giving. I knew that if I tried to follow the patterns just as the teacher had, then I would be able to get around that wall. The last group of people is those who choose to climb over the wall. Just like there are some people who are born with an athletic desire, there are those who are born with a desire to understand the relationships between mathematical concepts. I was not born into this group.
I believe people can learn to make a different choice. I have a family member who was the stopper. She was able to go around some walls, but always dreaded the next wall and rarely believed that she could get around it. As an adult she was faced with a dilemma – stay stopped in front of a mathematical wall called ‘The Test’ or she could choose to try to climb over the wall and follow in the career that she felt called into. She chose to climb, developed the understanding necessary to scale that wall and ‘The Test’ no longer stood between her and her dreams.
I am an example of the person who always walked around the mathematical walls until I arrived in graduate school. It was at UGA when I discovered that I would not make it through the PhD program by walking around mathematical walls. I was going to have to climb over some of them and boy were they hard to climb. I quickly learned that I couldn’t climb by myself, I needed help. We would spend hours (and sometimes hours and hours more) working together to understand a concept and guess what would happen when we found ourselves on the other side of the wall? We would rejoice! We would high five. We had worked hard, fallen, gotten scrapes, and sometimes even fights but we would always end rejoicing together. Then we would take a deep breath, start again and moan when it was time to climb another wall, but we didn’t stop. Mathematically I have stopped climbing walls but I have gotten so much better at understanding the relationships within mathematics in the early grades that I can pretty much leap over the old walls without much effort.
My cousin and I had a reason to try to conquer these mathematical walls; we had a long term goal that required us to. Young children usually do not have those long term goals to motivate them to try to climb over mathematical walls. In many cases these same children are also in classrooms of teachers who mean well but who try their best to protect their students from struggle, from discomfort, from frustration, and unknowingly from understanding.
This blog has become much longer than I thought. I have not completed my thoughts, but I need to stop. Look for the next blog where I continue my thoughts on discomfort and understanding…