Making sense of problems and persevering in solving them is a very important standard of mathematical practice. First you have to answer to yourself the question, “what am I trying to solve?” Then you have to be able to work your way through it no matter how hard it is.
This is the way it is with most things in life, not just math. For example, I recently had to figure out how to get people to know about this website. In fact, I’m still trying to figure it out. After much pondering I decided to start emailing teachers with a free worksheet so they would know about the resources this website has to offer. I’ve emailed a little over 3,000 teachers so far, only a hundred thousand or more to go. This has taken some perseverance, but it is starting to pay off. I’ve noticed a lot of people are downloading Chet’s Happy Holiday Themed Worksheet and that makes me happy. I hope they enjoy it and the kids get a bit of laugh. It’s about helping others and spreading joy.
Another problem I had to persevere through was how to keep making money while trying to help teachers out. One thing I came up with was to do some web design for a friend’s business. I didn’t know web design that well when I came it to it but he was willing to let me start at a lower hourly rate and learn. Every day I learn something new. Today I was optimizing a client’s SEO and I realized I have to do better with my own website. It’s just another way to solve the problem of getting people to know about the website.
Interestingly the answer to the problem, much as in math, has more than one solution. In this case if I combine my solutions I will have a better more solid answer. You can still draw parallels to that with math though. The more different ways you work through a problem the better your understanding of that problem.
It’s o.k. to start out with only knowing one way, or not even knowing one way and it’s o.k. after struggling with it to get some help. For instance last week I was dealing with an issue with Dreamweaver and after calling around without any help I would able to sort it out with the help of my friend. Because I struggled with it a bit and persevered for a long while I will never make the same mistake again. So if your a student, don’t be afraid to struggle with a math problem, we all go through it at some time or another.
In summary, perseverance is the most important thing a student can have when learning a math concept or dealing with any issue in life. If you are a teacher or a parent, don’t be afraid to let a student struggle a bit. I find that we, as math teachers, sometimes jump in to help a little too soon and if you are a student don’t be afraid if you don’t have the answer or don’t even know what you are trying to answer right away. Take your time, relax, and eventually you will figure it out.