I think of myself as an efficient mathematician. I can persevere through a problem. Even if it is very challenging, I will take a risk and go for it. Sometimes, if I don't know what the problem is or I don't understand it, then I move on to the next problem and come back to it later. There is one area in math though that I really struggle and I don't really understand. Circumference, pi, and diameter. For me it’s kind of challenging because I don't understand the way I would have to figure out the diameter if I know what the circumference is. The formula of Pi x Diameter = Circumference or something like that is really confusing for me.
Some habits of good thinking I have are that I persevere and am able to estimate a problem if it consists of very large numbers. Also, I reread the problem and put it in my own words so that I can understand it better. I first didn't understand what GCF &/or LCM was for, though when Ms. J explained when we use it, I could understand it better. I practiced at home and I feel way more confident in doing an LCM &/or GCF problem now because I kept on practicing.
I feel like I think very strategically when I’m thinking mathematically. I think of an answer the way I would think of it as a “battle”. I figure out the correct method to complete the problem.
I think that to be a “good” mathematician, you have to persevere in solving a problem. You can't just give-up and not do anything, you have to try, try, and try again. Using a different method each time to see which ones make the most sense. You would have to make sense of a problem and be able to put it in your own words and think, “Oh, so that’s how you solve it.” Or you should be thinking, “Hmm. I see that this method doesn't work. But wait a minute, this is finding the common frequency of events. So it’s LCM.”