This week I was able to look through various problems of the week posted by the Math Forum and different solutions that students have given. As you all know, when solving a math problem there are often various ways to do so. Sometimes you may solve a problem two different ways and get two different answers, but which one is the right one? Other times You may solve a problem the same way a few times, just to check your answer, and get different answers each time. And finally how many of you have solved a problem using a wrong method, or plugging in a wrong number and still got close, if not the right answer? It’s those final cases that you’re like “WOW that was lucky!” I’ve come to learn that if you check your answers using different methods and get the same answer for both, thats when they appear to be the most accurate. But if you’re getting a different answer using different methods that doesn’t necessarily mean they both are wrong, one technique may just be more appropriate for the type of problem you are doing.
This week I examined various student’s responses to problems. Before I could truly understand their thoughts, I of course had to do the problem myself. I noticed that I used the same techniques as some of the students, but also did completely different methods than others. I was working on a problem involving a building and one child made a completely unsupported assumption about the size of one side of the building, but still resulted in the correct answer. I had to look at this problem over and over again to try and figure out his thoughts. Once figuring it out, I figured that yes his assumption was unsupported, but I could definitely see why he thought that way. He definitely had one of those cases of getting the right answer and being like “WOW that was lucky!” It’s definitely important students know to try various methods when solving problems. If you’re not able to get an answer one way, or seem to be getting a really weird answer, then try a different way! You never know! The ability to guess and check is what makes math, well, MATH!