"Teaching Math" For Dummies

One of the biggest things that students hate about math is that it doesn't seem necessary. I don't think I made it a single day in high school without hearing someone complaining about math, specifically that they would never need to know the stuff they were learning after graduation. Even today, I hear people say that we should stop teaching higher level math classes in high school because it just isn't necessary for every  student to know that stuff. Obviously, I strongly disagree. Perhaps I'm a bit biased seeing as I'm trying to be a high school math teacher. I'm the most obvious example of someone who uses the math they learned in high school in their everyday life. I also would argue strongly for keeping as many math classes in high school as possible so that I have a better shot at having a job. If we ignore my bias for a minute, we can look at reasons for why math should stay for the students' benefit and why they should stop complaining about it (t...

I was asked to talk about an interesting algebra problem that I've done. Instead, I want to talk about an interesting problem/issue that comes up when teaching algebra that I've encountered that I think everyone (teachers and students) need to be aware of. Students learn whatever their teacher decides to show them. This can be an issue as sometimes students learn a specific method rather than the concept the method is covering. I remember thinking that math was so great because it wasn't up for interpretation. There was only one way to solve a problem and it produced a single answer. It wasn't until much later that I realized that it isn't as simple as that. Let's consider multiplying two polynomials. If you are multiplying a constant by a binomial then you distribute the constant to both of the terms in the binomial individually and then add the two products together. 3(x+1)=(3*x)+(3*1)  =3x+3  Easy enough. What about multiplying a binomial instead o...