Discipline-Specific Writing and Assessment

Again, before this post, I’ll mention that my discipline is in math. Thinking of my progression through school, It is interesting to think about the types of writing that I did; especially now seeing how proof are written and the lack of that type of writing all the way up through high school. Hardly ever, in my math classes, did I ever have to use anything besides mathematical numerals or notation.  Sometimes I had to read a textbook that used English as part of the math problem, but very rarely. I will admit that some story problems require understanding and using rational to solve a problem, but this was rare, and even when it was done, it was just to use rational to transform English into a typical math problem. Writing in math was extremely limited for me until college. I can’t think of any math teacher who actually even encouraged us to more than mathematical notation in order to solve a math problem. As I understand math now, I can see how much understanding I was missing while in high school math even though I was able to still receive a A grade. I believe the way I was taught was more of a mechanistic way of solving problem, instead of an in-depth understanding way of solving problems. I will accept that can be easier to understand the depth of a solution of a problem if you can already do the mechanisms of the solution process and don’t have to think about that as well. I guess what my observation is, is that because of time, or other reasons, teachers teach the mechanisms of math but run short on going into and teaching the in-depth reasoning behind solutions. Most teachers seem to just assume that students understand the in-depth reasoning behind of a solution instead of assessing that during a test. One way, that I am excited to do, in order to asses in-depth understanding, is to require an explanations of the concepts used in solving a problem, rather than just requiring a numeric answer. The word proof comes to mind. IS it too much to require a proof for the solutions a student gives on the test, or on homework? I understand that time greatly limits you as a teacher and assessor but it is important to require proof as much as you can.  I believe that a student understanding how to solve a problem is more important than a student’s ability to quickly do the mechanisms of a solution to a problem; not that that is not important, it is very. Wouldn’t understanding the in-depth part of a solution lead to doing the mechanisms quicker in that subject , or quicker in subjects to come later anyways. Other ways to asses students in-depth understanding, besides a proof, could be through application of the math. This could be through 3dimentional representation, like if you are teaching about volume. Having a student do something that requires in-depth understanding in order to do is another way. This could be having students write a story that represents a solution to a problem works since it requires association of a element of their story to an element of their math problem. There seems to be many ways of assess in-depth understanding, so it’s interesting to think about what reasons are preventing teachers from doing this more, now.