Reflecting on the Week--Thoughts on Solving Equations

I hope I am not alone in saying that we all have weeks where we don't feel we are effective teachers. This past week was one of those for me.

I started the week with a good idea that didn't quite work that way I wanted it to. Then I felt like I had to cram 3 days of instruction into 5 days--because another day this week we had a benchmark testing day. I had also promised my students we would be doing guided math/center time everyday. So I felt rushed to stay on schedule.

We were learning how to solve one-step equations. We had modeled how to solve one-step equations before Thanksgiving break using algebra tiles. The plan was to learn the steps for isolating the variable and solving for it by performing the inverse operation.

When I was in school--this was when I started not getting As in math. I was able to following steps and do exactly what I was told to do. But when problems were slightly different from what I was shown in class--I was not able to solve it. I didn't understand the reason behind what I was doing, so I couldn't figure out how to solve more difficult problems. It wasn't until I had College Algebra teacher explain things and when I was studying for the GRE that I read the reason behind the "tricks" I had learned.

I don't want my students to be in the same position I was in. Telling students to solve a one step equation just by performing the inverse operations does not work in every situation. When my students saw -4+x=12 they immediately said they needed to subtract 4 from each side. Well, that doesn't work here.

While using inverse operations will work in most situations with solving equations--it doesn't solve for 100% of problems.

Instead, my students need to have a good understanding of integer operations and commutative property to solve the above problem. If my students understood that -4+x was the same as x+-4 and then could change that last expression to x-4, then they could use the inverse operation and just add 4 to each side.

So this is where I am. If my students truly understood everything I taught them this year, they could apply that information to new situations. So I am on the hunt for ways to help my students apply the information they are learning.