Sometimes Simple is the Hardest

This update is going to just be about teaching and we will update the other areas tomorrow :)

This past week was eye-opening for me as a first year teacher. One of the hardest parts about teaching is being able to explain concepts well enough that students understand how to actually use and why they use it. It is also hard to try to explain things that you do everyday without thinking. One of the biggest challenges I have had through teaching math is trying to explain concepts that I do without thinking. For instance, why do two negatives multiplied together get you a positive? I have known this "rule since before middle school and now I am supposed to explain it to students so that they fully understand it and remember it. Well, it is because of these things called zero pairs. How do you solve for a variable when there are numbers all around it?

Suppose you have the problem 3x + 4 = 16 and you want to solve for x. Well, I have always done this without thinking too hard....you subtract the four from both sides then divide the new equation by 3 on both sides. Well.....what I think is simple as a math teacher has once again proven to be a challenge for my students.

This past week, I encountered a trend of misconceptions with my students. Many of my students were confused as to whether to get rid of that darn 3 or that 4 first. They all knew the goal was to get the x alone but they were unclear as to the order of the steps to take. Of course, you can divide by the three first but then you need to take into account the 4 divided by three as well. So, the simple method is to get rid of the four and then the three.....but WHY? How do you explain that to students so that they can fully understand the order?

I tried color coordinating, I tried just verbalizing it...none of these methods worked. Then it hit me, in the middle of a lecture one day, of how I could try to relate this math equation to their real lives. Kinda a goofy analogy but I was in the middle of teaching so you must give me some credit. So here it goes....this is how I explained it to my students.

You have the equation 3x + 4 = 16. Your goal is to get the x alone.

Think about this problem as if you were the x. You get up in the morning. You put clothes on and then you add on your accessories such as earrings, your purse, your wallet, etc. Now, think of your clothes as if they are glued to you and your accessories are just simple attachments to your outfit. When you get home at the end of the day, you cannot take off your "glued" clothes before your accessories right? Therefore, you must take off your accessories before you take off your clothes.

Now, if we go back to the equation at hand......the extra tacked on number is like our accessory. It is what we add on at the end of our initial dressing. The number with the x, is your glued part....like your clothes glued on until you take off your accessories. Therefore, in order to get  x by itself, you must first get rid of the accessories and then the glued part (aka...the 4 and then the 3)

I wasn't sure if this was going to hold but apparently it worked! Now, when I ask my students what our first step is when solving an equation....they pause and then all at once say "get rid of the accessory!" and I respond by saying "yes.....and what is our accessory? What is tacked on at the end?"....and they all seem to pick the right number!

I do not know if this analogy will hold but I sure hope it does. It seems to get the kids thinking about something they do everyday and how they can relate it to a random math equation. I was pretty excited about my idea and was so proud when my students started talking about the accessories and glued parts. Made me feel like I maybe, just maybe, helped these "at risk" students get out of the mind gutter and on to understanding how to solve math.

It is a great feeling and a wonderful way to end my first quarter of my first year teaching.