The Importance of an Internal Monitor

 Welcome back math bloggers! Today we’re going to discuss the idea of “developing an internal monitor” and the importance of connecting curriculum expectations with real life examples. As always we will begin with the math joke of the day!

“Developing an Internal Monitor” when Problem Solving

Today's problem was presented by my colleagues Dayton, Madison, Gagan and Allen. Their problem asked us to start with a 2 x 1 couch and find a way to move the couch in such a manner that it will be right beside its original position and be facing the same direction. The only catch was that it was extremely heavy and could only be moved 90 degrees on any of the corners. This problem was very engaging with a low floor high ceiling since there were multiple ways to solve it. Many of us ran up to the board to start writing, but one group stayed sitting and began to work out the problem with manipulatives (Using their phone as the rectangle and moving it). I took a different approach and immediately drew a graph and proceeded to work through the problem. After each step I was working to create a pattern or routine similar to solving a rubik's cube. I found a four pattern (steps 2-5) that would move my couch two positions to the right. I planned on using that same pattern to solve the problem. Here is my solution below:

As you can see, I never got an answer since I misunderstood the question. This correlates with one of my previous blogs as it’s important to clearly read the question and understand what it’s asking. This helped me identify the importance of internal monitoring. When working through these problems I need to continually ask myself “Is this what the question is asking me to do?”, “How can I manipulate and push the boundaries the question has created?” and “what can I do differently that I haven’t tried already”. By continually asking myself these questions my focus will stay directed on the problem instead of letting my mind wander when I become STUCK. I later attempted the problem on my own after class and using my new strategy came to a successful solution. 

Using Real Life Examples In Mathematics

For our next activity we did an exploration on Desmos! The activity asked us to graph 3 different graphs with varying ranges of interest compounded annually ( 5%, 10% and 20%). Me and my partner selected to start with only 10$ and see how fast the interest racked up. To our surprise it only took 14.25 iterations to double our initial investment at a 5% interest rate. This was an extremely valuable real world connection as I could see how fast the money starts to grow over time. When teaching this lesson to a group of students, It’s very possible that they will make a similar connection that could have a significant impact on their financial choices later in life. Expressing that it’s important to teach students how to apply mathematics concepts outside of the classroom!

Mr. Salmond