October 18 Math Reflection

     This week was another exciting week in my mathematics education where I was enriched with knowledge about how to teach mathematical concepts, but also how to be an effective educator. The concept that was focused on this week was rate, ratio, and proportional thinking with an emphasis on comparing fractions. Once again, my instructor gave tremendous examples at how fractions can be taught to children in a way that helps them visualize it and connect to real world scenarios. I remember when I was a student in the younger grades I was always interested in how the math that I was learning could apply to real life, and now I believe that this is integral to effective mathematics instruction. One particular example I enjoyed was the story of Mr.Tan’s broken piece of art that we put back together. In this activity students test their ability to visualize fractions through the broken pieces. In the picture below you can see how the different pieces represent a fraction of the overall piece of art. This would an interesting activity I think I could use in my practicum as an introductory activity to get my students engaged and to get their minds focused on math.  My instructor also began with a question that involved ordering fractions from least to greatest in a scenario that children could relate to. It is a great example of an effective question because everyone can begin, yet it can be altered in a way that can be challenging. Something that my instructor teaches that has always resonated with me is that effective questions have: “a wide base and a high ceiling.” This is a quote that I know I can take with me into my practicum when I am planning my lessons because it is an effective way to measure the effectiveness of the activity or problem I developed.

     

     The class was also one that revealed another important lesson for me as an educator, just because I was taught one way it does not mean that I should teach my students the same way. Unfortunately, I believe too many teachers today teach math in a way that they were taught, ways that were meant for computers not children. I found this to be true all too often when I was in school. Even to this day there are math concepts that I know how to calculate because I practiced the algorithm, but do not understand why. One example of this is in the picture below that demonstrates an algorithm for dividing fractions where instead of cross multiplying you simply divide the numerator and denominator. Here is just another example of how math can be simplified much better than the way it was previously taught. 

I believe that we owe our students the most updated information and not confine them to the way we were instructed. This represents the one theme that has resonated with me throughout this course; do not let the way you were instructed affect the way you teach your students. Hopefully, with this message, students today will think about math differently than we did. To end this post I will leave you with a video of Jo Boaler about the importance of being able to think about math in a conceptual manner.