Reflection One (week 1)

Chapters One of Making Math Meaningful to Canadian Students K-8, by Marian Small

starts with an introduction that is very comforting, as it breaks problems down and explains how that helps students. The example of 3X5=15 from page 3 was a great way to put it. A student who understands that multiplication is asking for 3 groups of 5 will understand all multiplication, while a student who just memorizes won't necessarily develop a deeper understanding. 

             One of the other things that stood out was: "understanding is most likely to develop in classrooms that focus on problems to be solved, rather than exercises to be completed.” (Small, 3)  This is very interesting because it aligns with the kind of educator I would like to become. 

Another one of the first things the textbook talked about was math manipulatives. This is something that was stigmatized when I was younger, like counting on your fingers, or having to write out all the steps to a problem, which increased my confusion and prohibited me from obtaining deeper understanding. I am thankful research has improved and that math manipulatives are now accepted and encouraged. While volunteering I witnessed students using them with great success, specifically on the grade 3 EQAO math test. Overall, I am excited to learn more about new and innovative math manipulatives and to continue breaking down the stigma about needing that little bit of extra help with math problems. 

Math Manipulatives. (2006-2016). Rainbow Resource Center. Accessed through http://www.rainbowresource.com/product/sku/MMMSST/

The other section I enjoyed reading was “Different Ideas to Many Strands” (Small, 18). This section explained how to take a suggestion that a theorist many have about math, in general, and to apply it to all the different types of math. If a student can understand the broader idea as a whole, they will find it much easier to apply it to any different kind of math question. The example the textbook used was how certain classes of objects behave in similar ways, when they applied that thought to geometry and fractions they found a pattern in how it appears. This connection can be invaluable to students who are struggling to apply big ideas to small concepts. 

Another thing I was interested in reading was from the “TIPS4RM: Mathematics Processes” article in which it detailed some core basics involved with learning mathematics. The subtopics included things such as: reasoning and proving, problem solving, reflecting, representing and connecting. These are all considered mathematical process skills, which the article explains, can empower students to have a positive outlook on math. The idea that small changes in the way we teach students math can change their entire outlook on the subject is very exciting.  The article uses charts provide a really excellent guide that will come in handy when I try and infuse these “big” ideas into any math lesson. One of my favourite subtopics was “connecting” because that is what I struggled with most as a student. I think making the connection between the lesson and actually doing the problem on my own was the hardest part. I did not find that the teachers knew how to support me in finding links between the concepts being taught and those I was expected to enforce. This section helped me see how I could use different strategies to prevent my students from falling into the same pattern. The connections between math, real life scenarios, and other disciplines is so strong, and I think emphasizing that would be really beneficial to educators and students. 

               These strategies all seem to be working towards students having greater understanding of why we do the math that we do. Instead of abstract work and tedious word problems that do not relate to everyday life, these theories and tools have encouraged me to a more positive outlook on mathematics and how they are being taught in a more positive, connecting, reflective way to students. I am hoping to use some of these and test them out for myself. I can’t wait to see how students react to these concepts!