Welcome back everyone!
Now I don't know if you guessed what I'm going to be reflecting on today from the title of this blog, but maybe you did! Well, if you still don't know, today I am going to be talking about the two fundamental processes of mathematics - specialization and generalization! These two processes will help anyone find their bearings for different mathematical problems in order to move closer to a resolution. Essentially, these two mathematical processes move students towards improved mathematical thinking.
I have really reflected on this week's reading as well as throughout lecture and I have consolidated some thoughts on these mathematical processes. I have designed a graphic organizer to debrief my key takeaways from the reading this week (Thinking Mathematically - Chapter 1) that I'll show you all.
This reading really made me think about how I approach different mathematical problems. I would consider myself to be a visual learner, so patterns are always a go-to strategy in problem solving for me. I like to analyze the problem at hand to see if I can detect any sort of repetition or underlying pattern first (generalization). After doing so, I test out my pattern observations in random examples to see if I am any closer to a resolution (specialization). Prior to this reading, I did not realize that I was actively engaging in these two processes when I approached mathematical problems. I definitely think that these two processes are crucial in the improvement of one's mathematical thinking because it allows the student to unpack the problem instead of seeing it in a close-minded way.
BUT WAIT... That wasn't the only thing I reflected on this week! Have you guys ever heard about this method of note-taking called RUBRIC notes? I had no idea what RUBRIC note taking was before this reading so don't worry. Basically, RUBRIC is a way to write yourself notes while problem solving to mark your train of thought and monitor your progress throughout the solution. You can use words like "stuck", "aha!", "check", and "reflect" to ensure you fully comprehend the resolution that you arrive at.
Personally, I wasn't a fan of RUBRIC because I felt like I got too caught up in the words that I would lose track of my thought process within the actual problem. I love the reflection component of RUBRIC though because I think it is really important to go back to your completed problems and reflect on each step that you took to ensure you understand and engage in the logic behind the resolution. But hey.. if RUBRIC note-taking works well to organize the problem solving process for some students, I am all for it! I am an organization freak after all.
As a teacher candidate, I think it is really important to motivate and encourage our students to engage in these fundamental mathematical processes because they will help improve their mathematical thinking. Therefore, as a future teacher, I will strive to minimize the math anxiety within students so that they can begin to develop a growth mindset. A growth mindset is really important for students to have; they need to believe that they can learn anything! Providing students with the opportunities to engage in mathematical problems that promote this growth mindset is our job as their teacher.
Overall, I believe that it is our responsibility, as teachers, to foster our students' mathematical thinking. I intend to remind students of the importance of making mistakes and trying again as this is how we learn! I want to teach my students not to be afraid of mistakes so that they can engage in the mathematical processes with confidence when approaching a problem.
Anyways, thanks for stopping by and listening to my reflections on the topic of mathematical thinking this week! This weeks topic really opened my eyes to how I want to be as a teacher in my future mathematics classroom. I hope I either taught you something new or opened your eyes in some way about teaching or problem solving. I love coming on here and sharing my thoughts with you guys. Feel free to let me in on any thoughts or reflections that you may have had on this topic!
See you guys next week!
Signing off,
Ms. Blackwell
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