The author's presented several ways to tackle the common feeling of being stuck. More importantly, they highlighted the importance of it in the process of thinking mathematically - that is, to get stuck is an imperative part of the process. I know all too well about being stuck and although had I known some of the methods taught in this chapter (like writing down what I know, what do I want to know, and what can I introduce) it may have helped me during my post-secondary career, I wasn't able to read the chapter with much enthusiasm. There was something looming over me that I couldn't put a finger on until I realized that it was the same thing that loomed over me while I was stuck doing problems in multivariable calculus or differential equations - what about the solution?
I understand the authors' approach and am supportive of it in the quest to instil exploratory mathematics as the basis of mathematics education however one crucial aspect is to address the inability to come up with the solution in many cases. Sometimes, you just don't figure it out and how can we address that with and in students? All those times I was in the library for hours trying to figure something out after finally giving up and searching Google for the answer, I never actually learned. I sort of went, "oh yeah, that makes sense" but it never added to my ability to think. I could never turn my assignment in to my professor or TA and be like, "look, I tried!" because that wasn't important as actually figuring it out.
The process is important, and fundamental to thinking mathematically however I would add it can only work if we remove the emphasis on finding the solution. I think that part was missing from this chapter, that sometimes it's ok to not figure it out.
You mentioned that the emphasis on finding the solution overshadowed the learning process for you during your studies. How do you think educators can balance teaching the importance of the process while also addressing students' frustration when they can't find the solution? How can we create an environment where not figuring it out is part of the learning experience?"
ReplyDeleteYou ask tough but thoughtful questions that I don't think I have the answer for yet - I'm assuming I'll have a better answer some time into my teaching career. For now, it almost seems mutually exclusive to me. I was thinking maybe if we centre projects around the process where there is no "final answer" and all students will have their own conclusions. For example a project for the equation of a where students create a cost function based on some fictitious restaurant of their choosing. This way students come up with the equation and all the features of it on their own. In a project like this there is no emphasis per se on the final answer since it will be subjective to each students'/group's project. In secondary education I think it's easy enough to convince students that the process is what's important and I can do that but showing them that that's what I as a teacher value in their assessments (not penalizing all the work if the final answer is wrong).
ReplyDeleteYour second question is a doozy. I guess it depends on what we value in our classroom. If I as a teacher get more excited when students are stuck they might feed off of my energy in that there is something good about the place they're at. If I constantly praise correct answers and never praise the work then this would create an environment that goes against not figuring it out being part of the learning experience. In all honesty, I'm not sure. If you have some words of wisdom I am all ears!