Today in class, we did a very interesting task. It was called the "s-pattern," and it involved a series of figures that increased in number. Although there were different questions asked, we were able to do as many or little as needed, as long as we all answered the question: "Determine an equation and explain how it relates to the visual figures provided." I found it very interesting how diverse the steps taken were by everyone in the class. Some people saw the visual pattern instantly, others manipulated the figures, and others went straight to creating a number chart and finding the pattern from there. However, we all came up with an equation and how it related to the figures, even if we took different paths to get there. I thought this was amazing to see, as it reinforced the idea that not everyone's minds work the same way, and that is more than okay. It also showed that although some people are good at following rules to get formulas, they are not good at visually seeing what those numbers look like, and although others are not good at getting the numbers quickly, they have a much better understanding of what the patterns actually mean.
I think a task like this is amazing for a classroom ! Regardless of what path people took, they were able to start out with what they were comfortable with, and then forced to work on their weaknesses as well. As I have talked about in other blog posts, I think this is extremely important. I am a firm believer that understanding the concepts and not just following formulas is a way better way to retain math skills, for the rest of students lives. It teaches students to problem solve and makes them realize that there is always more than one way to solve a problem.
Personally, I do not remember much of any class, unless I came up with the answer myself before following a formula or specific instructions. I found that if I was given the opportunity to explore ideas and felt safe being wrong, then a much deeper understanding was formed. Since I mostly took academic courses, where teachers did not embrace this idea as much, I found I forgot the content of the course as soon as I wrote the exam at the end of the semester. However, I was lucky enough to have a physics teacher who fully embraced the idea of self-exploration. Before he ever taught content, he got us to try problems on our own, or at least make us think of possible solutions first. He wasn't a big believer in just handing us formulas to use, and it helped me immensely. I was able to remember so much of what he taught me even once I left high school, that I found physics in university easy for the first year.
All in all, I hope to be able to instill this kind of thinking in my classes throughout my career as a teacher. I hope to be able to establish a safe space, where students enjoy the process of learning and don't feel like any subject is all about memorization.
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