Defend your solution

Teaching has changed my perspective as a student, and being an active student has also shaped the way I teach. I’ve developed my own teaching and learning styles mostly based on what feels right. There’s nothing really scientific behind my decisions. However, after reading parts of How People Learn for my education class, I’ve realized that people have actually done research and gone deeper to study why the strategies I use actually work. It’s pretty neat.

Just yesterday, I read an excerpt about three case studies on mathematics teaching. The reading goes into how knowledge of mathematics, pedagogical knowledge, and knowledge of learners all shape how teachers ultimately teach math. In the second case study, Deborah Ball has her third graders use models to conceptualize negative numbers. Most people grew up receiving a math education centered on computation. However, Ball’s goal is to show her students that the art of mathematics reaches beyond computation. She wants to develop “a culture in which students conjecture, experiment, build arguments, and frame and solve problems.” That’s definitely not the math education I received growing up, but the idea seems incredible.

My favorite part about Ball’s teaching methodology is her focus on having the students explore the models, come up with conjectures, and then defend their answers without relying on a textbook or teacher for confirmation of their correctness. When I first read that statement, I was taken by surprise. For many of my current classes, I still haven’t reached that level of proficiency. For instance, when I do my algorithms psets, I have no idea whether or not my answers are correct. I’m ashamed to say that I need to compare my answers with my peers or run my answers through with a TA in order to be confident in my work. But in all reality, that’s not the way it should be. If I really understood the material, I should be able to get an answer and not only be confident that it’s correct, but also be able to defend it. Clearly, I have some work to do, but I’m really glad I made this connection. After all, if I were planning to send a rocket into space, there wouldn’t be an answer key to my calculations. And the consequences would be pretty serious if I or someone else on the team made an error. Welcome to the real world, I guess.

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