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Lesson

4th grade math - Understanding Fractions

Clip 10/10: Summative Reflection

Overview

Michelle reflects on the learning segment as a whole.

Teacher Commentary

MICHELLE MAKINSON: In making my teaching public in this way, I had to be brave in a great many ways. This was a challenging group of students. I worked really hard with them all year, but I, watching the videos, fell in love with myself. Not in a conceited way, just like wow, I am good at what I do. This is evidence.

In these lessons, I wanted my students to grapple with multiple ways of representing equivalent fractions, and I needed them to see that they were separate, and I needed them to do a lot of work with partitioning in terms of making sense. They understood when they were making five circles and filling in one. That made sense that it was a little bit harder to do an area model and cut it appropriately into what was an even number. Then it was a little bit harder to make sure you use “groups of” language and really drill that in as a concept. It was hardest of all to partition a number line, to understand that that linear representation is the same.

I want to make sure not to introduce the error that truth is somehow a democratic process. Just because 85% of the kids think something is right, they could all be wrong! I've introduced that idea early on, and talked about not only do you need to know when you're wrong and be okay with it, but you wanted to send all of your ideas to the end, verbally and thinking-wise, until you yourself discover that it's wrong, or confirm that it's right. You don't want to just look around and go, "Oh, everybody else has something different. I must be wrong." Defend, defend, defend, until you realize, "Oh, that didn't work, and I see where I went wrong, and realize that that was very productive work to do that."

This way of teaching seems very inefficient, and people can make fun of it all over the internet like, "Oh, this is stupid. Why would you do that?" It's obviously not going to stay there, I'm going to solidify it in a place that's efficient, but the journey is not efficient. The journey is coming to understand what the algorithm actually is doing.