### wu on putting fractions in simplest form

My pointing out that 46/48=23/24 should not be interpreted as affirming the common practice of insisting that every fraction be reduced to the simplest form. There is no mathematical justification for this practice.

### what i think he’s saying

We waste a tremendous amount of time in classrooms simplifying fractions with no real purpose.

I couldn’t agree more.

Yesterday, while kids had no school, we had 6 hours of Wu…all fractions. It was a mix of elementary and middle school teachers at a district PD day. Good stuff.

I’m glad it was worthwhile.

It may appear that I have a beef with higher math. I do not. It’s lovely stuff. And I do wish all teachers responsible for teaching fractions could know the full mathematical story of fractions. It’s an elegant and compelling story.

But it is a story. And the story really does start with sharing. Fractions didn’t come from mathematicians noodling around with ordered pairs and equivalence relations. They came from sharing problems with leftovers. Human beings intuitively understand that a pound of wheat (or a cookie or a slice of pizza, etc.) that’s left at the end of equal sharing needs to be partitioned into smaller bits. Children

come to schoolwith an understanding of this.Where Wu loses me is his absolute insistence (in his writing at least) that mathematics cannot be built by formalizing these intuitive ideas. No, fractions

have to beabout number lines and ordered pairs from the very beginning. That’s nonsense unsupported by research on human learning.We want to get to number lines, for sure. I’m not sure whether we want to get to ordered pairs before undergraduate modern algebra, but I’m ready to be convinced. But the idea that we should ignore children’s intuitive notions in favor of the former mathematical ones is problematic for me.

So I’m very glad to know that the work Wu is doing with elementary teachers feels worthwhile to the teachers. I’m glad you (and others) are learning from it. I wish he could write as productively to his colleagues in math education.

I completely agree. I have done 2 month-long institutes with Wu, and was one of the district teacher-leaders who helped bring him to the Berkeley K-8 PD day this week. My math content knowledge has improved tremendously from my time in his courses. In terms of my pedagogical content knowledge…well in that regard, I take all of what he says with a very large grain of Kosher salt. I can’t imagine him successfully teaching my students. When he speaks and when he writes, he claims that math should be taught a very specific, formal way. I internalize it to mean that I (the teacher getting PD), can do my best to learn math from him in this formal way, and then I (the teacher who works with at-risk kids for most of my day), uses this content knowledge to improve how I think about the math I’m teaching to kids. His dogmatic approach loses a whole lot of people, and it’s too bad that he hasn’t quite figured out how to be more inclusive in his approach. So much of what he has to say is extremely valuable, and yet, he unfortunately makes the teaching of mathematics (and more importantly, the learning of mathematics) feel so black and white. But he has definitely made me a much better teacher with regards to my content knowledge. Working with him feels a bit like the function machine analogy…he supplies the input, and what comes out in terms of my instruction doesn’t look quite like what went in..but it’s related.

I quit requiring fractions to be simplified after taking a Wu fraction class last summer, best thing I ever did since giving up the pencil/pen battle.

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