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Funny story about showing your (math) work


Danae
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The 14 yo has started in-person high school last week.  His math teacher told him the first few days’ homework will be a series of worksheets to make sure they are in the right class. I looked over his shoulder this weekend.

Me:  What is this?

Him:  What?

Me:  Your handwriting is small and legible, you’ve got each line neatly lined up directly under the one before it with space between problems and the answer clearly marked at the end of each.  I’ve been trying to get you to do this for years and you NEVER do. 
 

Him:  Well you always give me hard problems and I have to think about them and my thinking is . . . <gestures swirly all over the page>. These I know exactly how to solve and I’m just writing the steps to demonstrate how to do it.

 

It made me think about what Ruth has written a few times, that you don’t actually want students to show their work, you want them to show how the math works.  

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35 minutes ago, Danae said:

Him:  Well you always give me hard problems and I have to think about them and my thinking is . . . <gestures swirly all over the page>. These I know exactly how to solve and I’m just writing the steps to demonstrate how to do it.

I've noticed this with myself, that the harder the problem, the messier my work becomes.  

36 minutes ago, Danae said:

It made me think about what Ruth has written a few times, that you don’t actually want students to show their work, you want them to show how the math works.  

Actually, as a math teacher (especially when I was teaching other people's children), what I wanted them to do was show me their thinking.

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1 minute ago, EKS said:

Actually, as a math teacher (especially when I was teaching other people's children), what I wanted them to do was show me their thinking.

I think maybe that depends on what stage of learning a new concept they’re at. 

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2 hours ago, EKS said:

Actually, as a math teacher (especially when I was teaching other people's children), what I wanted them to do was show me their thinking.

Yeah, same. I'd then try to mold it into something that was actually correct, though. 

 

27 minutes ago, ikslo said:

My DS started public HS last month and I could have written your post.  5 years of begging him to write it out yielded nothing but arguments. 2 weeks in PS and he writes it all out now. 

And this is why for the last 6 months, my home has had a "fake teacher" named Miss Swamp who is really me wearing sunglasses, lol. It's possible this sounds insane, but having a much more structured schooling experience has definitely helped us cut down on the whining and the not listening. We pretend I'm not EXACTLY their mother during school time. Amazingly, it works wonders. 

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2 minutes ago, Not_a_Number said:

Yeah, same. I'd then try to mold it into something that was actually correct, though. 

Absolutely! 

The idea is that eventually their thinking and what is correct will merge.

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1 minute ago, EKS said:

Absolutely! 

The idea is that eventually their thinking and what is correct will merge.

Right. I try to spin off from what they are thinking. A lot of the time, there's a seed of an idea in it, they just don't have the confidence to follow it through. 

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That makes perfect sense. I would encourage him to DO the messy thing, to work out the hard problem whatever messy way he needs to, and then re-write his solution as if he is explaining it to a person who is unfamiliar with his thought process.
That is hard (much harder than following a cooking recipe for writing down well-rehearsed processes), but he will learn a ton by doing that extra step.

Edited by regentrude
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Haha ODD also started BM as a freshmen recently and now has the pretty math papers I've ever seen.  Not at all like before.  It's all review right now they do a trimester of review and a test before the start of Pre-Calc to make sure no one moves onto that level without actually having the knowledge.

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DD11 just started writing out her math problems neatly, but the impetus was getting problems wrong because she couldn't read her own writing, and I couldn't read it to help her. She HATES getting answers wrong. So she cried, I yelled "THIS IS WHY I SAID TO WRITE IT ON LINED PAPER" rather than scribbles with the mouse on a scratch pad on the teaching textbooks app. It wasn't pretty, but now her math is, lol. 

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5 hours ago, Not_a_Number said:

And this is why for the last 6 months, my home has had a "fake teacher" named Miss Swamp who is really me wearing sunglasses, lol. It's possible this sounds insane, but having a much more structured schooling experience has definitely helped us cut down on the whining and the not listening. We pretend I'm not EXACTLY their mother during school time. Amazingly, it works wonders. 

Oh, I love that! Mrs. Swamp. 😊

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5 hours ago, Not_a_Number said:

Yeah, same. I'd then try to mold it into something that was actually correct, though. 

 

And this is why for the last 6 months, my home has had a "fake teacher" named Miss Swamp who is really me wearing sunglasses, lol. It's possible this sounds insane, but having a much more structured schooling experience has definitely helped us cut down on the whining and the not listening. We pretend I'm not EXACTLY their mother during school time. Amazingly, it works wonders. 

Hello Viola, old friend!

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4 hours ago, regentrude said:

That makes perfect sense. I would encourage him to DO the messy thing, to work out the hard problem whatever messy way he needs to, and then re-write his solution as if he is explaining it to a person who is unfamiliar with his thought process.

Especially in college, I would have rough drafts for all my homework. At work I kept 2 notebooks for the longest time, one for my thinking and one for keeping a record. (Bullet journaling/notebook dropped me down to 1). 

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