KTM User Pages
10 Mar 2006 - 00:36
For excellent examples of problems that teach, try Math TV at Action Math. The video solutions for some of the fraction and ratio problems even use Singapore methods. Christopher may really enjoy these. Greg DeMatteo
Norwood Middle School
I'm thrilled to get these — will report as soon as I've watched! (Sorry. I'm developing a slight THING for animated gifs....)
back again Action Math is a BLAST! Here's the first problem:
A new movie theater opened up in town.
The theater contains 40 rows of chairs.
The first row has 10 chairs.
Each additional row has two more chairs than the row before it.
What is the seating capacity of the theater?
This brings up something important. I think early word problems should be written exactly this way, as a list of sentences, not a paragraph. This helps 'disaggregate' basic working memory and 'environmental dependency' issues from the math problem itself. The child isn't constantly having to search back and forth in a paragraph to re-isolate the individual sentences.
These videos are incredible! You MUST go see them. Wonderful. I've just gained more conceptual understanding of algebra watching one video than I did in 3 years of high school! (I'm pretty close to serious about that....)
Greg, THANK YOU!
OK, now I'm sick. If Christopher had had a teacher like the one on this website all year long.....we wouldn't be studying for the state test. Compare her step-by-step explanation of the solution to the non-explanation of this Extended Response problem Christopher was given early this year:
challenge? or teach?
Virtually all of the problems Christopher has been given this year have been 'Challenge' problems. That's what the Assistant Superintendent in charge of curriculum told me about the Extended Response problems: "These students need to be challenged." (Christopher brought home a whole batch of challenge problems last night; I'll post some of them tomorrow.) Virtually none of the problems Christopher has been given this year have been Teaching problems. There is a vast difference between challenging a student and teaching a student.
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Catherine, I did both current problems from MathTV..SO MUCH FUN! However, I did problem #2 (Santa's Workshop) using bar graphs and the answer was so obvious. It seems like the solution shown was much more complicated. I'm not sure what to make of it other than bar diagrams are truly amazing. -- NicksMama - 10 Mar 2006
Is that cameraman flipping the bird? ;-) -- CarolynJohnston - 10 Mar 2006
omg it almost looks like that Nick's Mama ISN'T THAT SITE INCREDIBLE????? IT IS A BLAST!!! I'll do Santa's workshop next! This website is a FIND. Who does it??? Do we know?? -- CatherineJohnson - 10 Mar 2006
NicksMama?, You are certainly right. This is a very easy problem to solve with bar models. Just convert 2:3 to 4:6 and you find that you only need one more block to reach your target ratio. I made the Math TV videos for my 7th and 8th grade students who are learning formal algebra. Every time I show them how simple it is to solve a problem with bar models they give me that "oh wow, that's easy" look but inevitably ask how to do it with X. So to appease the masses, I used the more convoluted approach after setting up the visual. For reasons I don't yet understand, they are comfortable with that. Catherine, Thanks for the accolades. I really appreciate it! Infinity Quick -- KtmGuest - 11 Mar 2006
Infinity Quick - who are you?? You're a teacher who created these for your class?? THESE ARE BRILLIANT I WAS BLOWN AWAY I've only done the theater problem at this point, and I'm serious when I say I suddenly GOT the connection between algebra & geometry. (I had been 'getting' it all year.....but that one problem was SO powerful.) Incredible. Thank you for creating them. -- CatherineJohnson - 11 Mar 2006
What's so incredible about Action Math is that the ONE problem I've seen so far is very, very far removed from being either simple or easy. AND YET IT IS NOT PRESENTED OR TAUGHT AS A CHALLENGE PROBLEM. It is a teaching problem. -- CatherineJohnson - 11 Mar 2006