KTM User Pages
20 Dec 2005 - 19:57
Becky C tracked down an important website for parents of children using Connected Math: Connected Math for Parents.
I was trying to dig up information on Investigations this weekend to assist me in connecting the boys' curriculum at school with our Singapore curriculum at home. The parent letters given out with each Investigations unit, and the game rules for each homework activity, are inadequate to explain the point of each activity. The desirable, final, procedural, and conceptual point of each activity. Lacking a Teacher's Guide, I have to rely on my Superior Reasoning Skills to figure out the point. Until January, when I may get up the courage to ask for my own copy of the Teacher's Guide, to keep. Which is probably illegal. But for you, you can check out this parent guide for Connected Math. Go through the Concepts and Connections link for any unit, and then download a PDF of the C and C document. I was AMAZED and favorably IMPRESSED that these folks have the courage of their convictions to put this out for parents to see and to work with. It must be the same as what's in the Teacher's Guide for Connected Math.
I thought the first 3 pages of the fractions homework were pretty good. After that the lesson seems to unravel a bit, with numerous references to 'different ways students may do this,' etc. I'm curious what others think.
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Wit and Wisdom -- CatherineJohnson - 20 Dec 2005
Thanks for your indulgence here. I'm not real sharp on 6th grade fractions because I am just approaching the teaching of 4th grade fractions with my kids, but I will dive in and give one reaction to what the editors of CMP say, and how they say it, and whether it helps or hurts. Logically different... or the same? The following page is their discussion of different approaches to division by a fraction in 6th grade. The left hand column is background, and the middle column contains the three sample problems posed, with three different strategies employed to solve the problem. So, which is it? Are the three strategies logically different or logically the same? And note, there is no help for parents (perhaps not for teachers either) to discern which strategy is worth understanding, or if it's desirable to work through all three with every child, in order to "grow" every child's mathematical understanding. Yes, "grow" "understanding" rather than "target" a, uh, "learning". Problem 1: realize that we will get 1/5 as many since each is 5 times longer ouch. maybe it's just late and I'm tired, but does any kid think this way? This first problem is posed in a partitive way -- "find the number of groups". But is the strategizing...partitive? Problem 2(a): it appears that... and still no algorithm to take out for a test drive? This second problem has no words to wrap it or motivate it. Why not illustrate the use of common denominators to approach 2/1 divided by 5/6? Problem 2(b):Extending this... requires knowledge of reciprocals? Problem 3:This strategy works for mixed numbers... but not the other kinds of fractions? Have kids been practicing manipulating symbols so that they are ready to take apart, nay, mindlessly sever 8 from 5 in the third step? And, what was the word wrap for this problem? While I appreciate their desire to connect the sentential representation of a problem with their ordering of the steps for "multiplying" and "dividing", i.e. distinguish partitive from quotitive, I don't think they actually did it. And why didn't they use the same numbers, with different word wraps for each, throughout? -- BeckyC - 22 Dec 2005
Reading this through quickly, I find it mystifying. -- CatherineJohnson - 22 Dec 2005
I don't have the patience to sit down and work this through (especially seeing as how I have yet to work through the Parker & Baldridge chapter on partitive & quotitive division...) But I'm just not seeing, at all, how these problems imply different kinds of division approaches. The explanation for the teacher is horrifically unclear. I would have to sit down and PLOW through this if I were an elementary school teacher. And I wouldn't do it. That's a funny thing form.....Liping Ma? Possibly. No one reads the teacher's manuals. Ever. Apparently the writers of teachers manuals assume they won't be read. If J.D.'s around he can tell us whether this is true. -- CatherineJohnson - 22 Dec 2005
This nicely illustrates the problem with constructivist math. It's added three layers of confusion to an easily taught procedure that would have worked with each of the different problems. No wonder why kids who learn this way make mistakes and can't solve problems reliably. With the techniques they're taught there are just too many places where the child can get confused and make a mistake. -- KDeRosa - 22 Dec 2005
I think there are the elements of a decent lesson there, but that lesson is not well written. Were it me, I'd: 1) Start with the mechanics. 2) Describe the different definitions of division. 3) Show an example of the first definition followed by very explicit use of the mechanics described in 1. 4) Repeat step 3 until I ran out of definitions. 5) Explain why the same mechanics work for each problem. -- DougSundseth - 22 Dec 2005
It's added three layers of confusion to an easily taught procedure that would have worked with each of the different problems. right confusing = challenging -- CatherineJohnson - 22 Dec 2005
slightly off-topic, I had never been taught the definition of subtraction as 'difference' I'd never even heard of it I learned it from a bar model I put together an extremely simple black-and-white lesson on subtraction as difference, and the little girl in my class just lit up after reading/working through it -- CatherineJohnson - 22 Dec 2005
-- CatherineJohnson - 22 Dec 2005
-- CatherineJohnson - 22 Dec 2005
These are the two pages. I wish you could have seen her face. (The other kids were refusing to pay attention, so they didn't really get this.....I need MAJOR work on classroom management skills....) This is incredibly simple and clean. After I went through this page with her, I had her do some subtraction-as-comparison problems. The next week, with zero practice in between, she remembered the two kinds of subtraction. -- CatherineJohnson - 22 Dec 2005
I just realized: I should also have the sentences, "How much more is 5 than 3?" and "How much less is 3 than 5?" Are there others? -- CatherineJohnson - 22 Dec 2005
ok, I fixed it other sentence? -- CatherineJohnson - 22 Dec 2005
Did Dillon EAT the other 5 cookies? -- GoogleMaster - 22 Dec 2005
you betcha -- CatherineJohnson - 22 Dec 2005
he gobbled them right down -- CatherineJohnson - 22 Dec 2005
why does that say "Dillon had 12 cookies?" -- CatherineJohnson - 22 Dec 2005
typing numbers is hopeless -- CatherineJohnson - 22 Dec 2005
alright, fixed I just have to pray none of those kids' parents ever looks closely at their materials -- CatherineJohnson - 22 Dec 2005
ok Dillon had 12 cookies he gave away 2 + 2 cookies he had 8 cookies left he ate them -- CatherineJohnson - 22 Dec 2005
From a recent Baby Blues cartoon: Mom to Son: Dan had five dollars and five friends. He gave one dollar each to two friends and no dollars to three friends. What did Dan have left? Son: Two friends. Mom: I think this problem is about money. Son: That's what his three ex-friends probably said. -- KtmGuest - 22 Dec 2005
heh -- CatherineJohnson - 22 Dec 2005