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Thanks SO much for the comments on teaching students how to distribute a negative -- I can't tell you how much I appreciate your taking the time.
You are all good deed doers!
Unfortunately, I haven't actually read all you've written.
I was in the midst of reading when I had to break off mid-stride, load Andrew into the car, and drive the two of us around a sketchy part of Yonkers* for one hour, after dark (not a lot of street lights in Yonkers, not a lot of street signs, either), with cars honking at us and drivers yelling out their windows (RUDE DRIVERS IN SKETCHY YONKERS!) searching for and not finding ARC,* where we had an appointment to try and get Andrew's weekend aide hired because the agency she's been working for is kaput. Ed called the guy who runs it and reported back that the owner had been 'vague' as to what has transpired. Distressing, because we thought the world of the guy, and so did everyone who worked for him, it seemed.
Anyway: Mission Not Accomplished.
Next time I am going to ask Garmin to take me to 265 Saw Mill River Road in Hawthorne. We'll see how that goes.
No time to read this morning, either, as I am attending a two-hour workshop at my local college on how to pass the course I teach. My college gives exit exams to students taking the remedial courses, which I think is a great idea. The workshop is for students, not teachers, but still. I figure I'll attend and find out what it is they think I'm teaching.
Then, if it just so happens that I am somehow not teaching what it is they think I'm teaching, I'm going to start teaching it right away.
For the moment, I have a quick follow-up question: what do you think of yourteacher.com? I discovered last night that yourteacher has an algebra app (update: a pre-algebra app, too!) Fifty bucks, but I'm seriously considering springing for it. I'm not experienced enough to be teaching the distributive property on the fly.
* No numbers on the buildings and a paucity of signs announcing who was inside or why: a neighborhood in which a number of the local establishments appeared to have concluded that it makes good business sense not to advertise their whereabouts or even their existence. Curious! Question: what kind of enterprise is housed in a run-down, low-rise office building with a dozen shiny late-model cars crammed together outdoors beneath an oversized carport? I spoke with the two proprietors, who came outside to ask me what I wanted (I wanted directions), and wish now I had asked what they wanted.
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--When a kid has trouble writing, the mental math and number bond practice helps. You want instructional materials--go get Singapore's Primary Mathematics books, and the Home Instructor's Guides or Teacher's Guides. Those are where to start with this stuff. Do the "number bonds" stuff and practice the mental math exercises. Spend your $50 there. At least you'll know the sequence is right.
There's a great geometrical proof of the distributive property in Euclid's Elements (Book 2, Proposition 1)
http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII1.html
I've got the books & the guides; the issue is having something short-and-sweet I can show my student.
This is the problem: I am, by the terms of my employment, 'sequence-free.'
Nevertheless, it's probably time to work my way through the Singapore Math books.
I've been contemplating proposing to his mom that we just start over and go straight through Singapore Math. She would probably be up for that, but she's in the same position I was always in with C.: he's got a test tomorrow.
I used to teach to crammery, now I tutor to crammery.
I had a thought today that tickled me.
I've spent years reading teacher complaints that kids would do better in their classes if they had better parents.
Guess what?
Tutors probably feel exactly the same way about teachers.
kcab wrote - I believe that she has used the technique of drawing arcs between the inner terms and that on the outside.
His teachers have told him to do that and he refuses!
This is another rookie moment for me: I should have insisted. I didn't because I find watching him write **slightly** painful --- it just seems so hard (and, of course, I'm so inexperienced that I simply can't tell whether the effort is worth it).
The distributive property is hard for kids to learn. I remember two successive years of 6th graders in the accelerated math class having a **huge** amount of trouble with it when it was introduced early in the year.
lgm wrote: On the handwriting, he may do better if he slows down and makes an effort to write big.
He's already slow -- he's quite slow. (I guess that's what I mean when I say it's slightly painful watching him.)
I wonder if writing bigger would help even though he writes slowly - ?
If his school district has a contract with castle learning or study island he might find practice problems with solutions there.
Thank you!
I'll ask his mom to bring it up---
I've had success using graph paper with kids who can't read their own writing. Not the smaller "quad ruled" but the big 1/2 inch squares. It really helps them keep their long division columns straight.
As far as making him draw the little "arcs", that is not as important as associating the sign of each term with the term itself, instead of thinking of it as a "verb" between terms.
Nevertheless, don't take any lip from this kid. If you want him to draw arcs, he needs to do it your way. If you want him to take two lines to draw fractions, rather than cramming the whole thing into one line, he needs to do that too. Algebra is "square dancing with symbols" and everyone needs to do-si-do the same way.
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