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21 Jan 2006 - 15:17

a problem for Carolyn and Ben?


I've been thinking about Carolyn's at peace with cross multiplication post:

...lately we've been dealing with problems like d/36 = 7/4, and whatever he learned about cross-multiplication last summer is gone.

I've wanted to teach Ben to do them using isolating-the-variable methods. It's difficult to get Ben to take this step-by-step approach. One problem is that he always wants to do the problems in Saxon 'the easy way' -- and I can't tell you what the easy way is, for Ben, because from where I sit, it looks as though the answers just come to him. It's a bit uncanny. I think he visualizes the proportions, somehow.



doing things the easy way

First of all, there's one thing to be said for sending your child to a school that will stomp him with D's and D+'s.

If you don't reach the point of actual School Refusal (we were getting close there), the kid is motivated not to get more D's and D+'s. Brute force has its uses.

Once your child has had his ego mulched, there's a chance he'll listen to reason.

For all of you parents-of-little-ones, let me add that it's not much of a chance.


here's the sequence:

1. big test coming up on material not taught to mastery, not learned, and not comprehended in any way, shape, or form

2. parent points out, logically, that child has not mastered, learned, or comprehended material; therefore he will need to study a lot

3. child rolls eyes, screams, yells, sobs, claims stomachache, headache, exhaustion, etc.

4. parent persists in patient, logical explanation

5. child rolls eyes, screams, yells, etc.

6. parent persists

7. child screams, yells

8. parent loses control of patient, logical tone

9. child screams, yells

10. parent levels threat to take away allowance/PlayStation/TV

11. child says, 'I don't care'

12. parent asks 'do I need to tell your father?'

13. child says, 'Daddy never yells'

14. parent, etc.

15. child, etc.

16. parent, etc.

17. child, etc.


Talk about scripted instruction.

Notice that throughout this exchange, no actual math is getting done. In our house we call this running out the clock.

My point is: the day the 'D+' comes back on the test we have crying.

By the time the next test is upon us, the D+ is history.

Ed and I are still traumatized; Christopher has moved on.

Nevertheless, since Christopher got his D (make that D's plural as of yesterday) he is willing to listen to us when we tell him to write out each step of the solution.



I love this problem:

-x = -5



I don't know where I found it; not Prentice-Hall, I'm sure. I think it was in a workbook — maybe Instructional Fair or Kelley Wingate.

I'm wondering whether this might be a good problem to do with Ben.

Here's what I love.

  • First of all, it's incredibly simple visually and mathematically. The load on working memory has to be small.

  • Second, you can show, in just one problem, that adding, subtracting, multiplying, and dividing are still related even though you're solving equations, not learning inverse operations.

  • Third, you can almost use it the way people use simple proofs and demonstrations; it's so simple and pristine you can ask your child to write out the steps on more than one occasion - and to justify each step, and to solve it using addition/subtraction AND multiplication/division.

  • Fourth - somebody else will have to fill this in. There's something about this problem that starkly shows the 'equalness' of equations, as well as the do-the-same-thing-to-both sides principle. I can't express it, but I can see it.

  • Fifth, it demonstrates the fact that a 'minus sign' is the same thing as a coefficient of -1.

Christopher can't write out the steps to solve this problem — although he does now 'see' that the answer is x = 5 — but I'm going to see to it that he can.



solving via addition & subtraction:

-x = -5

-x + x = -5 + x

0 = -5 + x

0 + 5 = -5 + x + 5

5 = x



solving via multiplication and division:

-x = -5

(-1)(-x) = (-1)(-5)

x = 5



Wal Mart homeschooling

wow

Wal-Mart has a huge selection of books for homeschoolers.

They have a bunch of Instructional Fair books. I like the pre-algebra workbook.


0978088012866_150X150.jpg



Illinois Loop likes Kelley Wingate's workbooks, and I see that at least one Core Knowledge course uses her series.

cd-3731.gif


Wal-Mart is apparently selling a cheaper version of the IF workbook I have, which costs $12.99. Wal-Mart's is $2.81.

You can find Kelley Wingate in various places. Homeschooling Supply has the pre-algebra book for $12.31.

These things aren't cheap.

I should talley up all the money I've spent on materials for re-teaching math.

Not to mention the cost in lost work time.


-- CatherineJohnson - 21 Jan 2006

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META FIELD Title Title a problem for Carolyn and Ben?
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META FIELD SubjectArea SubjectArea MiddleSchoolMath, ParentsTeachingKids
META FIELD LogDate LogDate 200601211009

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Revision r1.1 - 21 Jan 2006 - 15:17 - CatherineJohnson