kitchen table math, the sequel: throwing money at the problem

Sunday, February 4, 2007

throwing money at the problem

OK, so I went through our upcoming State Test and pulled out a rough version of topics to be tested.

Then I went through my five gazillion workbooks looking for suitable worksheets.

Results?

I don’t have any worksheets on Venn diagrams.

Or on circle graphs.

Or on problems like “The diameter of a circle is X; find the radius.”

Or on counting and permutations.

Also, I don't remember what counting and permutations are.

So I’ve just ordered ... oh, maybe another hundred fifty bucks worth of workbooks that will eat up the remaining free space on my office floor and possibly make the difference between a 3 and a 4 on the state test not to mention that between amnesia and something akin to mastery on the critical skill of constructing a circle graph.

I don't know why I'm doing this.

After all, the slim little $11 practice workbook the school just made us all buy ought to be plenty.

Say you're a 7th grader who's constructed one circle graph in your life, and that was last year.

What do you need to do this year to be prepared to construct a circle graph on the state test?

Construct another one!

Just one!

In your slim little $11 test prep booklet!

One circle graph last year, one circle graph this year.

That'll do it.

____________

see also:

to do

state test coming right up (2006)
throwing money at the problem
more stuff only teachers can buy
help desk 1
state test coming right up (2007)
help desk 2
my life and welcome to it
inflammatory
canadianteacher.com
progress report
despair
28 out of 30

18 comments:

Anonymous said...

"The diameter of a circle is X; find the radius.”

That's not a "problem" so much as applying a definition. Whatever the diameter is, the radius is half of that.

I have pages of exercises of finding the area and circumference. Would that be useful or do you really need many exercises where the child practices dividing the value of the diameter by 2? Does he need to work backward, given the circumference he must find the radius?

Instructivist said...

I have my students do circle graphs from scratch. One problem I made up deals with a hypothetical classroom of, say, 28 students who receive the full range of grades from A to F. Specify how many students receive each grade, e.g. 5 As, 7 Bs....Then have them calculate the ratio for each grade in decimal form, multiply by 360 deg, use a protractor for the graph and label the sectors with the respective percentages.

This exercise taps into a whole range of sub-skills and is wonderful practice. Students love it.

The workbooks I have seen don't do things from scratch this way.

Catherine Johnson said...

That's not a "problem" so much as applying a definition. Whatever the diameter is, the radius is half of that.

right

he's just had NO conceptual teaching at all, virtually

his knowledge - and he does have some knowledge - isn't just inflexible; it's practically fossilized

Catherine Johnson said...

Would that be useful or do you really need many exercises where the child practices dividing the value of the diameter by 2? Does he need to work backward, given the circumference he must find the radius?

I need to study Saxon closely....I've developed a more intricate sense of how he does what he does....but I need, one of these days, to sit down and analyze those books.

Saxon, I think (not sure) constantly tries to give you the experience of SEEING (figuratively speaking) that a principle or procedure you've learned in one context applies to another context and another.

I think (again, not sure) that after you've had this experience numerous times you start to be "on the lookout."

(I'm making this up as I go.)

Christopher's knowledge of math is utterly fragmented. It is BEYOND Liping Ma; that's how fragmented it is.

And fossilized.

Catherine Johnson said...

Would that be useful or do you really need many exercises where the child practices dividing the value of the diameter by 2? Does he need to work backward, given the circumference he must find the radius?

To actually address myself to your question (!) I'm not sure.

I don't think he needs lots of practice finding area & circumference, though I intend to have him do lots of those problems.

I think he needs lots of practice "undoing" finding the area and the circumference.

Back when we worked through Saxon 6/5 he so had the concept of inverse operations.....

hmmm....

I think I might try simply teaching him "undoing" as an extension of inverse operations (is that correct? logical? should I be saying this a different way?)

Saxon used to have these wonderful fact family exercises.

He'd give the child 3 numbers - 1, 2, & 3 for instance and have the child create a "four-fact family."

1 + 2 = 3
2 + 1 = 3
3 - 1 = 2
3 - 2 = 1

These four fact families made a huge impression on Christopher.

I think I'm going to have him do and undo some area and circumference problems.

This is misery.

I'm seeing, so starkly, the utter, utter waste of time - the destruction of time - when you teach nothing to mastery, ever.

We are constantly starting over again, constantly back at square one.

Catherine Johnson said...

Myrtle, thank you!

That remark has sparked this idea.

I'm going to see if I can adapt the "four fact families" to teaching beginning algebra.

Catherine Johnson said...

instructivist

They don't do circle graphs from scratch??

RUSSIAN MATH has you do all your circle graphs from scratch.

I'm going to do the grade problem, only not with math grades!

Instructivist said...

"They don't do circle graphs from scratch??"

I can't pinpoint the workbooks. All I remember is that I was disappointed that pie charts weren't done from scratch. There must be some that do, I would imagine.

I forgot to add that another sub-skill that is practiced with this exercise is rounding. Specify to the nearest tenths or hundredths.

Some students don't understand the rounding instruction (to the nearest tenths or hundredths). This is an opportunity to point out and rehearse the distinction between cardinal and ordinal numbers as it applies to place value for natural numbers and decimals (e.g. tens vs. tenths). This linguistic clue helps to understand what kind of rounding is to be done.

Catherine Johnson said...

Some students don't understand the rounding instruction (to the nearest tenths or hundredths).

As I recall, RUSSIAN MATH used them for that, too.

Those were great problems.

Lots of fun.

rightwingprof said...

I'm not sure what you're looking for, but see here and here.

Anonymous said...

WTF is a circle graph and why is it important?

-prices

Anonymous said...

"Circle graph" sounds like a new name for what I would call a "pie chart."

-m

Catherine Johnson said...

yup, it's a pie chart

Catherine Johnson said...

I'm still not in a position to have a firm opinion on whether a concept is worth teaching.

For me, pie charts seem valuable....(and of course the fact that Russian Math teaches them extensively makes me feel that's correct).

They seem to offer a way to embed a fairly large number of skills and concepts inside one "procedure" that isn't utterly bewildering....

My problem isn't that he's going to have to do one on the state test.

My problem is that he's probably only constructed one in his life, and that was a year ago.

Catherine Johnson said...

rightwingprof

Thanks!

That's IT!

Catherine Johnson said...

I'm going to add that to the list of links.

Ben Calvin said...

Besides, Catherine, an understanding of pie charts is intergal to the use and abuse of PowerPoint.

Catherine Johnson said...

Ben

lolllll!