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What is the answer to this question?

Phil has a summer reading list of 12 books.
If he has to read three books, how many different sets of books can he choose to read?

ummmm....

Is this a combination or a permutation?

I think it's a combination.

I mention combinations, because combinations aren't in Christopher's textbook.

Ms. K covered combinations in class, but Christopher forgot to tell me, and of course there was no review sheet, because why would there be a review sheet when you've covered 18 or 19 or 20 brand-new topics in probability, some of which aren't in the book, in 2 weeks' time and now you're going to give a test?

Maybe there was something on edline.

If so, it's not there now.

So I had no idea combinations were going to be on the test, so I didn't teach myself combinations and thus couldn't reteach combinations to Christopher & assign practice problems, etc., etc.

So he missed the combination problems.....

....also, there seems to be a new mystery concerning POINTS OFF for crossing out incorrect work on your test paper.

Christopher is under the impression that Ms. K. has told them she has to take POINTS OFF for any crossed-out incorrect work, because the state tests don't allow you to cross out incorrect work.

So: POINTS OFF.

In the middle of chewing that one over (POINTS OFF! FOR FAILING TO OBSERVE MANDATORY STATE TEST STYLE AND USAGE REQUIREMENTS! I'M PRETTY SURE I'M AGAINST IT!) I was seized by an impulse to check.

What are our mandatory state test syle and usage requirements, anyway?

[pause]

As far as I can tell, there aren't any:

Listed below are the policies to be followed while scoring the Mathematics Tests for all grades.

1. If the question does not specifically direct students to show their work, teachers may not score any work that the student shows.

2. If a student does the work in other than a designated “Show your work” area, that work may still be scored. (Additional paper is an allowable accommodation for a student with disabilities if indicated on the student’s IEP or 504 Plan.)

3. If the question requires students to show their work, and a student shows appropriate work and clearly identifies a correct answer but fails to write that answer in the answer blank, the student should still receive full credit.

4. If the question requires students to show their work, and a student shows appropriate work and arrives at the correct answer but writes an incorrect answer in the answer blank, the student may not receive full credit.

5. If the student provides one legible response (and one response only), teachers should score the response, even if it has been crossed out.

6. If the student has written more than one response but has crossed some out, teachers should score only the response that has not been crossed out.

7. For questions in which students use a trial-and-error (guess-and-check) process, evidence of three rounds of trial-and-error must be present for the student to receive credit for the process. Trial-and-error items are not subject to Scoring Policy #6, since crossing out is part of the trial-and-error process.

8. If a response shows repeated occurrences of the same conceptual error within a question, the student should not be penalized more than once.

9. In questions that provide ruled lines for the students to write an explanation of their work, mathematical work shown elsewhere on the page may be considered and scored if, and only if, the student explicitly points to the work as part of the answer.

10. Responses containing a conceptual error may not receive more than fifty percent of the maximum score.

11. In all questions that provide a response space for one numerical answer and require work to be shown, if the correct numerical answer is provided but no work is shown, the score is 1.

12. In all questions that provide response spaces for two numerical answers and require work to be shown for both parts, if one correct numerical answer is provided but no work is shown in either part, the score is 0. If two correct numerical answers are provided but no work is shown in either part, the score is 1.

13. In all 3-point questions that provide response spaces for two numerical answers and require work to be shown in one part, if two correct numerical answers are provided but no work is shown, the score is 2.

So it's a mystery.

Did Ms. K tell the kids she has to take points off for crossed-out work because you aren't allowed to cross out work on the state tests?

If so, is that what cost Christopher 2 points on his answer to number 17 (I'm thinking no. I think he got it wrong.)

And....here's the biggie.

Does the school need to dig out all the state tests Ms. K scored and check to see how many points the kids lost for crossing out incorrect work?

Have I mentioned that each school corrects its own students' tests?

Have I mentioned that the degree of training and attention to inter-rater reliability appears to be practically nil? [UPDATE 12-7-2006: Wrong. Christopher's English teacher says they get quite a bit of training. I doubt it's enough - this would be the state's fault, not the school's - but it's not nil. Of course parents don't know this because we pretty much know nothing of substance that goes on in our schools. We're constantly interviewing each other to try to find out what's coming up next.]

What a mess.

update

I have good news and bad news.

The good news is: Christopher knows how to do combinations.

He learned how to do combinations in class.

Then he remembered how to do combinations on the test, without having studied combinations the weekend before the test.

That's the good news.

The bad news is that apparently I can't understand what the he** he's talking about any more than I can understand what Ms. K is talking about half the time.

I wish I had a digital recording of the whole long series of permutation-combination exchanges Christopher and I have had today.

"Christopher, you got that answer wrong." [re: the answer Ms. K has in fact marked wrong]

"No, I didn't."

"Yes you did."

"No, I didn't, I got it right."

"I called L. She did the problem. You got it wrong. It's a Combination, not a Permutation."

"It's a permutation on the line."

"It's a combination."

"I crossed it out, I got it right."

"It's a combination."

"It's a combination."

"Christopher! That's what I just said! I said it's a combination. Your answer is a permutation, not a combination."

"It's a combination. I know it's a combination. I got it right."

"Who's on first?"

Now I'm starting to wonder.....maybe the book did cover combinations.

I mean....the whole section on selection without replacement...doesn't that get us into Combination territory?

I have no freaking idea.

I do, however, grasp the events of this our most recent foray into Phase 4 Summative Assessment.

1. Christopher recognized item number 17 as being a Combination problem.

2. Christopher correctly worked the problem, arriving at the correct answer. 220.

3. Christopher then decided that item number 17 was not a Combination, but a Permutation.

4. Christopher crossed out the computations for the Combination.

5. Christopher wrote the Permutation answer in the blank. 1320.

6. Ms. K marked it wrong, correctly citing as her authority in the matter item #6, above.

I'm too old for this.

how CA does it

-- CatherineJohnson - 19 Nov 2006

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