Thursday, February 18, 2016

Math problems of the week: new SAT math problems

A recent article in the NY Times raises concerns about the reading demands of the new SAT questions, even in math. The article links to the following sample problems:

Extra Credit:

Does anything else stand out to you about these new SAT math problems, besides the excess verbiage?

Auntie Ann said...

Any kid halfway through algebra should be able to do those in a second. If you've done SM, you probably don't even need algebra either.

lgm said...

I will have to disagree about excess verbiage. The usual excess verbage examples contain red herrings. These are straightforward word problems. Even the answers are not tricky.

Niels Henrik Abel said...

Along lgm's lines: Students do need to learn to separate the wheat from the chaff. There is something to be said for extraneous numbers in a word problem, if for no other reason than to weed out the kids that are just grabbing any numbers they see and performing mathematical operations on them. Believe it or not, I have encountered such students as a tutor. These are students who have a vague idea that they're supposed to calculate *something*, so they just start punching away, without trying to sort through the information given in the word problem and see how it all fits together.

But the word problems that delve into so much backstory - meh. I get tired of all the cute little scenarios, and the weird names. Nobody's named Mary or Jack anymore, apparently.

Niels Henrik Abel said...

That being said, there are students who, on the other hand, completely ignore pertinent information in word problems. I tend to tell my students that generally speaking, story problems are not in the habit of giving excess information, so if there is unused data/info, they'd better look and see if they're overlooking some crucial fact. It seems like students tend to fall into the ditch on one side or the other, because they can't differentiate between pertinent and extraneous information.

ChemProf said...

Yeah, these were remarkably straightforward. And only one even required you to do any algebra (or a bar model, anyway).

treehousekeeper said...

My Algebra I student just asked me yesterday if any of what he was learning would be on the SAT. What I see here, he could easily do right now, and he is only a third of the way through the book.

lgm said...

Now that my internet isnt intermittent and captcha is working I would like to answer your ?. The other thing I notice is the strange terminology. 'which of the following' rather than 'which expression' in 1, 'what is the meaning of the value 108 in this equation' rather than 'what does the term 108 represent in this equation', the equation in 3 is referred to as a model.

I was going to post some examples from Dolciani Alg 1, the text used by 50% of students in my high school, all of whom were prepared to take Alg 1, none socially promoted in to it. What you would notice would be the use of decimals and numbers that require pencil and paper rather than mental math for the computation stage, as well as 2 step thinking. I doubt the internet will be stable long enough for me to post, so I will settle for encouraging the reader to look at their own copy .

Auntie Ann said...

lgm, as I've said before, I think a lot of the tortuous wording in modern tests comes from having them computer based. When kids could work things out on paper, then fill in a bubble, the problems could be of a different nature than today, when kids can only think about the problems and not work them.

lgm said...

Its the same torturous wording we see in texts written for below grade level students. It appears a readability formula has been applied.

Scrap paper is allowed on the math exams. One always had to use scrap on Regents Exams as there wasnt always enough room in the problem box area. Same for local tests for gr 4 -12.

Jen said...

Scrap/scratch paper has never been allowed on the SAT (or at least, not for decades). You have the spaces on the pages of the test booklet.

Even the new SAT is not computer based, at least not yet for most students: "Computer-Based Testing: The new SAT will be available in paper booklets at every testing location, but the SAT will begin to offer tests on a computer in select cities."

For a computer based test, I imagine they will have to hand out scrap/scratch paper (in a specified quantity, I'm guessing).

Unknown said...

Did I miss something or does question 4 not make sense. They tell you the number of salads that were sold in the sentence and then they ask for the number of salads sold for the answer, (which is not included as one of the offered solutions.)

lgm said...

Its is given that 'a total 209 salads and drinks' were sold in one day. The word 'of' might be after the word total, but snipped so we dont see it. The word total signals the reader to understand that 209 is salads plus drinks, not solely salads.

Katharine Beals said...

The word "of" is after the word "total" and hasn't been snipped. You can see it here.

But the wording is indeed poor: "a total of 209 salads and drinks" is inherently ambiguous.

In one interpretation (the one that to me leaps out at first as the most obvious one), one distributes the "total of 209" across "salads and drinks," yielding 209 salads and 209 drinks: 209(s + d) = 209s + 209d.

Only easiness of that question and the lack of a correct choice for that interpretation rules out this interpretation.

lgm said...

Part of problem solving and sharing solutions is defining assumptions and understanding conventions. If it was a total of 209 shoes and socks, would you assume it was 209 of each? If you did and you worked the problem that way, you might not find your answer amongst the choices, depending on the test maker's purposes. More likely you would recall the exercises you did in class, where 'total' and 'altogether' were key words noticed that defined a set and the correct interpretation. This test is summative, so it assumes correct instruction.

The word 'of' is not visible to me, nor are the rightmost three characters of most lines. The formatting is not optimized for my device apparently.