Lift Up Your Hearts!

I haven't written much on the Common Core school standards mess (just this), but since Florida give us the opportunity to take sample tests, I couldn't resist checking out what was expected of third graders in mathematics.  I was a math major in college and usually enjoy taking standardized tests, so it should have been a piece of cookie, as we say in our family in honor of one of Heather's college math instructors, who was, Ziva-like, idiom-challenged in English.

I'm strongly in favor of holding students, teachers, and schools accountable for what is learned in school.  What's more, I have always had little sympathy for those who whine about the standardized testing that comes with a welcome concern for such accountability.  For endless years schools have failed to work with parents, to open their doors and records to parents, and to provide parents any reasonable assurance that the massive amount of their children's time spent at school is not being wasted.  They brought it all on themselves with their high-handed, "we know best, you just have to trust us" attitude.

And to those who complain that too much time is being wasted in school with teaching to and practicing for the tests, I always say the fault is not in the test, but in teaching to it and practicing for it.  Any generalized testing system worth its salt should be able to count on the fact that test results are a representative sample of a student's knowledge; teaching to the sample undermines its reliability.

All that said, this is a test that requires practice, and specific, test-related teaching.  First, doing math by mouse clicks instead of paper and pencil is a non-trivial exercise.  In this I was aided by my hours of Khan Academy math work.  But certainly students need time and practice to learn the specific testing interface.

Second, and most important, even with a bachelor's degree in math I found questions that made me stare blankly at the screen.  I don't just mean i didn't know the answer:  I hadn't a clue how to begin answering the question.

I'd like to tell you how I did on the test, but when I finished I was presented with this annoying screen (for all images, click to enlarge):

Now that's just lazy website design.  Being lazy myself, and fully confident of most of my answers, I didn't bother to confirm them.  However, I did pull up the answers to the two questions I couldn't figure out for love nor money.  Here are the problems, for your own amusement, edification, or frustration.  (Scroll down after the second problem to see the answers.)

If I wanted to graph the data, I would simply set Blue to 3, Green to 6, Brown to 12, and Hazel to 9.  But what does "Use a scale of 3" mean?  That on the Number of Students axis, the number 1 actually represents 3 students?  If so, I need to make the Eye Color bars 1, 2, 4, and 3, which is not only ridiculous but can't be done:  the bar heights snap to multiples of three.  Does it mean that I should scale each entry up by a factor of 3?  No, because then I'd need one entry to be 36, which is beyond the range of the graph.

Okay, this seems reasonable at first, with the little trick thrown in that one X on the graph means 2 students.  I'm glad to see that third graders are expected to notice such subleties.  So I plot "Two students like camping" with a single X.  But wait a minute.  "At least 5 students like playing basketball."  What am I supposed to do with that?  I can plot 2 1/2 X's, but there's no obvious way to indicate that the number might or might not be higher than 5.  And what about "Twice as many students like hiking more than playing basketball"?  Who cares if they like hiking better than basketball?  Maybe they like camping better than either one.  And twice as many as what?  Even if you rewrite it as "twice as many students like hiking best as like playing basketball best," you're still left with the problem of how to graph "at least."

Scroll down for the answers:

It seems that all they mean by "use a scale of 3" is that the vertical axis labels should be multiples of three, which is totally unnecessary, and thus confusing, since the axis is already labelled.

Except for the poor wording, this turns out to be a good puzzle, and I like to think that if I hadn't been rushing through the test—because I was in a hurry, and it was for third graders, after all!—I would have caught it.  Assuming that "twice as many students like hiking best as like playing basketball best" was meant, embedded within the graphing question is a simple algebra problem:  if B = the number of students who prefer basketball, then the number of students who prefer hiking is 2B, and thus 3B + 2 = 32, or B = 10 and 2B = 20.  But for third grade?

My limited experience more than once made me question the language abilities of whoever wrote the questions, but I have to say that a problem of this complexity on a third grade test is impressive.  It's not a hard problem, but it requires realizing that it is not a simple graphing question.  That's a subtlety I'm not accustomed to on standardized tests at this grade level, and might be indicative of an exam that actually measures students at the higher levels of skill and knowledge, instead of levelling them all out at "99%."  Unless, of course, you teach to the specific questions.

I came out of the exercise with no strong feelings one way or the other about the new Common Core approach to math.  All in all, it's very like the Khan Academy approach, so there's plenty of practice available for those who want it.  But I'm not sure what I think of the Khan approach.  It's not unreasonable to demonstrate multiplication of multidigit numbers via diagrams like the one below, but is it useful as a primary teaching method?  Does it really increase mathematical insight?  That's more than I know.  But I'm pretty sure that taking someone who already knows how to multiply and making him spend much time on this kind of exercise is less helpful than educators would like to think.  Especially if it's just to pass a test.