kitchen table math, the sequel: oops

## Tuesday, August 21, 2012

### oops

Sorry to be out of touch -- our Long Goodbye (Chris goes to college tomorrow) is taxing, and taxing is time-consuming.

Am checking in to leave this image from the new issue of Education Week. The legend says it was "adapted from Smarter Balanced Assessment Corporation."

Apparently something was lost in translation. (Page 5)

Like the meaning of two-fifths.

Consortia Provide Preview of Common Assessments
By Catherine Gewertz
Published in Print: August 22, 2012

Anonymous said...

Some of us are slow.

-Mark Roulo

Anonymous said...

I don't know. I agree entirely with the redesign. The first question isn't a math question at all but a "guess what the teacher means" question. A, B, and C all represent 2/5 equally well, because they all show 2/5 shaded. Mathematically, they are all equally good answers. But instead of a math problem it's a mind-reading problem, and students are supposed to guess that Teacher likes one of the three correct answers (probably B) better than the others. Students whose mind-reading skills are poor will get the same grade as students who don't know what 2/5 is.

The redesign to the second format is much improved, and more likely to demonstrate actual math knowledge rather than test-taking or mind-reading ability. To be precise, of course, students should be allowed to take this test with a ruler.

Michael Weiss said...

The wording of the stem of the first question is odd: What does "best represents" mean? A, B, and C all represent 2/5, but presumably one could argue that (according to some unstated criteria) one of them represents it "better" than the others. Since no criteria are available, however, the question is ambiguous and there is no clear answer.

It strikes me that wording like this is more common on tests of teacher knowledge, but there one (usually) states an intended purpose: "A teacher wants to show that ______. For that purpose, which of the following best represents 2/5?"

And now, for a test of teacher educator knowledge:

How could you fill in the blank in the above stem so that the correct answer is A?

How could you fill in the blank in the above stem so that the correct answer is B?

How could you fill in the blank in the above stem so that the correct answer is C?

Anonymous said...

I like the redesign. It's a significant Improvement over the original.

The redesign is clearly ascertaining if the test taker knows what two fifths is. I do not know what the original test was ascertaining.

kcab said...

I think the problem becomes clear if you look at the document that was linked ("Smarter Balanced ASsessment Corporation"). B (in redesign) is considered an incorrect answer, because the rectangles are not all the same size. Personally, I can't tell this at all from the figure displayed here. (But then, I also have difficulty proving I'm not a robot in order to post a comment.)

Anonymous said...

"B (in redesign) is considered an incorrect answer, because the rectangles are not all the same size."

Then the question is *HORRIBLE*.

The sizes *look* the same, *and* this is true for (a), (c), and (d) as well. If the sizes in (b) are meant to be different, then they need to be obviously different.

As it is, it sounds like the redesign teaches that "orientation" is part of fractional size.

Sigh.

-Mark Roulo

Anonymous said...

For completeness, you should probably consider the possibility that you *ARE* a robot. Like in Demon with a Glass Hand.

-Mark Roulo

Michael Weiss said...

"B (in redesign) is considered an incorrect answer, because the rectangles are not all the same size."

Then the question is *HORRIBLE*.

I could not agree with this more.

Anonymous said...

Could be a translation to computer issue....might be more clear in print. If it is clear in print the rectangles are different sizes, then I'm pro the rewrite of the question. The original is bad either way.

It's important for kids to understand that 2 fifths is only well defined if the fifths are the same size. If it is not clear in print, that's a problem.

kcab said...

If it's a translation to computer problem (seems likely), that could arise in testing too.

I agree with your second point, but I think the sections need to be clearly different sizes to someone with OK, but maybe not perfect, vision.

Catherine Johnson said...

Have only read Mark's first comment, so everyone may already have discussed this .... but what struck me was the fact that the Ed Week artist mis-drew the original question: "Which model below best represents the fraction 2/5?"

In the original, only one image actually represents 2/5.

In the artists adaptation, three of the images represent 2/5 (or at least appear to).

I'm jumping to conclusions, but it seems to me that neither the artist nor the editor has much idea what 2/5 means ..... I don't think you could make a mistake like this if you did.

And, btw, I don't think you need a deep understanding of fractions NOT to make the mistake that was made here.

Michael Weiss said...

Ah, I see now. We were looking at the two versions in the Ed Week article, whereas you were looking at the original version in the linked PDF on p. 5. In that one, the other options are more clearly wrong: C, like D, shows a part / part comparison (2 columns shaded, 5 columns unshaded) rather than a part / whole comparison. I still think A is ambiguous: although the vertical rectangles are skinnier than the horizontal rectangles, they are also longer, so it is at least plausible that they are equal in area. But this is where the phrase "best represents" finally makes sense: A may represent 2/5, but B represents it better, not because the orientation of the parts matters but because the parts are more unmistakably equal in area.