## Friday, August 1, 2014

### A Sloppy Computerized Test

My college is running a program called Math Jam for two weeks before the semester begins, and it sounds fabulous. I'll be teaching it for the first time, starting on Monday. We use MyMathLab, and our director said students in prior years (who loved Math Jam) found the program helpful. So I will use it with my students next week, along with lots of other, more interesting mathematical explorations.

I checked out the first test just now, and got below 90% in a Beginning Algebra, or perhaps pre-algebra, topic. Let's look at why. I had 3 questions at least partly wrong out of 22.

#1
On an equilateral triangle, they asked for the height. I found it, rounded to tenths as requested, and got that right. Then they wanted me to find the area using the rounded answer. I did not do that. I did what I teach my students to do: Use the exact answer in your calculations, and only round at the end. My answer did not match theirs.

I can't get back to their problem now, so I will make one that's similar. Suppose the sides are length 6in. Then the height is 6*√3, or 10.3923.... If they are asking us to round to hundredths, we'd report 10.39in for the height. Now they want area, and they ask me to use my 10.39 as the height. But the proper area (in sq.in.) is 62.3538... and by their method we'd get 62.34 sq.in. I put the proper answer of 10.35 sq.in. and got it wrong.

#2
I got 0.55 as an answer, which they asked me to round to tenths. Both 0.5 and 0.6 should be right, as 0.55 is exactly in the middle of these. But only 0.6 counts as right on this test, and I had (randomly) chosen 0.5.

#3
This one is the most interesting. They gave the diagram below, which looks a bit badly done to me. The right angle mark toward the left does not seem to coincide with the line below it, making it seem like the angle isn't really a right angle. Not a big problem, I can still assume a right angle there. But they have only marked two right angles. I do not believe I have enough information to determine the area of this figure unless I know more about the angles. I believe the one unmarked line segment has an unknown length. I think they meant to show two attached parallelograms (or a parallelogram attached to a rectangle), but that's not a given from this diagram.

What do you think?

I think they need to learn more about rounding, and more about what one can read from a figure. Hmm... I wonder if all their tests will be this sloppy.

#### 10 comments:

1. #3 doesn't appear to be well-constrained. I haven't done the calculations, so I'm only 99.9% sure that the area isn't a constant, but I suspect the difficulty makes it a bit much for an algebra/pre-algebra test...

2. Yes. Can we describe the area as a function of the one length not given? That would make a very interesting problem. (They are almost surely assuming a bunch of parallel lines in this.)

I took the next one, and got 100%. (Which to me means they got 100% on doable, but ...) They asked for names of properties displayed. I don't like that sort of question. Does knowing the words for distributive and associative properties help students in any way to *do* algebra?

3. Ugh... MyMathLab. There are so many things that I would change about it. So many things...

The most frustrating was when I taught College Algebra and Business Algebra at the same time, but the courses used different textbooks. The exercises associated with the College Algebra textbooks were decent enough, but the ones associated with the Business Algebra were... not.

And the pricing! My god, talk about overpriced. I think that was my biggest beef with the whole thing. It was a product that I think was worth \$30 maybe. And they charge \$90 for it.

4. Neither I nor the students are paying for it, thank goodness. I'll have more to say after using it for two weeks.

5. Really interesting. As a middle school teacher who writes a good chunk of my own curriculum (read: questions students answer, problems students solve) because I don't have one I like to work with, I catch these types of mistakes in material I create all the time. I often compensate by being descriptive (shown below are a parallelogram and a rectangle) but it's not the same as a well-written set of textbook problems that fits the scope and sequence you are teaching. If we want students to truly Attend to Precision, we need to Attend to Precision ourselves... definitely something for me to work on, either in writing or finding great materials.

1. Similar to Sue's suggestion, I'd encourage you to make explicit the idea that there might be mistakes in the way problems are posed and bring it out as part of the curriculum. It might help to give students a bit of a recipe for how to respond, for example:
(1) write down why you think the problem is wrong/missing information/has conflicting information/etc
(2) If you are missing information, can you work out a case where you fill in the missing data?
(3) Can you think of another way to salvage the question?

Also, I think the best lesson about attending to precision is when they see examples that aren't precise and then see the consequences of that imprecision. In improv comedy you can experience this viscerally: students pretend to give each other blind offers (handing a mimed, empty box or shouting and pointing "My goodness, what's that?!") and then the next student has to continue the scene. Students who get vague offers (as in my examples) will almost always feel frustrated that the whole burden has been thrust on their shoulders. Students who are given more information ("my goodness, what's that elephant doing here?") have a much easier time continuing.

6. Dear 5-12-13, please don't pick on yourself over mistakes. No one is losing points on a standardized test that could be high-stakes, based on the problems you write. And if you tell your students they get extra points for finding your mistakes, then it's a win-win every time you make a mistake. ;^)

Whereas this was made by a big publisher, costs someone lots of money (in my program I believe its coming from a grant), and because it's coming from 'above', the students might think it knows more than I do. I think I can get past that quickly, and may take my own advice. Cheers and possible rewards or awards for students who find similar mistakes in the tests. Let's make it a detective game, which is more my idea of what math is than these tests.

7. Hi Sue,

I enjoy your blog. Did you contact MyMathLab customer support about these problems?

8. Not yet. I think it would be wiser to get a better big picture before contacting them. But that is definitely a good idea.

9. If the segments marked 1.8 are parallel, then the answer is unique. There is no indication that they are parallel. Perhaps a right-angle mark on the other end of the dashed line?