Shifting Assessment in a World with WolframAlpha

Oct 12, 2010 by

I let my students use Wolfram Alpha when they are in class and when they are doing their homework (um, how would I stop them?).  Because of this, I’ve had to shift how I assess on more formal assignments.  For the record, it’s the same adjustment you might make if you were using ANY kind of Computer Algebra System (CAS).

The simplest shift is to stop asking for the answers to problems, and just give the students the answers.  After all, they live in a world where they CAN easily get the answers, so why pretend that it’s the answers that are important?  It’s the mathematical thinking that’s important, right?  Giving the students the answers turns problems into “proofs” where the evaluation (grade) is based on the thought-process to get from start to finish. It also eliminates the debate about whether to award points for a correct answer with no correct process.

Here are two examples of problems from a recent Calculus exam (old and new wording).

I wish I had thought to do this years ago, because students who insist on just doing the “shortcut” (and not learning what limits are all about) now have nothing to show for themselves (the answer, after all, is right THERE).

Again, a student that knows the derivative rules might get the right answer, but the right answer is now worth zero points.  The assessment is now clearly focused on the mathematical thinking using limits.

Another reason that I really like this is that it allows students to find mistakes that they are capable of finding “in the real world” where they can quickly use technology to get an answer.  They are now graded solely on their ability to explain, mathematically, the insides of a mathematical process.

Wolfram Alpha also allows me to pull real-world data into my tests much faster.  Here’s a question about curve shape (the graph is just a copy/paste from W|A):

If you haven’t begun to think about how assessment should change in a world with ubiquitous and free CAS, you should.  You don’t have to change all your problems, but I think some of them should change.  Otherwise, we’re just testing students on the same thing that a computer does, and that doesn’t sit well with me.  If you can be replaced by a computer, you’re likely to be replaced by a computer.  Let’s make sure we’re teaching students how to think mathematically, not how to compute mathematically.

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Help Students Pay Attention to Test Details

Oct 7, 2010 by

Students lose SO many exam points because they just don’t read the directions and pay attention to details.  On the first exam, they usually discover this … but they don’t REMEMBER it for the other exams.

This is a very simple exercise that takes about 1 minute at the beginning of the test.

Just have the students repeat after you:

I promise … to read all the directions … for all the problems on the exam …

And if I finish early, … I promise … to RE-read all the directions … to make sure I haven’t missed some detail … or forgotten to come back to some question I skipped.

I understand that … it is not important to finish quickly … it IS important to demonstrate what I know … and once the points have been lost … the points cannot be regained.

Believe it or not, this results in a remarkable number of students that stay until the bitter end, making sure that they have been careful and answered every question completely.

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A Better Mousetrap for Multiple-Choice Math Tests

Dec 19, 2007 by

We’ve been having a rather spirited discussion in my department about a common final exam for one of the math courses, and the need for an easy-to-score learning assessment (i.e. multiple choice).

The two biggest problems regarding math and multiple-choice tests are

  1. Students cannot show and get credit for work.
  2. Students can too easily “try out” answers to each problem (especially on factoring problems and equation solving problems).

Regarding #1, there is, I think, a point in the semester when students should be able to demonstrate that they can do problems, correctly, to completion. Especially in algebra-level courses, there is often not a lot of work that they could show that I might give them credit for.

If it’s a 50 question final exam, and each problem is worth 2 points for 100 points total, how much partial credit can there really be? Students who get every single problem 75% right do NOT deserve a passing grade of 75%. Every problem 75% right means 100% of the problems done with some kind of mistake. That is not a “passing” performance.

Now… on to issue #2. I think I have a solution to this problem… seriously. Why do we have to use the five choices on scantron tests as only 5 unique answers? Why not let these five choices (A,B,C,D,E) generate 25 unique answers instead? Take a look at my new take on “multiple-choice” and tell me what you think:

It’s about time we thought outside the box on these scantron forms!

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