Tuesday, February 4, 2014

What are tests good for?

Second post!  What are tests good for?

I recently came across a blog post asking  What does a test “test”?  Given that the last comment was from 2011 I am clearly late to the game on this post, but it sparked some thinking on my part.  To recap the post, the major thrust is that tests do not measure what it is generally assumed they measure.  To quote:
….  Tests are usually thought to be reliable indicators (if not measures) of how well students  engage with the material being taught to them, and is often believed to be related in some correlational way with their mathematical ability.
Where a student ranks – their class standing – on a test may well be an indicator of both those things.
I want to argue, however, that what a test really tests is the teacher. A test, in my view and experience, tests a teacher’s ability to set a test at the “right” level…..
Franky [sic] I feel we put too much emphasis on tests and examinations. My own preference is for more collaborative project work in which students can exercise their ability to think, to reason, to plan, and to work toward a goal, utilizing their skills and talents in conjunction with others.
First things first: my department has common post tests for each class.  The exam is roughly 20 questions that cover the basic learning objectives for the course.  We actually have created a test bank for the questions to help with test security, but basically everyone is giving the same exam.  So that means in some sense I have to train the students toward that even if I personally wanted to never give a traditional exam. 
In that vein, I first and foremost see tests as a deadline.  So in that sense a test exams how well you can learn when there is a deadline on learning the material.  I see this as the difference between me saying “You know, at some point I would like to learn about Project Based Learning and use it in my classes,” and me saying “”I just put in a proposal to discuss how I did Project Based Learning this coming semester.”  The second forces me to plan my time accordingly rather than keep putting it off. 
(2)        This relates to my second idea about tests, they allow me as a teacher to know what the students know when we launch into a new set of ideas.  So I have a test in my calculus classes over basic derivative rules before we discuss chain rule.  Then I have some assurance that the students know the basic rules before we launch into chain rule.  Likewise, I have a test over derivative rules before we get into relative extrema for many of the same reasons.  As every teacher knows, having a test does not mean the students will all learn it, but having a deadline seems to help.
(3)          Third, I think tests can be used as a measure of understanding.  For example, after discussing the definition of derivative and the idea of rates of change, the derivative as the slope of the tangent line, and the basic derivative rules we have a test.  On that test I typically include a question like the following:  (Very similar to a question from the Hughes-Hallett Applied Calculus)

The growth graph in the following figure shows the height in inches of a bean plant during 30 days.  On the 15th day, the plant was growing about _____ inches/day.  Round to 2 decimal places.

In my mind, this question is asking a student to identify the concept in a new area.    In a real sense, this is also helping to differentiate the A, B, and C students.  Almost all of the A students get this, a majority of the B students get this, while a large number of the C students will answer 11/15 instead of 14/15.

(4)          Tests can also be a summative assessment.  Basically, I give a similar problem at the start, in the middle, and at the end of the unit of material.  Then I measure how much the student progressed on the material.  As I said above, at some point I have to distinguish what this student knows about the material in order to assign a grade.  I may not like it, but that is the way my job is set up right now.
(5)          Finally, (because I am tired of writing this, not because I have exhausted all of the ideas behind testing!) there is a test as an indicator of limitations.  You might think of this as showing off by the instructor.  As I say to my students, I can write a test that would take me most of the class time, but that would kill all of you.  But what does that prove?  That I am better at this material than you right now?  We knew that at already.  I think this last point is some of what the blog post is getting at.
To that end, I am trying out group tests in both my statistics classes and my liberal arts classes this semester.  I plan on posting about this in about a month once the first couple of rounds are done.

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