Tuesday, December 13, 2011

One Size Fits All!

If you are like me, you feel skeptical any time you see "One size fits all," on an article of clothing. If we question it when it comes to a piece of fabric we intend to drape over ourselves occasionally, why would we accept it when it comes to our education? Yet, is this not what we are doing when we advocate for standardized test and uniform classes?

It is getting to the point where it is difficult for me to talk about education here, simply because I have so many posts on the subject. While I don't wish to assume that you have read all my previous posts, although I egotistically wish that you had, I also don't wish to rehash old thoughts at length. So, in an attempt to compromise between competing necessities, I shall give an overview of a thought when I introduce it, sufficient to get through this post, then link to a more comprehensive post for your further investigation should you so choose.

Of course the idea of "standardizing" tests and making classes "uniform" appeals to our sense of fairness. Casual logic, it seems, supports the idea that if we make everybody do the same thing then we must be treating them fairly. Unfortunately, this seems erroneous. Setting aside more heady problems, like the exact nature of fairness, one might simply note that some people test better than others. Simply picking an arbitrary method of evaluation and then applying that rubric to everyone in no way guarantees fairness. If fairness is not the ultimate goal of standardization, what is then?

I would argue that it is interchangeability. I have previously introduced the idea that education is being industrialized, and just as identical, interchangeable parts make it easy to keep the literal machines of industry running, interchangeable workers make it easier to keep the metaphorical machines of industry running. If position P requires knowledge K to perform correctly and degree D signifies that the degree holder possesses knowledge K, then if the worker holding position P becomes inoperable, replacing them is as simple as finding candidates with degree D. If this all sounds cold, inhuman, and mathematical to you, then welcome to the Enlightenment.

Of course, arguing that something makes the economy run more smoothly does not a justified criticism make, even I will acknowledge that. Even arguing that it causes the devaluation of skilled labor because skilled workers are easier to replace only seems like a first world problem. However, I would argue that it is simply a bad way to educate people.

Consider what forms of thought lend themselves to standardization. Facts are quite standard; no matter who you are, the names and dates of historical figures remain the same, the main character of the Odyssey is unchanged, and the ratio of a circle's circumference to its diameter will be pi, local legislation notwithstanding. Procedures too remain unchanged; the quadratic formula will give you the roots of a second degree polynomial, one can construct a haiku if they know what a syllable is and have seven fingers, and soda will erupt in a bubbly gyser if a bunch of pills are dumped into it. What is lost is understanding. What a haiku means, what the message of the Odyssey is, even what the significance of the roots of a polynomial is will change from person to person.

Worse still, since we seem to understand that understanding is important, we attempt to brutalize it until it shapes up, gets in line, and conforms. When asked what the main message Stopping By Woods on a Snowy Evening is the young might say it is about dying, the old that it is about living, and the naturalist about the enduring importance of nature. You cannot standardize understanding because it is as unique as the person doing the understanding, and people are not interchangeable, nor should we be.

So then, if one accepts my hypothesis that standardization is inherently bad and cannot be redeemed by making the tests easier or more relevant, what is to be done? I think a promising beginning would be to alter the nature of evaluation. When I simply talk with my students about mathematics I get a highly subjective idea as to their level of proficiency, which nonetheless is occasionally more accurate than the results I get from exam scores. I also like the idea of group examinations, where classmates are able to teach each other so the exam becomes both an evaluation tool and a learning tool. One could question students individually afterwards on the content of their answers to make sure all group members understood the groups method for solving the problem.

Even the traditional method of individual test taking could use serious reform. I wrote a rather lengthy post focusing on the fairness issues of giving timed exams. Left to my own devices I would prefer to give students whatever length of time they required on an exam. Personally, I don't feel that extra time is all that helpful, as one will generally know what one is doing or not, but if it would be helpful to the student, why not allow it? Even more radically, why not allow the student to attempt the exam as many times as they need? Of course, not the exact same exam, but one over the same concepts, this is how online tutoring programs such as the Khan Academy pace their students. A dismal exam grade should reflect a dismal understanding of the material, and why would one accept that a student has a dismal understanding of a subject and just move on? The only reason that I can see to move on would be if one had a predetermined goal which all students were supposed to meet by a common deadline, in short, standardization.

Of course, reforms such as these would require great bravery. We would have to trust that educators know what is important and how to determine whether their students have learned it. I think that even the first is problematic, but I can hardly fault them for that, as they themselves are products of a rote education more focused on memorization than understanding. I do believe that our educators are intelligent people capable of actually learning their subjects if given the chance, and I believe the same about their students!


Karen said...

I think that "the system" would be anxious about your suggested ideas because they are concerned about having a measurable way to determine whether or not kids are learning/teachers are doing their jobs. I think most educators agree that standardized tests aren't very good measures of success; the question is, would it be better for our students to not have to be measured by these tests? It's hard to tell since that isn't terribly measurable. :)

Regarding your new test-taking ideas, I will say that those are all ideas that were discussed while I was in teacher-education mode. I apologize if I have told you this before, but when I was student teaching, one of my cooperating teachers went to a conference where they suggested that teachers should pick some core things that math students SHOULD know/be able to do to pass the class. To show their abilities, they could take "the same" test over and over until they got the problems all right. We tried something like this (with a total of 10 problems from one unit, I think) in our Algebra II classes, and they took those tests over... and over... and over... and over...

I wrote maybe 3 versions of that test while before I completed my teaching, and then the teacher (and his next student teacher) continued for awhile longer in the spring. I eventually asked, and it sounded like in the end they finally just gave partial credit and got a score in the book.

I think what I learned from this is that students haven't been trained to aim for accuracy on problems. A lot of the students would make small arithmetic errors over and over again, and thus get the problems wrong each time. Perhaps we give too many partial-credit points out? Quite possibly, in fact. We don't give students a reason to not be sloppy. They know that they should generally know how to do something, but they don't necessarily have the discipline to carefully complete a problem and find their own errors. That's unfortunate to me because I view that as a valuable life skill.

Anyway, these are the things that I think about as I consider how I will grade exams next term... !

Max said...

I can suggest another reason for "moving on," which is that even in your core concept model there may be multiple cores that a student must understand before they are accepted to leave education and join the workforce.

And in any class of more than two people, wouldn't it be very boring for the students who picked up the concept quickly, to wait and circle back through a topic? Sure, there is always more to learn, but you risk the Math 111 problem where people stop showing up because they think the rest of the term will be just as easy... which it isn't.

Kenny said...

Yes, a measurable way to determine whether the kids are learning and teachers are teaching is all well and good and fuzzy like baby teddy bears, but how much good is it really doing if it isn't measuring those things? I'm not advocating we abandon tests altogether, just give the tests to the educators, and have some sort of peer oversight, because I think educators are a lot more competent to over see each other than administrators are!

I agree, partial credit is annoying, and it makes grading much more time consuming than it would be otherwise ;) However, one of the benefits of having something with an actual brain in charge of evaluating student successes is that you can tell when a student has learned, for example, how to take a determinant, and is only getting the answer wrong because after multiplying small integers together 20 or so times almost everyone must make at least one mistake.

One skill I think students don't develop for some reason is the ability to proofread their own mathematics. I was asked by a student during the final exam if he should be suspicious that an area turned out negative. Of course I agreed that he should be suspicious, and quickly noticed that he'd reversed the bounds on a definite integral, but since this was an exam I didn't want to overtly correct him. Nonetheless, had he noticed that error it would have been very easy to fix. Obviously he was not a physicist, as they would have simply turned the negative positive and assumed there was an orientation problem somewhere ;)

Max: I definitely agree that lecture cannot stop as long as at least one student is progressing satisfactorily through the material. However, if the students could learn it from lecture then they wouldn't be in there unfortunate situation, assuming, of course, that they come to lecture. I envision students who need to spend more time on a subject doing it outside of the formal classroom. Or, and this is a cute idea I think, we could further partition classes, so you would do chapter 2 and then if you didn't do chapter 2 satisfactorily you would switch to another cohort who was going through chapter 2 as your previous cohort moved on to chapter 3. Of course, this seems to be the idea of breaking math up into separate classes, but since a class is such a large investment of time and energy it seems so much more troublesome to repeat it as necessary. In short, I think students should just work with teachers in sort of a Greek academy style learning environment, none of this required syllabus for a class nonsense, you learn that which you learn ;)