Chapter 3 - Test Corrections

At about this point in my geometry classes, the students would have had at least one test. I'm sure we all know that students and teachers have very different opinions about testing. The students perhaps think that tests are just an ordeal that they must endure, and after they have fnished taking a test may feel "I'm sure glad that's over!"

Teachers, of course, know that the purpose of a test is to assess student's knowlege. Perhaps another reason that teachers "give tests" is in an attempt to "make" the students study; maybe students would not study unless there were a test approaching. But in any case, when the test is over, the students feel that (however well or poorly they did on it) it is over and done with, "past history", a "done deal".

But truly, the most important outcome for the students would be for them to learn from their mistakes, if any. Every part of the school day, including testing, should be a learning experience. It is for this reason that I ask my students to write "Test Corrections".

In their test corrections, my students are required to do the following for each test question that they did not answer correctly:

1) Write the question. If the question was multiple choice, write the question and each of the choices. If the question was a proof, write the Given and the Prove statements.

2) Write the correct answer to the question. If the question was multiple choice, write not just the letter or number of the correct choice, but the word or words. For example: "B) the angle bisector". If the answer was a proof, write the whole proof.

3) Write at least one complete sentence explaining exactly and specifically why you got the problem wrong. You may not use generic reasons such as "I didn't know how to do it" or "I forgot what an angle bisector is" etc. For example, if the problem was to find the area of a given triangle, your explanation might say "the problem was to find the area of an equilateral triangle with sides 6 cm. I had the correct formula for area of a triangle: 1/2 base times height, and the base was, of course, 6. I knew that I needed to find the height, and I knew that in an equilateral triangle the angles are all 60 degrees. So I drew the triangle and the altitude. This formed two 30/60/90 degree triangles. I should have realized that the altitude was the longer leg of each of the triangles, but in my calculations I used 1/2 of the base and then took 1/2 again in the formula 1/2 base times height which meant that I used 1/2 twice so my answer was 1/2 the answer it should have been."

Here are some more examples of student work; my comments are in red:

My students were expected to write "reflections" on many of the assignments in this writing-intensive geometry class. In his reflections on the process of writing test corrections, Todd said: "At first I was very unwilling to do the test corrections. However, after doing some, I found that they helped a lot. Doing test corrections forces me to understand what I did wrong, and so I can avoid making that same mistake again. The fact is, after I have done my test corrections, I really do know what I am doing!"

Some of my students not only wrote clear and detailed explanations in their test corrections. Kristen not only wrote well, but also drew beautiful diagrams as you will see in the examples below:

As always, the students wrote reflections on their experiences. I was impressed by the students' candor, and touched by their honesty and sincerity. In a reflection on a particular set of test corrections, Richie said: "All right, I'm especially not proud of my big fat F on this test. I can't believe that I even got that. That's what I get for not studying the material. The thing is that I was just not ready for it and I didn't understand most any of it. Anyway, I am totally proud of these corrections. I finally understood the material and got every one of them right. I felt very confident when going into the next test and from then on I have not had any problems. I worked very hard to get back on my feet and I am proud of myself for being able to fight my way back up to the top."

Nicole had this to say about test corrections: "I really like test corrections because I think they help me to understand what I have done wrong and how to do it correctly next time. I always use them as a reference when studying for the next test. I learn a lot more than I would if I weren't forced to go back and figure out my mistakes. Even though they are a pain, I think that without them we would keep making the same mistakes again and again.

Christine added this comment: I really do think that I finally understand the purpose of test corrections. I learned to be more careful, for one thing, because so ofter my mistakes were caused by carelessness. In one case, I subtracted wrong. In another, I assumed too much from a diagram. I have to admit, I learn a lot more when I have to look my mistakes right in the face. Not only do I teach myself techniques for taking tests, but I have also learned to slow down, be careful, and check your work so you don't have to do the problem all over again!

And Jean had one last thought on this issue: "Although Test Corrections are just the biggest pain to do, the good news is that if I do a good job on them, and learn to avoid the same mistakes over again, I might not have to do test corrections next time!"

From the teacher's point of view, sometimes it may seem like too much trouble to not only grade tests, but then have to grade the test corrections after that! Whenever I have found myself thinking that way, I think about what my students have said about their experiences with this process, and I realize that it is worth the time and effort. After all, isn't that whey we chose to be teachers?

"The primary question was not what do we know, but how do we know it."

Aristotle