A couple semesters ago, I had an incident in my developmental math class that has transformed my philosophy on education.
Let’s set the stage:
This was a MAT 65 class (Beginning Algebra for those not familiar with Hopkinsville Community College’s courses). We were getting near the end of the course. This course is heavy in algebra manipulations (i.e. what steps do you do to get the right answer). At the time we I was teaching the course, the departmental philosophy was to not allow calculators in the class…or at least on the common tests. While I adhered to this rule for the common tests, I tried to do as many applications as possible during the course as appropriate. I try to impress upon the students that the skills are nice, but the real world rarely has “nice” numbers. Using a calculator is essential many times, so I allowed it at these times. While most of the class was able to manage on the quizzes without the use of a calculator, I had one student who really struggled. He had the algebra concepts down pretty good (or at least as good as the rest of the class), but when it came to taking the tests he struggled. I eventually realized that his skills in basic addition and multiplication were his weakness. He knew what steps needed to be done, but wasn’t getting the right numbers.
Near the end of the course, I gave the class a project one day.
I took it from an episode of Seinfeld. In this episode, the character Newman noticed that recycling in Michigan paid an extra 5 cents per can than in New York. He thought that if he rounded up enough cans, he could take them to Michigan and collect a larger reward. The character Kramer tried to convince him that the costs of transporting them from New York to Michigan would be more than the profit gained.
I gave a similar problem to my class. I asked them to create a scenario for transporting cans from Hopkinsville to Michigan. The algebra (at the level of the class) involved in this problem was minimal. It was mostly some arithmetic calculations mixed in with a few geometry formulas. I let the students use a calculator.
What I noticed as the students got started
was that most of them struggled to get started. They were able to find the numbers that they thought they needed, but when it came time to do the appropriate calculations, they were lost. They would’ve known how to do the calculation, but didn’t know what to do.
Conversely, the one student who struggled without a calculator was the “class champion” for this activity. He immediately knew what numbers he needed to get, what do to with them when he got them, and how to get the final answer. He easily had the best summary in the class and got it much faster than anyone else.
So here came my epiphany
….what is our job as teachers? Are we simply to cover the material as presented so the students can be successful on the tests (teaching math in my case) or are we supposed to arm the students with the skills and make sure that they are able to know how to use them when they are called for (quantitative literacy in my case)? The results of this class activity have transformed my philosophy of teaching. It doesn’t do me or the students much good to teach them material just so they can perform on a test. If they don’t know why they need these skills and how to use them when asked, then I feel I have not done my job properly.
In the time since this incident I have tried to re-organize all of my classes.
I am trying to minimize the use of exams and instead have created more activities/projects like the one described above. Students will be graded on how well they can use the material that I teach them as opposed to simply memorizing it. I am finding that this approach is working well. As a teacher, I am less likely to teach a skill unless I have a good activity to show the students why it is relevant. It has taken a lot of work to create activities and projects that incorporate the needed skills that can be completed in a timely manner, but I am getting there. It also involves telling students on the spot “this isn’t right” as opposed to a number on a test paper as it is returned.
However, I am finding that once the students realize what is expected of them they are working harder to actually learn the material. I am also finding that the students are accepting their lack of understanding of the material. When asked to perform on the spot, students are quick to admit that “they don’t know it”. When these occasions happen, I find that those students have a much better attitude about learning the material for the next time.
Oh, and one final effect of this activity:
When I shared this story with my colleagues, we decided to re-visit our departmental philosophy on calculators. We now allow calculators in the MAT 65 course since we realized that the lack of success for some students was not the conceptual ideas that we were supposed to be teaching….it was the number-crunching. Allowing calculators, we are finding we have more time to spend on the concepts as we don’t have to continue to re-teach the arithmetic portions.