As we approach the end of the school year, I find myself getting more and more frustrated about my students’ struggles with high-level thinking. Every year, it seems like they’re less and less able to figure out how to solve problems that are different from the ones they’ve seen before. Each year, I lose a little more ground.
I can remember in my elementary school math classes having to figure out how to represent word problems with mathematical calculations, and having to do proofs of simple concepts, such as the distributive property of multiplication over addition. As I went through middle and high school, those proofs incorporated newly-learned skills of algebra, geometry, and trigonometry, but at every level, the curriculum taught the necessary skills, and then applied them to a goal of figuring out what a problem was asking, representing the problem symbolically, and then solving it. Using Jean Piaget’s terminology, we were taught the building blocks of formal operational thinking starting around fourth grade, and most of seemed to have a reasonably well-developed ability to think in abstract terms by the time we graduated from high school.
In this No Child Left Behind era, schools are judged on their students’ performance on standardized tests. The tests measure the kids’ ability to solve specific problems, so their teachers teach them to solve those specific problems. Most of the test questions are given to students already in mathematical notation, which means they can pretty much get away without having to come up with representations of problems on their own. Instead, they learn step-by-step techniques for solving specific problems, and how to recognize which set of steps apply to which problems. If they’ve never learned a plan for a given kind of problem, they don’t know how to even begin solving it. In high school, they’re firmly grounded in concrete operational thinking, and they resist tooth-and-nail any attempt to push them toward formal operational (abstract) thinking.
Because chemistry (and physics) are largely applied math, science teachers in those disciplines have depended for years on these problem-solving skills being developed in early math classes. Students would come into science classes with the problem-solving skills needed for the class; the science teacher’s job was to teach the basic scientific concepts, and then leverage the students’ problem-solving skills to teach them how to solve the complex problems presented by the specific scientific discipline.
When science teachers can no longer depend on students arriving in our classes already possessing the problem-solving and high-level thinking skills that they need for the class, we have to choose between two undesirable options. Either can take class time to teach those high-level thinking skills, which leaves less time to teach the curriculum of our own discipline, or we can teach mnemonics and low-level methods that allow students to solve specific subsets of high-level problems (most of the time) without actually understanding what they’re doing. The state DOE mandates the curriculum and writes the test that is supposed to assess the curriculum. This means that, while the students are better served by the first option, they’re better able to pass the state tests if we choose the second.
So science teachers now end up contributing to the problem. There’s a fundamental assumption in education that basically states that if a student can reliably get the right answer to a class of problem, then the student must understand the problem, the solution, and why the solution works. In my experience, this is simply not the case. As an illustrative example, I was helping an honors student (who has another chemistry teacher) with her end-of-the-year review project yesterday. The student asked how oxidation numbers related to binomial nomenclature. After a little questioning, I discovered that this student did not understand the connection between an element’s placement on the periodic table and the number of valence electrons, why it’s necessary to balance the charges in an ionic compound, and the connection between the charges and oxidation numbers. At one point, she said, “I never understood how to use the periodic table. I just memorize what I need whenever we have a test.”
I don’t know what the solution to this problem is. I suspect that any real solution would involve a shift in focus from specific content items to thinking and problem-solving skills. However, specific content items are easy to teach and easy to test using a machine-scoreable multiple choice test. Problem-solving skills are much harder to teach, and much harder to test. A focus on problem-solving skills would probably also require schools to place a lot more trust in teachers, which would mean divesting themselves of the opinion that the solution to the problem is to hand a foolproof script to a bunch of certified trained monkeys.
However, given the politics of the situation and the fact that those politics aren’t going away, I honestly don’t know if there is any way to reverse the trend.
