There was a movement back in the 90’s to stop teaching rigorous mathematics and replace it with group work, calculators, and guesswork, with the idea being that students would learn the material better if they discovered it on their own (with some guidance from the instructor). It sounds like a good idea at first, but the result is students who can’t do even basic math. They may have some “feeling” about division, but don’t you dare ask them to actually do it. This approach drags down the people who would ordinarily be high achievers by covering less material less rigorously than a traditional course. The emphasis on group work results in what is essentially an exercise in effective cheating. Motivated students do the work while the rest of the group writes down answers, learning nothing in the process. Motivated students who somehow manage to get paired with other motivated students wind up splitting up the workload, so they end up doing less and having a weaker grasp of the material.
I see the results of this “education” in my classes. For example, there are many engineering majors who don’t know how to resolve vector components. If we get lucky, at some point they saw an example that involved trig functions, so they just randomly guess until they arrive at the right answer. Does x = r cosθ? r sinθ? r tanθ? What is θ anyway? That’s the good scenario. The all-to-common reaction is a blank stare; the students simply have no idea where to even begin. They know conceptually that vectors can be resolved into components, but haven’t the foggiest notion of how to go about doing it.
A similar disaster is unfolding in physics education. Translating problems from words on a page to mathematical formulas that can be manipulated to get useful results has been de-emphasized and replaced with conceptual ideas and misguided notion of self-discovery. While those conceptual ideas are important, that’s only one part of the whole story. I have students who, despite having spent months in calculus-based physics, have no idea how to solve a basic kinematics problem. Conservation of energy is a neat idea, but they can’t use it to solve problems. Conservation of momentum is a powerful technique, but it requires being able to calculate momentum, which they can’t do. Of course, this assumes the students even know what these things are, and there’s a good chance that they don’t, since using physics terminology is apparently too difficult and we should instead assume the students are limited to a third-grade vocabulary.
Students make it all the way to the end of the intro sequence without even knowing how to add vectors. They get through the sequence by relying on drawing diagrams and writing about what things they might take into consideration when solving problems in the event that they actually knew any physics. You may not be able to use conservation of energy, but if you can draw a bar graph that looks halfway reasonable and write down some assumptions, you can still scrape together enough points to pass.
Those who teach this curriculum have some diagnostic test results that they can point to and argue that their methods are better. Having given these tests, it’s no surprise that classes which teach touchy-feely concepts over mathematically rigorous problem-solving score better. The questions require little in the way of problem-solving skills or mathematical ability. The tests measure conceptual understanding, which those who promote the approach then pass off as evidence that their students learn more. Such a conclusion is clearly preposterous.
Having graded students work and worked with them on problems, it is obvious that they have not developed problem-solving skills and mathematical ability to any reasonable level. What they demonstrate seems more appropriate for junior high than college.
In time, this approach will be shown for the disaster it is, much like “reform math.” Unfortunately, it’s already too late for many people who haven’t learned what they should and don’t have the skills they need.
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