Constructivism

Constructivism: You can think of this as the new "New Math." It’s a theory of learning (which was making the rounds in the 90s when I was teacher and grad education student) that starts from the innocuous premise that knowledge is not taught by the teacher, but rather "constructed" in the mind of the learner. This statement is correct as far as it goes, but then constructivism devolves into absurd instructional techniques that remove the teacher as authority figure and turns him into a “first among equals” kind of role. Of course, this is absurd since the teacher knows the subject matter and the students don’t, but no matter. As you could expect, from this bizarre confluence of obvious theory and dubious application, you arrive at some of the most bizarre arguments I have ever seen, arriving at conclusions such as:
* first graders should be given calculators with which to learn arithmetic (news flash: they don't learn it - DUH!)
* students should do all work on a computer starting in middle school
* high schools should not teach algebra-geometry-precalc-calculus, instead focusing on statistics
I will probably elaborate later, complete with references to the National Council of Teachers of Mathematics curriculum standards, but the above is sufficient to follow the next couple of paragraphs.

I did some research on constructivist teaching of statistics. Basic statistics can be taught quite easily by explaining how to set up simple counting rules for the various possible results from an experiment, and then having students use these basic rules to solve increasingly complex problems. Statistics has been taught this way since it was invented. I learned it that way and the professor of math educ with whom I was working learned it that way, but the purpose of this research project was to inflict constructivism on some students and prove that they learned better than with traditional methods (yes, that's the way much education research is performed nowadays -- the conclusion is predetermined and then you look for evidence to support it). The student was given a computer and a (poorly-written) simulation program and asked to solve some problems by creating an appropriate simulation. (Oh, yeah, that will work! Students who do not understand basic statistics are *quite* adept at designing computer simulations.) Many problems could never be solved because the student stared at the computer, unable even to begin the simulation (and the teacher is not allowed to assist because that would put the teacher in an "expert" role -- excuse me, but that's what I want from my teachers!) Even in the few cases where the student set up a simulation, the answers meant nothing because the student did not learn any BASIC principle that could be applied in multiple situations. Each problem had to be approached from scratch. And of course, problems that could have been explained in 5 minutes (which I have done when I have taught stats) took 2 hours and the student still didn't really understand what had occurred. But the experiment was a success. Constructivism was somehow proved to be better, and the professor got a publication out of it.

My master's thesis in education. I designed the experiment. It involved four summer school geometry classes, two consisting of students who failed during the school year and two consisting of enrichment students who wanted to take it during summer so that they could take trigonometry or pre-calculus instead of geometry during the following school year. Two classes (one remedial, one enrichment) would be taught using traditional methods; the other two would be taught using constructivist methods. With my professor, I created the curriculum and learning objectives. I wrote the lesson plans for the traditional classes; my professor designed the constructivist exercises that would be used in the constructivist classes. I enlisted four teachers and two fellow students to assist me by doing the actual teaching (the constructivist classes required TWO teachers -- an indication right from the start that something was probably very wrong). For 6-7 weeks, I observed classes, I watched students performing the exercises, I interviewed students and teachers and parents, I evaluated assignments, I even eavesdropped on students once or twice. Each student in every class was evaluated twice, with a constructivist tool and with a traditional paper and pencil exam. The traditional students, from both the remedial and enrichment classes did very slightly better on the constructivist "final exam" than the constructivist students who had been exposed to this type of idiotic "critical thinking" exercise all summer, even though they had never been told anything about this type of assessment. And the constructivist students did ridiculously worse on the paper and pencil exam, with many scores very close to zero and almost nobody passing the exam, even among the enrichment group. For months after this exercise had reached a conclusion for me (as I'll relate in a moment) I felt absolutely horrible about what I had done to the constructivist groups. We gave a passing grade to every single student -- since everyone "passed" at least the constructivist exam even if not the paper and pencil exam. For the remedial groups, this probably was just fine since I'm sure they weren't really interested in learning anything, although I'm sure I intensified their math phobias (that's not just an opinion -- that conclusion follows from an analysis of my interviews with them). But what about the enrichment group? How many of them went into trig or pre-calc without the tools to be successful? Might some otherwise promising engineering or science students have been put off math forever? With the problem of grades solved, I began writing my thesis. The truth was that constructivism was proven to be a worthless pathetic failure. Of course, nobody ever gets a thesis accepted and published by bucking established theory, so I watered down my conclusion to a much weaker (but still true) statement: "No evidence was found that the constructivist methods are better than the traditional method." Professor read my first draft and turned it down outright. He told me to re-analzye my data so that I could state the constructivism was better or I would never graduate. So I walked out of his office and never graduated.