Tuesday, August 6, 2013

Another aspect of faculty's role in the decay of higher education..."Math Education"


Faculty’s Role in Higher Education, part 2

By Professor Doom


     Last time around, I discussed how administrative control of hiring contributed to the decay of higher education: they tend to hire only faculty that will help in that decay. That’s only half the story, however, because this could only work as long as some faculty in every discipline could be found to contribute to the decay.


     Administrator: “It’s algebra without the algebra.”

--All we could do is sit there and look slack-jawed as our course content was literally being deleted without discourse.


     Some disciplines, especially math and sciences, were short on such faculty.  These types of disciplines are all about rules, fundamental rules (like how gravity works) that can’t be changed via administrative fiat, and these disciplines devoutly believe that words have meaning. Thus, a course called “calculus” is supposed to have calculus in it, not book reports, group projects, and eighth-grade arithmetic.

     In the previous essay I identified that to become a faculty member, one first had to get a graduate degree, only acquired after 6 to 10 years of a successful academic career. Next, one had to usually suffer through years of poverty as an adjunct, demonstrating a willingness to accede to administrative demands; the latter is for most disciplines, but not so much for the technical disciplines, which have so few graduates that there’s no glut that would put up with adjuncthood. When it came time to get hired, admin couldn’t abuse people in these disciplines so easily.

     Administration found a way to get around the issue of disciplines whose followers had at least a tendency of have spines, by undermining the “small population problem” in degrees that required specific skills, an even more efficient method than simply removing course content, which could only be done on a per-campus basis: Education degrees, which could count for any subject.


A candidate for a position is demonstrating her ability to teach the material:

“Consider the system:

 2x + 3y = 7

4x + 5y = 6

The best way to solve this system is substitution, first by solving for y:

y = (-2/3)x + 7/3

y = (-4/5)x + 6/5

Now that we’ve solved the system, let’s move on to a different type of problem common to College Algebra…”

--Discussion given as part of a sample lecture presented by a candidate for a permanent position in the math department. No math faculty were on the hiring committee, but this part was passed on to me by a committee member who knew an easier way to solve the system, and knew that the candidate had not, in fact, solved the system, only done the first steps on solving it in a confusing way. Most of the committee thought the candidate unsuitable for the position, but was hired all the same. The candidate had a Master’s Degree in Math Education, and was hired by an administrator also on the committee (and not capable of realizing the issues in the above discussion).                       

     I don’t know how it is in other fields, but there’s considerable confusion by administration between mathematics as a field, and “math education” as a, and I hesitate to use the same word, field. As near as I can tell, administration believes the two subjects are interchangeable, and since math education degree holders promise higher retention rates, there is an additional level of competition for mathematics positions, between those that actually know the material, and those that presumably know how to teach mathematics without knowing any mathematics.


“Is f(x) = |x| differentiable at x = 1? Let me look that up.”

--Holder of a Master’s in Math Education trying to answer a question at a student competition. She had taught Elementary Calculus 1 many times, and this question is comparable in difficulty to identifying an adjective in a sentence.


     I don’t mean to cast aspersions on what might be a legitimate area of study, but having personally met so many advanced degree holders in “math education” with a stunningly limited grasp of undergraduate mathematics, I’m hard pressed to take such degrees seriously, at least when it comes to teaching college level mathematics courses.


“A differentiable function is continuous, and a continuous function is differentiable. They mean the same thing.”

--A Math Educationist teaching calculus wrong. I don’t expect everyone to know how wrong this is, but it’s about as bad as a Historian saying in all seriousness that” George Washington conquered Japan before subduing Stalinist forces in Indonesia.” “I’ve been teaching it that way for years,” said the Educationist when I tried to explain that she was wrong…much like the book says explicitly with numerous examples.

     Nevertheless, I was puzzled why these “colleagues” of mine repeatedly demonstrated that they knew nothing of the material they were teaching. I sought to learn why.  Institutions that offer graduate degrees in math education put their entire curriculum online. Thus, it’s simple to see what you need to know to get a degree. Here are the course topics taken from one school, though all such schools require a similar curriculum for the degree:


*  Foundations of Teaching

*  Instructional Planning and Presentation

*  Pre-Clinical Experiences

*  Demonstration Teaching

*  Research Fundamentals

*  Mathematics Education


     Each topic covers 3 to 6 credit hours; get through them all, and you’ve got your degree. Now, there’s lots of education topics in there….but where’s the math? The first five clearly have no math in them, just educationist theory. The only topic that might have math in it is “Math Education”, which has two parts to it. Here’s the first:


Mathematics Learning and Teaching
In this course candidates will develop the knowledge and skills necessary to be an effective practicing mathematics educator. Candidates will learn principles and models of teaching for understanding, and gain familiarity with the standards and best practices of mathematics education. Candidates will learn how to select appropriate resources, use multiple teaching strategies, use assessment to guide instruction, and plan for all students. Emphasis will be on using research-based methods and problem solving.


      This is just one course, and there are certainly enough topics in there for a course…but how much of that is math? The only thing that looks like math comes at the end. “Problem solving” is about it….perhaps one week of something math related in this course, and that really won’t prepare the educationist to teach an entire college course of material.

     Maybe the other course is math:


Mathematics History and Technology
In this course candidates will learn how to effectively integrate mathematics history and technology into learning activities to motivate students and increase student learning. Candidates will analyze major historical developments and cultural contributions to modern mathematics, select and use a variety of technological tools to solve problems, and analyze emerging philosophies and research-based strategies for incorporating mathematics history and technology into learning activities.


     The history of mathematics is a fascinating topic, I admit…but not exactly mathematics. I’ve discussed earlier the games of technology, no math there whatsoever, just bogus tricks to increase retention without any learning going on with the students.

     So, a Mathematics Education degree holder will learn no mathematics to get a graduate degree. Perhaps the math will be learned as an undergraduate? It’s possible, but once again the schools that offer these graduate degrees make it clear that to enter the program, you don’t need a mathematics degree, an undergraduate degree in Education is just fine. When I applied for a graduate Math Education program, every single school accepted me, and not one asked what my degrees were in…if I had a credit card or was willing to write a check, that was all I needed.



“The probability that the mean is in a 95% Confidence Interval is 0.95”

--An Educationist attempting to teach statistics, and doing it wrong. Again. If ‘probability’ and ‘confidence’ meant the same thing, we’d call them probability intervals. The probability is actually either 0 or 1. An expert would know this sort of thing…but this is what students in an educationist class learn. Now that I know how bad it is, it might well be better for Educationist-taught courses to have no content in them at all, since then the students would not be taught falsehoods.


     Think about that: a faculty member with a Master’s in Math Education might not have seen math since high school. And now I have no wonder, no wonder at all how it is that Math Education degree holders don’t know any math. There’s no reason whatsoever to expect someone with a graduate degree in Math Education to know any mathematics at all…and yet they easily get jobs teaching math in higher education. Again, I can’t make this stuff up.

     To be fair, these degree programs are really intended for high school teachers, but administrators in higher education don’t care, and hire them to teach college material, material they don’t know.

     On the other hand, enroll in a Master’s program in mathematics and every course is math, there won’t be a single course on “education” at all. Words have meaning.


The mathematics faculty are gathered around a machine that tracks how fast a person is moving.

Faculty: “Anyone want to try to move in a way that would make a non-differentiable function?”

A Math Education faculty member gets up, and tries…he can’t.

Another  Math Education faculty member gets up and tries….and can’t.

Another Math Education  faculty member gets up and tries…and can’t.

A faculty member with a mathematics degree: “Shouldn’t we already know that no single person can move in a non-differentiable way?”

Two faculty members move, crossing paths in front of the motion detector; the graph makes a sharp change in direction where the cross occurs, a change not possible for a single object in motion to make.

---Seriously, this happened. It was the beginning of my realization that Math Educationists don’t actually learn math. Before this, I just assumed the blunders I kept witnessing were just mistakes that could happen to anyone. Mistakes I just kept seeing over and over again.


     Many departments are now “mixed” with Educationists and mathematicians both teaching the courses, but the difference between the two is wide. I know of at least one college that has zero math teachers with mathematics degrees…all the teachers hold “Math Education” degrees. Since these teachers might never have taken calculus, statistics, or any college level course, they have no idea what’s supposed to be in the course, or what students will need to know to progress in useful skills, so don’t have any issue when admin tells them to take another chapter out. I’ve presented a few examples, above, of the wild cluelessness, but I fear to imagine how bad it would be in a department with literally no mathematicians to occasionally teach the material properly.


     Since there is no process by which an administrator could tell that such people aren’t qualified, people with this degree can go on for years teaching subjects they know little about…they get good retention, I’ll certainly grant, and that’s all administration cares about.

     There are graduate “Subject Education” (English Education, Music Education, etc) degrees in a variety of other subjects, so it wouldn’t surprise me to hear that this problem is not unique to math. An administrator sees the degree requirements as close enough, not realizing or caring that such a degree really isn’t appropriate for teaching college courses. As long as retention rates are good, a Math Education degree holder can teach anything without interference from administration. Being barely qualified for the position, these types of degree holders are deeply unlikely to stand up to administration. I’ve certainly never seen one do so, or even approximate doing so. Graduate math education degrees are easier to get, greatly increasing the pool of spineless faculty for hire.

     I’ve seen many a legitimate complaint about courses that teach “bad” material like feminism or racial studies or whatever, giving very slanted views on history and the world. At least those courses could generously be called biased, but now that Educationists have created their own degrees giving them influence over any subject at all, they can now teach even technical subjects…this teaching can’t even be called biased, as, in many cases, it’s flat out wrong, literally setting back human knowledge in the process.

     What’s going to happen when there are Brain Surgeon Education and Airline Pilot Education degrees? I joke, but in the real world, brain surgery and piloting are taught by people that actually know brain surgery, actually know how to fly a plane. Does it even remotely make sense that real skills should be taught by people that don’t know the skills? How did it come to pass that institutions of higher education somehow decided that it did make sense? It’s a question that occurred to me, and I’ll be answering it soon, although “better retention” is certainly part of the answer.

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