How common is it for math majors to teach low level courses?

[Apple_Mango]

At the college I go to, there is somebody with a PHD in math who teaches Algebra 1. How common is this?

 

[FactChecker]

It's very common. He may be a great teacher. The freshman physics class I took was taught by Halliday, who was the department head and wrote Fundamentals of Physics by Halliday and Resnick, a very standard physics text. Feynman gave a famous series of lectures on physics even after he was famous. If they love the subject, they often love teaching it.

 

[jtbell]

When I saw "math major" in the thread title, I thought you meant someone who is still an undergraduate, or possibly with only an undergraduate degree in math. One normally doesn't use that term to refer to someone with a PhD.

 

[Dr. Courtney]

The lowest level math course at the Air Force Academy is called Basic Math. Due to their performance on the placement exam, as well as a review of their math backgrounds, about 5% of incoming cadets (students) get placed in it. In my first year on the math faculty there, I determined that these cadets tended to do very poorly in downstream STEM courses that required algebra (Physics, Calculus, Engineering, etc.) and that WAAAAAY to many of these cadets ended up flunking out of the Air Force Academy as a result.

The chain of command made it a very high priority to improve the retention and graduation rates of this cohort of students (referred to by some as the "trailers and failers.") Since I shared some unique ideas for improvement and had succeeded previously at revamping similar math courses at a community college, it wasn't long before they put me (a Physics PhD) and another experienced faculty member (a Math PhD) in charge of the course.

We shifted the focus away from mechanical manipulations (solve this equation) toward modeling (word problems). What had been an 80/20 split mechanical/modeling became a 40/60 split on most homework assignments. Tests were 100% word problems (much better prep for Calculus, Physics, and Engineering which were the same). We dumped all the material that was rarely used downstream by non-STEM majors (sec, csc, cot, completing the square, complex numbers, law of sines, matrices, etc.) to focus on material that was heavily used downstream (SOHCAHTOA, substitution, lines, quadratics, graphing, parametric equations, coordinate systems,etc.) We also acquired funding and provided opportunities to get these (weakest 5%) involved in publication quality research. Consequently, success rates in downstream courses dramatically increased.

It's not that the junior officers (with Masters degrees in Math) who had been teaching the course in prior years were doing a bad job - they were doing exactly what their chain of command had told them to do - teach a defined list of topics from a defined textbook. But the focus was overly mechanical (solve this equation) and followed typical high school math topics too closely without due emphasis on the material actually needed downstream. The PhDs were able to apply a higher level approach: why does this cohort of students tend to do so poorly downstream, and how do we fix that? We were empowered to identify and fix the problem, and we were bold enough to make the sweeping changes needed to do it. Teaching the same course in the same way would have yielded the same results, even if we were marginally better classroom instructors.

One key in success teaching college is realizing that much more learning occurs in the 2 hours of preparation students should be doing outside of class for each class hour than can occur in the classroom itself. There is more to be learned and mastered in a course than is usually possible in the 45 hours or so total of class meeting time. Directing how students spend that time outside of class and designing what happens in class to support and encourage that is more important than being able to explain each and every concept with perfect clarity. Directing students to the best resources to maximize their out of class productivity is also key. The final key to success is shaking students out of their fantasy that they might succeed in college with the half-hearted efforts that got them through high school.

PhDs are not universally better at these things than those with Masters degrees. But we do tend to be a bit better at seeing the forest for the trees, thinking about the bigger picture, having the boldness to make the required changes, and not being manipulated by all the tricks students pull to attempt to pass without working very hard.

 

[bhobba]

When I did my degree we often had the best and most qualified teachers teach introductory courses - really high caliber people like Feynman and his famous lectures to freshman.

Why?

If you don't get the basics right it can do irreparable damage - only your best teachers can ensure its done right.

You didn't encounter them again until your final year subjects where they taught the advanced materiel - as you would expect.

Thanks
Bill

 

[symbolipoint]

At the college I go to, there is somebody with a PHD in math who teaches Algebra 1. How common is this?

Common; maybe increasingly common.
Teachers at a C.C. will have either Masters' degree or PhD, and the trend is for university graduates at least to try to get PhD.
C.C. students have higher proportion of lower level Math students than university have (which is really just my guess - I have no statistical data to support).

 

[mathwonk]

It depends on the funding available to the department and the College. In my university in Georgia, the math department was treated as a cash cow by the administration, in that it was expected to earn double what it consumed in wages. This meant many lower level course, but not all, were taught by people with no PhD. One summer my Dean complained that I, a full professor was allowed to teach a calculus course for high school teachers, because I cost more, and he forbade it in future. Nonetheless, I taught undergraduate calculus, in larger classes, more than once a year for over 30 years.

 

[Dr.D]

I have had a PhD for many years now, and I have taught a number of intro courses at various schools. I've also taught upper level and graduate courses. Having a PhD does not make you too good to teach an intro course, nor does it prevent you from doing so. This really seems like an odd question.

 

[mathwonk]

as i observed above however, it does make you too expensive for some universities to be willing to allow it. so i don't find it odd. it speaks to the commitment of your university to teaching. the size of the classes is also relevant; e.g. at the university I attended as an undergraduate, full professors did teach some freshman calculus classes but they tended to be honors classes with over 140 students, so the wages they spent on the full prof were offset by the extra tuition they received. smaller classes with 25 or so students were taught by grad students. When my son took freshman calculus at Ga Tech, there were 175 students in the class. In fact I think it is more common than not in the US to exploit freshmen in this way in beginning calc classes.

 

[mpresic3]

When I was a Freshman I was taught calculus by Arthur Harold Stone. Stone was mentioned as a classmate of Richard Feynman, I think it was "surely you're Joking..." Dorothy Maharam Stone taught me Differential Equations when I was a sophomore. Both were prominent american mathematicians.

 

[PAllen]

I had a Nobel prize winning physicist in freshman physics. I had a Fields medal winner in sophomore math.

 

[mathwonk]

my freshman calc class (of 135 students) was taught by the famous mathematician John Tate, but we didn't know he was famous. The person we knew was famous, and so we struggled to get into his section, was the zany humorist, then grad student, Tom Lehrer.

 

[DaveE]

I might also add, just for balance, some of the very worst lecturers I had to deal with were well respected researchers, full professors, and such. Usually because they just didn't care to teach well, they were recruited to do research and measured by their publications. Much depends on the institution and the level of the class.

 

[PAllen]

I might also add, just for balance, some of the very worst lecturers I had to deal with were well respected researchers, full professors, and such. Usually because they just didn't care to teach well, they were recruited to do research and measured by their publications. Much depends on the institution and the level of the class.

Very true, but orthogonal to the OP question. I was lucky that the freshman Nobel laureate had, late in life, become highly interested teaching, and the Fields medalist was motivated to show that Dieudonne (Foundations of Modern Analysis) could successfully be used to teach second year students real analysis.

 

[mpresic3]

I replied earlier that I had highly regarded professors in my first few years undergraduate. However there is another side of the coin. I agree that at the level of most (if not all) incoming students, they can just as easily learn from a well motivated professor or grad student with a comprehensive knowledge of the material. I do not agree that you need the most highly regarded teacher to teach you "the right way" and that if someone else teaches you, they might do it wrong, and you may never recover.

When I was entering college though, Neil Armstrong was teaching an aerospace engineering class. The (I think it was a private) university could make this a big "draw" to get undergraduates to apply and come to that university rather than another. Most high school students would rather take a freshman physics class from Feynman, than a freshman physics class from, say, (I'm making up the name) Christiansen.

The fortunate circumstance is that Armstrong or Feynman are already established and can devote a great deal of time to their students and the curriculum etc. They often do a good job. But there are cases where students might be better served with a well motivated lower ranked faculty or grad student.

The best coach for a novice chessplayer, is more likely to be a chessmaster or possibly an international master, or even below this level, than a world class grandmaster, like Bobby Fischer, Gary Kasparov, or Magnus Carlsen

 

[mathwonk]

This motivated me to do some research on the physics professors i had as a freshman. the first term professor, in the physics course for science and engineering majors, was an elderly and uncommunicative gentleman, so unpopular that there was a general revolt against him by the class. My impression is that a student delegation to the department carried the message that we deserved better. So much so that he was replaced the second term by a younger, much clearer, more energetic and better liked lecturer. But by then I had pretty much given up on the class and failed to attend regularly. I have forgotten exactly who these men were, but when I googled the names that did come to mind, two of them were Nobel prize winners, including both men I thought were possibly the terrible lecturer.

By contrast, the freshman math course I took was taught by an excellent, dynamic and brilliant lecturer, and I would up majoring in math. Maybe the difference was that the math course was an elite honors course and the physics course was a standard course, although for science majors. perhaps the lesson is to try to get into honors sections, where the better teachers may be found.

 

[ohwilleke]

When I saw "math major" in the thread title, I thought you meant someone who is still an undergraduate, or possibly with only an undergraduate degree in math. One normally doesn't use that term to refer to someone with a PhD.

The usual title of a PhD teaching an undergraduate or remedial math course would be "teaching assistant" or "instructor". A "teaching assistant" is under the supervision of a professor who has primary responsibility for the class, and would usually teach mostly in smaller sections and grade papers, as opposed to offering large group lectures. An "instructor" would be autonomous with all of the functional roles of a professor but lower pay and no tenure.

 

[atyy]

I have forgotten exactly who these men were, but when I googled the names that did come to mind, two of them were Nobel prize winners, including both men I thought were possibly the terrible lecturer.

Any chance you had Edward Purcell?

 

[mathwonk]

I hesitated to mention him, since I remembered him as one of the worst, and assumed that I must have been wrong, when I learned he was a nobelist. But my memory is not quite accurate at this point, and I was unable to find a list of lecturers in physics 12 a from 1960. So I do not want to accuse him, but yes that is the name that came to mind after 60 years. If true this would violate my rule that the most knowledgeable lecturers are always valuable in some way, or else it would accuse me of being a poor student.