So, a mathematics major and a mathematics education major may sit in the EXACT SAME math classes for four years (Calculus III and other advanced math classes that go well beyond anything a secondary math teacher would be required to actually teach in a high school setting)..
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So, be careful about assuming that anyone with a secondary education degree is inferior to those with content-area degrees in terms of content knowledge at the collegiate level.
I appreciate your insight. But this is not even remotely true.
I majored in math at a Tier 1 public university and ranked 2nd in the 20 math grads in my graduating class.
Here is my perspective.
At the end of the day, Calc III is still just fancy arithmetic. In most math departments, Calc III is something you were expected to have taken in high school. In fact, many math majors today take it while freshmen in High School. And in the top math programs in public schools that prep their students to do it, Calc III is covered in the 10th grade.
The number of students in my college's math department relative to the student body was very small. We had 5-10 students in the first year math courses, like Analysis and Abstract Algebra. Compare this to the 100 or so engineering majors in similar courses as Freshmen. The first and second year math major classes often had other students in there from other STEM majors. These were seniors or grad students and they routinely got C's or just dropped the classes when they saw how hard they were.
None of the students in the math department were there for secondary education teaching certification. Some did go on to teach, but as TA's and then later as college professors.
When the math majors took electives, we took upper division courses from the other STEM departments. I tested out of the usual electives and many core courses when I entered college - stuff like biology, geology, English I and II, etc. I took Orbital Mechanics, Quantum I and II, Thermo I and II, Computer Algorithms, Biostatistics, and some EE and Grad Math courses. I also took immersion courses in one foreign language and upper division classes in Greek. My last three semesters I carried 20+ hours. Due to my math preparation, the STEM upper division classes were easy and I had the highest grades in those classes. And on the side, just to get them out of my math advisor's hair, starting as a Junior and just for fun, I worked with PHD biology candidates and their professors on statistics problems and did QA on papers being submitted to top journals.
I do not think my experience as a math major from a good college prep HS who attended a major university was unusual.
let's compare that to a typical top flight math teaching program.
Looking at the top MAT programs ( "Master of Arts in Teaching: Mathematics" ) I do not see that MAT grads are REQUIRED to take even the Freshman level math classes.
http://www.stonybrook.edu/spd/graduate/matmathLooking at this MAT program, only nine semester hours of "math" are required (after a survey course) and can be chosen from such classes as Algebra "for teachers", Geometry "for teachers", and Probability and Statistics "for teachers". Only two classes look remotely like college math major classes.
Clearly, MAT grads do not take ANY classes a real math major takes.
To make an analogy, comparing a MAT grad to a BS in Math is like a JV HS football player vs a first round draft rookie in the NFL.
In sports in the US, top freshmen prospects are taught by the top coaches in the HS Sports and they spend summers training at special camps. There is a full certification program for coaches, almost all of whom were top players as well.
But, for our top STEM kids, they send out people who have "math teaching certs" whose highest college math classes were Algebra and Geometry. And to top it off, the MAT grads think they know math.
Anyone wonder why education stinks and why many GT kids resent education? This is why.
Another data point.
A former boss of mine rose to the top of the corporate ladder then quit to raise her kids. She now teaches STEM at a smaller suburban school district. She teaches the honors math and physics courses from 9th to 12 grade. She has a masters in math from the same school I went to - along with an MBA. ALL of her students score 4 or better on the AP Calc exam every year. One or two students a year are really good at math and she does independent study with them on Analysis or Abstract Algebra and works with their college to get them college credit for it. THAT is the difference a real math major makes with merely bright kids.
GT kids need people who know real math to teach them math. Your typical MAT grad will be outgunned intellectually by the time a GT kid is 12. That means the kid will stagnate until they get to college.
This is why parents must check the CV of the higher math teachers at their schools. A hard degree of any kind is preferable to a teaching degree and a math degree is a must once Geometry is reached as Geometry is the first class with proofs.
This is how math should be taught at the secondary level.
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/119385/Plano_math_rocks_program.html