Gifted Issues Discussion homepage Forums General Discussion SAT scores of teachers by subject taught

I'm sorry Austin, but you are incorrect on this one.

If you scroll down a bit, you'll see as a minimum requirement for application:

"An academic major in Mathematics, Applied Mathematics or the equivalent (see below) with a minimum of 36 credits in Mathematics." *

"*These 36 credits must include courses in single and multivariable calculus, linear algebra, and at least two of the following four more advanced subjects: abstract and/or applied algebra; analysis or advanced calculus; geometry, including non-Euclidean geometry; probability and/or statistics. You must also have taken at least one mathematics course that significantly uses computers and/or graphing calculators."

So, the students in this program take plenty of courses that "real" math majors take...because they need to be real math majors as a minimum requirement of the program.

I didn't major in math, but it seems to me that introductory probability and statistics courses aren't the most demanding courses in the world of maths, nor are they "advanced" mathematics. I'll say the same for the requirement for "any" course that using computers or graphing calculators significantly. First semester calculus would satisfy that requirement. In all honesty, to make the claim that these courses are advanced kind of makes Austin's point for him.

Single and multivariable calculus is covered in introductory-level textbooks. Linear algebra is the real thing, but if only one course is required, it's the introductory-level course that they sell For Dummies books for. So, again, not advanced in my book. Real math, yes, but not very advanced.

I couldn't agree more with Austin about needing someone mathy by the time GT students get into geometry. For one reason why, see this thread.

Real Analysis and Abstract Algebra are core introductory math major courses, not advanced courses. If you cannot do proofs, then you are still doing arithmetic. A degree without significant coursework beyond these classes is not a math degree. Its engineering mathematics of some sort.

And almost all of the MAT curriculum deals with non-abstract math.

A mathy kid will be ready to move beyond applied math prior to HS and your typical MAT curriculum will not equip the teacher to do that.

This is why we have reports of teachers dropping proofs from Geometry and then omitting critical stuff like right triangles as well. They cannot teach the abstract stuff and then are not literate enough in applied math to know what is critical.

I think a teacher who did well in these courses would be prepared to teach math in high school, but in the beginning of this thread I noted that the average math SAT of math teachers was 590. I think a math SAT of 700 is needed to handle these courses, unless they are quite watered down. Probably most math teachers do not have the background you have described?

I'll be the first to argue that our teachers need to have a strong background in the content they teach. However, I think the MAT (Masters of Arts in Teaching) programs are the wrong target. Students who are pursuing a high school certification generally have an undergraduate degree in their content area, and then add the pedgagogy and additional content.

Some undergraduate programs might be a fairer target for criticism. Students often have fewer courses in the content area than a student who majors in the subject.

My comparison was made between students who are doing undergrad mathematics vs. undergrad secondary mathematics education.

Cut-and-paste from one undergrad program...

MATHEMATICS EDUCATION:

Required Mathematics (36 credits):

MATH 122 - Analytic Geometry 3 credits
MATH 131 - Calculus I 4 credits
MATH 132 - Calculus II 4 credits
MATH 231 - Calculus III 4 credits
MATH 323 - College Geometry 3 credits
MATH 341 - Probability and Statistics 3 credits
MATH 380 - Introduction to Abstract Mathematics 3 credits
MATH 410 - Introduction to Analysis 3 credits
MATH 411 - Theory of Numbers 3 credits
MATH 412 - Abstract Algebra 3 credits
MATH 413 - Linear Algebra I 3 credits

Elective Mathematics (6 credits):

6 credits from:

MATH 320 - Discrete Mathematics 3 credits
MATH 333 - Differential Equations 3 credits
MATH 430 - Real Variables I 3 credits
MATH 431 - Complex Variables I 3 credits
MATH 441 - Theory of Probability 4 credits
MATH 442 - Mathematical Statistics 4 credits
MATH 490 - Topics in Mathematics 2-6 credits
CHEM 321 - Analytical Chemistry 4 credits
CHEM 461 - Physical Chemistry I 4 credits
PHYS 215 - Modern Physics I 3 credits
PHYS 216 - Modern Physics II 3 credits
PHYS 310 - Analytical Mechanics 3 credits
PHYS 341 - Electricity and Magnetism 3 credits

MATHEMATICS MAJOR:

Required Mathematics (27 credits):

MATH 122 - Analytic Geometry 3 credits
MATH 131 - Calculus I 4 credits
MATH 132 - Calculus II 4 credits
MATH 231 - Calculus III 4 credits
MATH 380 - Introduction to Abstract Mathematics 3 credits
MATH 410 - Introduction to Analysis 3 credits
MATH 412 - Abstract Algebra 3 credits
MATH 413 - Linear Algebra I 3 credits

Elective Mathematics (12 credits):

Select 12 credits, 6 of which must be at the 400 level, from the following:

MATH 320 - Discrete Mathematics 3 credits
MATH 323 - College Geometry 3 credits
MATH 333 - Differential Equations 3 credits
MATH 341 - Probability and Statistics 3 credits
MATH 411 - Theory of Numbers 3 credits
MATH 430 - Real Variables I 3 credits
MATH 431 - Complex Variables I 3 credits
MATH 441 - Theory of Probability 4 credits
MATH 442 - Mathematical Statistics 4 credits
MATH 490 - Topics in Mathematics 2-6 credits

The actual "math content" for a math ed major at the undergrad level is CLEARLY greater than plain-old "Algebra" and "Geometry." In fact, a student in the secondary undergrad math ed program at this particular college (a four-year "state university") actually takes MORE college math courses (42 credit hours) than a student who is majoring in mathematics (39 credit hours)!!! There are too many people who incorrectly believe that the highest math class a math ed major takes at the college level is "Calculus for Dummies" or something like that, with the majority of their classes things like "Writing on Chalkboards 101" and "Taking Attendance II."

As a second data point, here's the comparison from one of our 4-year state universities. Compared are math major with teaching certification (MM), and secondary ed major with math option (SE).

2144 (SE only, but a prereq for 2153) Calculus I
2153 (both) Calculus II
2163 (both) Calculus III
2233 (both) Differential Equations
3013 (both) Linear Algebra
3613 (both)Introduction to Modern Algebra
4023 (MM only - can count as an elective for SE)Introduction to Modern Analysis
4033 (both) History of Mathematics
4403 (both) Geometry
4583 (both) Introduction to Mathematical Modeling
4663 (both) Combinatorial Mathematics.
4713 (both) Number Theory
CIED 4003 (MM only) Teaching Fundamental Concepts of Mathematics.
CIED 4053 (MM only) Teaching Geometry in the Secondary School
STAT 4013 or 4023 (both) Statistical Methods I or II
CS 1103 or 1113 (SE only) Computer Programming or Computer Science I

12 hours from below(MM) / 3 hours from bolded courses below and/or 4023 (above) (SE):
4013 Calculus of Several Variables
4143 Advanced Calculus I
4153 Advanced Calculus II
4233 Intermediate Differential Equations
4263 Introduction to Partial Differential Equations
4283 Complex Variables
4453 Mathematical Interest Theory
4513 Numerical Mathematics: Analysis
4553 Linear and Nonlinear Programming
4583 Introduction to Mathematical Modeling
4613 Modern Algebra I
4623 Modern Algebra II
4713 Number Theory
4813 Groups and Representations
5023 Advanced Linear Algebra
5213 Fourier Analysis and Wavelets
5303 General Topology
5593 Methods of Applied Mathematics

6 hours of MATH or STAT (4000 or above) or upper-division CS or PHYS (MM only)

In CA, you do not have to have a Mathematics major or a mathematical education major to teach math. You only have to have a bachelor's degree (in something) and a year's worth of teacher preparation classes, plus pass the state exam.

The test includes:
CSET: Mathematics: Algebra; Number
Theory (30 multiple-choice items; 4
constructed-response items: 3 in
algebra, 1 in number theory)

CSET: Mathematics: Geometry;
Probability and Statistics (30 multiple
choice items; 4 constructed-response
items: 3 in geometry, 1 in probability
and statistics)

CSET: Mathematics: Calculus; History
of Mathematics (30 multiple-choice
items; 4 constructed-response items: 3
in calculus, 1 in history of
mathematics

I think the main issue is that with the undergrad standards where they are right now (certain SAT scores acceptable for program admission...courses that undergrad teaching candidates have to take...etc.), we still have a shortage of teachers in STEM-related areas. It's obviously a supply-and-demand thing. If our supply is already lower than demand, we can't just insist that we tighten up our standards. Yes, money is a factor. Average salaries don't mean as much as starting salaries. Also, no matter how talented a beginning teacher is, there's usually a "pecking order" to go through and a first-year teacher is more likely to be teaching Algebra-for-sophomores-who-failed-it-last-year than advanced mathematics classes to students who are mathematically gifted. A few years of that can be defeating to a teacher who went into the profession with aspirations of mentoring young, talented students who enjoy math, but there are only so many "advanced math classes" to around. There's also a definite lack of "status" in our society when it comes to teachers. As a highly-gifted student who was the only girl in her advanced high school math courses, almost every teacher and adult in my life tried several times to talk me OUT of teaching because "I could do so much better than THAT!"

With all of that being said, I'm an elementary school teacher who had top-notch SAT scores and several passed AP tests under my belt before I entered college. I feel like I'm very good at what I do. However, some of the absolute best teachers that I work with admittedly struggled in school themselves. In some cases, I'm sure that gives them an ability to empathize with struggling students and be able to come alongside and help them intuitively in ways that I have only read about in textbooks.

I think we need to do a better job of encouraging our bright kids to consider a career in education, and we need to be willing to pay them both an appropriate salary AND the respect they are due for what they choose to do. I do not think that we need to completely close the door to the profession for those who may not have been National Merit Scholar material in school themselves, though.