I would disagree about the “nonsense” (which I’ve seen on other threads too).
Developmental psychology, History of Education, and History of your subject are all essential context (in the same way premed pre-reqs include Physics, English, Psychology). Subject methodology is CRUCIAL to teaching efficiently. Student teaching with observation and group discussion also.
BTW just because some states have laughable requirements doesn’t mean all do; one way to change that is to organize a state-wide group including not just parents but also teachers, school administrators and professors in the subject to increase the subject content requirements.
For example, these are the requirements in Minnesota:
MATH 1271/1371/1571H Calculus I
MATH 1272/1372/1572H Calculus II
MATH 2243/2373/2574H Linear algebra and differential equations
MATH 2263/2374/2573H Multivariable calculus and vector analysis
MATH 2283/3283W Sequences, series and foundations
- 2 from the following:
Theoretical Algebra
MATH 4281 Introduction to Modern Algebra
MATH 5248 Cryptology and Number Theory
MATH 5251 Error-correcting Codes, Finite Fields, Algebraic Curves
MATH 5285H Honors: Fundamental Structures of Algebra I
MATH 5286H Honors: Fundamental Structures of Algebra II
MATH 5385 Introduction to Computational Algebraic Geometry
Applied Algebra
MATH 4242 Applied Linear Algebra
MATH 5705 Enumerative Combinatorics
MATH 5707 Graph Theory and Non-enumerative Combinatorics
MATH 5711 Linear Programming and Combinatorial Optimization
MATH 5485 Introduction to Numerical Methods I
- 2 from this list Analysis List
MATH 4567 Fourier Analysis
MATH 4603 Advanced Calculus I
MATH 4604 Advanced Calculus II
MATH 5486 Introduction to Numerical Methods II
MATH 5525 Introduction to Ordinary Differential Equations
MATH 5535 Dynamical Systems and Chaos
MATH 5583 Complex Analysis
MATH 5587 Elementary Partial Differential Equations I
MATH 5588 Elementary Partial Differential Equations II
MATH 5615 Honors: Introduction to Analysis I
MATH 5616 Honors: Introduction to Analysis II
MATH 5651 Basic Theory of Probability and Statistics
STAT 5101 (equivalent to MATH 5651)
MATH 5652 Stochastic Processes
MATH 5654 Prediction and Filtering
- Combinatorics + Probability + Geometry I.
In New York State
A.
Single-variable Calculus; Multivariable Calculus, Linear Algebra, and Differential Equations; computer literacy; Advanced linear algebra
B.
• MAT 200 Language, Logic, and Proof;
• MAT 312 Applied Algebra OR MAT 313 Abstract Algebra
• MAT 319 Foundations of Analysis OR MAT 320 Introduction to Analysis
• MAT 336 History of Mathematics
• MAT 360 Geometric Structures
• AMS 310 Probability and Statistics.
C. Professional educational requirements:
- MAE 301 Foundations of Secondary School Mathematics
- MAE 302 Methods and Materials for Teaching Secondary School Mathematics
- MAE 311 Introduction to Methods of Teaching Secondary School Mathematics
- MAE 312 Micro-Teaching
- MAE 447 Directed Readings in Mathematics Education
- PSY 327 Human Growth and Development in the Educational Context
- SSE 350 Foundations of Education
- CEF 347 Introduction to Special Education
- LIN 344 Language Acquisition and Literacy Development
- MAE 451 Supervised Teaching - Grades 7-9
- MAE 452 Supervised Teaching--Grades 10-12
- MAE 454 Student Teaching Seminar