Subject-Specific Content and Pedagogy (illustrated with PGT Mathematics)
Subject Content and Pedagogy
This domain carries the largest weight and splits into advanced subject content plus the pedagogy of that subject. The structure below transfers to any PGT subject; substitute your own syllabus content and keep the pedagogical reasoning identical.
Content map (Mathematics)
Algebra and theory of equations, sequences and series, trigonometry, coordinate geometry and conics, differential and integral calculus, differential equations, vectors and three-dimensional geometry, matrices and determinants, linear algebra (rank, eigenvalues), abstract algebra (groups, rings, fields), real analysis (limits, continuity, uniform convergence), complex analysis, probability, number theory, statistics.
Pedagogy
- Van Hiele levels: visualisation → analysis → informal deduction → formal deduction → rigour. A student can be in class 11 and still be reasoning at level 3.
- Bruner's concrete → pictorial → abstract sequence; Polya's four steps: understand the problem, devise a plan, carry it out, look back.
- Error analysis: treat a wrong answer as evidence of a consistent rule, then teach against that rule.
- Assessment: objective items for content recall, rubrics for proof and problem solving; NCF 2023 stresses reasoning over rote procedure.
Worked example
Number of onto functions from a 4-element set to a 3-element set. Reasoning: total functions = 3⁴ = 81. Subtract those missing at least one element in the range: choose the missing element (3 ways) × 2⁴ = 48. Add back the double-subtracted cases where two elements are missed: 3 × 1⁴ = 3. Answer = 81 − 48 + 3 = 36. What should be taught is the inclusion–exclusion structure, not the arithmetic.
Traps
- Confusing one-one with onto; onto requires every codomain element to be hit.
- Assuming a continuous function is differentiable.
- Skipping Polya's 'look back', so domain and sign errors survive unchecked.
- Answering the content items well but missing pedagogy items that ask how the same idea should be taught.