This fully structured teaching concept provides a clear, curriculum-ready framework for teaching polynomial functions and curve analysis in upper secondary mathematics.
It is specifically designed for Eduki EN and bilingual (CLIL) math classrooms, combining precise mathematical language with conceptual clarity and strong classroom usability.

Rather than treating curve sketching as a checklist of procedures, this teaching concept focuses on understanding how algebraic properties, derivatives, and graphs are connected.

Didactic Focus

Students develop a deep and transferable understanding of polynomial functions by learning to:

• analyse functions step by step using a systematic structure,

• interpret derivatives as tools for describing slope, extrema, and curvature,

• connect algebraic calculations with graphical behaviour,

• identify and avoid common misconceptions,

• justify mathematical results using precise reasoning,

• apply curve analysis to real-world and modelling contexts.

The concept supports language-sensitive instruction, making it well suited for bilingual and international classrooms.

Structure of the Teaching Unit

The teaching concept is designed for approximately 16–24 lessons and includes:

• clearly defined lesson phases (introduction, exploration, application, reflection),

• progression from basic properties to full curve analysis,

• worked examples and guided classroom discussions,

• differentiation for mixed-ability groups,

• guidance for assessment, tests, and exam preparation.

Core Topics

• polynomial functions and their properties

• zeros and multiplicities

• symmetry and end behaviour

• first and second derivatives

• extrema and inflection points

• monotonicity and concavity

• curve sketching strategies

• modelling tasks and applications

• limitations of mathematical models

Classroom Use

• Bilingualer Mathe-Unterricht (CLIL)

• upper secondary mathematics

• exam preparation and revision

• concept-based calculus instruction

Best for

• CLIL and bilingual math classes

• upper secondary / advanced high school courses

• teachers seeking a complete teaching concept rather than isolated materials

Keywords

Keywords
Bilingualer Mathe-Unterricht, polynomial functions CLIL, curve analysis teaching concept, upper secondary mathematics, calculus modelling