Switzerland Secondary II Syllabus - Baccalaureate > Mathematics

This information is based on the "Rahmenlehrplan für die gymnasiale Oberstufe" (Framework Curriculum for the Upper Secondary Level) for Mathematics, published by the Berlin Senate Department for Education, Youth and Sport. While this document pertains to the Berlin school system, it offers a potential model for understanding the structure and content of a Swiss Gymnasium mathematics syllabus, particularly given the shared emphasis on preparing students for higher education. It is important to note that the specific content and requirements of the Swiss Maturität (Baccalaureate) may vary by canton. Further research into cantonal guidelines is recommended for precise details.

Introduction Phase (Einführungsphase)

The introductory phase aims to bridge the gap between Secondary I and the Baccalaureate program, solidifying prior knowledge and preparing students for the rigor of advanced mathematics. This phase focuses on building a foundation in core mathematical concepts and introducing students to the different approaches required for standard and higher-level courses.

• Fundamental Areas:
• Semester 1: Probability and Statistics (Stochastik): This semester introduces fundamental concepts in probability and statistics, including data analysis, graphical representation, probability calculations, and combinatorial principles.
• Semester 1: Coordinate Geometry and Functions: This semester reviews and expands upon coordinate geometry and functions, covering topics such as Cartesian coordinate systems, linear and quadratic functions, exponential and logarithmic functions, trigonometric functions, and optimization problems.
• Semester 2: Calculus (Differentialrechnung): This semester introduces the concept of derivatives, focusing on understanding derivatives as rates of change and tangent slopes. Students will explore the derivatives of various functions and apply them to problem-solving.
• Specialized Courses:
• Semester 1: Discovering, Justifying, Proving: This course delves into mathematical reasoning and proof techniques, covering direct and indirect proofs, and proof by induction.
• Semester 2: Sequences and Series, Limits: This course explores sequences, series, and limits, providing a foundation for understanding infinitesimal processes in calculus.

Qualification Phase (Qualifikationsphase)

This phase focuses on advanced mathematical concepts and problem-solving skills necessary for university studies. The curriculum emphasizes the development of key competencies, including problem-solving, modeling, argumentation, communication, and cooperation.

• Core Subjects:
• Analysis (Calculus): This subject covers differential and integral calculus, including applications to real-world problems, such as optimization and modeling of growth and decay processes.
• Analytic Geometry: This subject explores geometric concepts using algebraic methods, including vectors, coordinate systems, and equations of lines and planes. It also covers spatial reasoning and problem-solving.
• Probability and Statistics (Stochastik): This subject builds upon the introductory phase, delving into more advanced topics, such as binomial and normal distributions, hypothesis testing, and statistical inference.

Course Structure (Kurshalbjahre)

The qualification phase is structured into four semesters, with specific content outlined for each semester in both standard and higher-level courses. The curriculum also allows for additional specialized courses, such as incidence geometry, non-Euclidean geometry, logic, number theory, numerical mathematics, differential equations, infinite series, Markov chains, elements of function theory, conic sections in analytic geometry, pathologies in analysis, and introduction to multidimensional differential and integral calculus. These courses offer students the opportunity to explore specific areas of interest in greater depth.

Assessment (Leistungsfeststellung und Leistungsbewertung)

Assessment in mathematics includes class participation, homework, written tests, and examinations. The curriculum emphasizes the importance of individual feedback and guidance to support student learning and development. It also highlights the role of written assignments and oral presentations in developing communication and presentation skills. Special attention is given to preparing students for the "Besondere Lernleistung" (special learning achievement), which promotes independent, research-oriented learning.