**General****A10**- Comprehensive works on mathematics. Reference
books, encyclopaedias and dictionaries

- textbooks see U20
- materials for repetition see U90
- comprehensive works on special disciplines see each discipline
- mathematical tables see U70

**A20**- Recreational mathematics

- educational games see U60

**A30**- Biographies. History of
mathematics and of mathematics teaching

- innovations in education see D30

**A40**- Sociological issues. Political education in
the mathematics classroom. The profession of teaching.
Careers in mathematics, labour market

- sociological aspects see C60

**A50**- Bibliographies. Information and documentation

**A60**- Proceedings. Conference reports

**A70**- Theses and postdoctoral theses

**A80**- Standards

**A90**- Picture stories. Cartoons. Fiction. Games

**B10**- Educatioal research and planning

**B20**- General education

- syllabuses see B70

**B30**- Vocational education

- syllabuses see B70

**B40**- Higher education

**B50**- Teacher education (Teacher pre-service and in-service education)
**B60**- Out-of-school education. Adult and further education (Summer schools, working groups, student competitions. Private study)
**B70**- Syllabuses, curriculum guides, official documents

- testing of syllabuses in pilot classes see D30

**C10**- Comprehensive works and surveys

**C20**- Affective aspects (Motivation, anxiety, interest,
attitudes, feelings. Self concept. Attention. Affective development)

**C30**- Cognitive processes. Learning, learning
theories (Thought processes, information processing, concept formation, problem
solving, understanding. Learning. Memory. Perception. Cognitive
development)

**C40**- Intelligence and aptitudes. Personality
(Talent, intelligence, abilities and skills, creativity. Behaviour.
Personality traits, personality development)

**C50**- Language and verbal communication (Verbal
classroom communication. Language acquisition. Verbal
teacher-student-interaction. Communicative competence. Language
difficulties, multilingualism. Teaching and learning mathematics in a
second language. Learning with texts)

**C60**- Sociological aspects of learning (Group dynamics. Interpersonal interaction. Social learning. Roles. Social, economic and cultural influences)
**C70**- Teaching-learning-processes. Evaluation of
instruction (Relations between teaching-processes - e.g. teacher attitudes,
teaching methods - and learning processes - e.g. student attitudes,
achievement. Effective teaching)

**C80**- Other psychological aspects (E.g.: test theory, neuropsychology, research methods in psychology)
**C90**- Other educational aspects (E.g.: special education, vocational education, curriculum theory, andragogy)

**D10**- Comprehensive works and surveys on mathematics
instruction in general and at different school levels and types.
Comparative studies on mathematics education in different countries

**D20**- Philosophical and theoretical contributions to
mathematical didactics. Research methods. Theory of mathematics education

**D30**- Goals of mathematics teaching. Curriculum
development (Mathematical formation. Formation of general abilities by
mathematics instruction. Minimal competencies. Objectives and content of
mathematics education, also with regard to cultural demands. Impacts of
new technologies on mathematics instruction. Innovations and trends.
Curriculum research. Curriculum evaluation. Interaction with other
subjects)

**D40**- Teaching methods and classroom techniques. Lesson preparation. Educational principles (E.g.: classroom conversation, classroom organization, teaching approach, ability grouping)
**D50**- Teaching problem solving and heuristic strategies
(E.g.: methods of problem solving, classification of exercises, problem
solving in the curriculum)

**D60**- Achievement control and rating (Mathematics
achievement. Assessing pupils performance. Control and measurement of
knowledge, abilities and skills. Examinations, preparation for
examinations)

**D70**- Diagnosis, analysis and remediation of learning
difficulties and student errors

**D80**- Teaching units, draft lessons and master lessons

**E10**- Comprehensive works on the foundations of mathematics and their teaching. Methodology of mathematical research
**E20**- Metamathematics. Philosophical aspects of
mathematical Epistemology

- history of mathematics see A30

**E30**- Logic. Acquisition of logical verbal reasoning
abilities in mathematics instruction

- Boolean algebra see H50

**E40**- Language of mathematics. Formalization. Defining.
Axiomatics and axiomatic methods. Acquisition of mathematical concepts

**E50**- Proof methods. Reasoning and proving in the mathematics classroom
**E60**- Sets. Relations. Set theory

- mappings and functions see I20

**E70**- Miscellaneous

**F10**- Comprehensive works on arithmetic and the teaching of arithmetic
**F20**- Prenumerical stage. Number concept, counting
**F30**- Natural numbers and operations on natural numbers.
Place value. Pencil and paper arithmetic, mental arithmetic

**F40**- Integers. Rational numbers. Arithmetic operations on integers, fractions and decimals. Extensions of number domains
**F50**- Real numbers, powers and roots. Arithmetic operations on real numbers, powers and roots. Complex numbers.
**F60**- Number theory
**F70**- Measures and units (Quantity concept, operations
with specified measures and units)

- areas, volumes see G30

**F80**- Ratio and proportion. Rule of three. Percentages
and calculation of interest. Mixture problems (E.g. proportional
quantities, inversely proportional quantities)

- mathematics on vocational training see M20

**F90**- Practical mathematics, real
problem solving (E.g. real life problems)

**G10**- Comprehensive works on geometry and the teaching of geometry
**G20**- Informal geometry (Spatial orientation. Basic
geometrical shapes)

- prenumerical stage see F20

**G30**- Areas and volumes (Lengths and areas, volumes and
surface areas)

**G40**- Plane and solid geometry. Geometry in
multidimensional spaces

- geometry transformation see G50

**G50**- Transformation geometry (Isometries, similarity transformations)
**G60**- Trigonometry, spherics
**G70**- Analytic geometry. Vector algebra
**G80**- Descriptive Geometry
**G90**- Miscellaneous (E.g.: convex sets, packings,
coverings, tessellations, non-euclidean geometries, finite geometries)
- fractal see I90

**H10**- Comprehensive works on algebra and the teaching of algebra
**H20**- Elementary algebra (Variables, manipulation of
expressions. Binomial theorem. Polynomials. Finite sums)

- theory of equations see H30

**H30**- Theory of equations and inequalities

- variables, terms see H20

**H40**- Operations. Groups, rings, fields

- computational rules see H20

**H50**- Ordered algebraic structures. Lattices.
Boolean algebra

- propositional logic see E30

**H60**- Linear algebra. Multilinear
algebra.
(Vector spaces, linear mappings, matrices, determinants, theory of equation)

- vector algebra see G70

**H70**- Miscellaneous (E.g.: algebraic topology, algebraic geometry)

**I10**- Comprehensive works on calculus and the teaching of calculus
**I20**- Mappings and functions. Elementary properties of
functions (Concept of function, representation of functions. Functions of
a real variable. Monotonicity, continuity, limits)

**I30**- Sequences, series, power series. Convergence, summability (Infinite products, integrals)
**I40**- Differential calculus (E.g.: curve sketching, extremum problems)
**I50**- Integral calculus. Measure theory (Integrals of different types. E.g.: applications on bodies of revolution)
**I60**- Functions of several variables. Differential geometry
**I70**- Functional equations (Definition of functions. Differential equations, difference equations, integral equations)
**I80**- Functions of a complex variable, conformal
mappings

- complex numbers see F50

**I90**- Miscellaneous (E.g.: functional analysis, set theoretical topology, catastrophe theory, non-standard analysis, fractals, chaos theory)

**K10**- Comprehensive works on stochastics and the teaching of stochastics
**K20**- Combinatorics (Classical combinatorial theory,
configurations, latin squares)

- tessellations and packings see G90

**K30**- Graph theory

**K40**- Descriptive statistics, statistical data handling, graphical methods of data representation, data analysis
**K50**- Probability concept and probability theory
**K60**- Probability distributions, stochastic processes, limit
**K70**- Statistical inference (Methods, non-parametric methods, robustness, Bayesian approach, methodology and foundations)
**K80**- Correlation and regression analysis. Multivariate statistics (Discrimination, cluster analysis, factor analysis)
**K90**- Applied statistics (E.g.: simulation, decision theory, reliability, quality control)

**M10**- Mathematization, its nature and its use in
education. Interdisciplinarity. Comprehensive works on applications of
mathematics

**M20**- Mathematics on vocational training and career
education

- see also F80 , F90

**M30**- Financial mathematics. Insurance mathematics
**M40**- Operations research, economics

- mathematical programming see N60

**M50**- Physics. Astronomy. Technology. Engineering. Computer science. Earth sciences
**M60**- Biology. Chemistry. Medicine. Pharmacy
**M70**- Behavioural sciences. Social sciences. Education
**M80**- Arts. Music. Language. Architecture
**M90**- Miscellaneous (e.g. sport)

**N10**- Comprehensive works on numerical mathematics and its instruction
**N20**- Representation of numbers, rounding and estimation. Theory of errors and computation with approximate values. Conditioning
**N30**- Numerical algebra (Iteration methods for the solution of nonlinear equations and systems of linear and nonlinear equations, numerical linear algebra)
**N40**- Numerical analysis (Numerical solution of
differential and integral equations, numerical integration and
differentiation)
- interpolation and approximation see N50

**N50**- Approximation, interpolation, extrapolation
**N60**- Mathematical programming
- operations research see M40

**N70**- Discrete mathematics (Finite methods in various mathematical fields, especially used as theoretical foundations in other disciplines)
**N80**- Mathematical software. Collections of computer
programs
- software for special disciplines see each discipline
- computer as a teaching medium see U70

**N90**- Miscellaneous (e.g. experimental mathematics)

**U10**- Comprehensive works on instructional materials, educational technology and media research
**U20**- Textbooks. Analysis of textbooks, development and
evaluation of textbooks. Textbook use in the classroom
- textbooks for special disciplines see each discipline
- learning with texts see C50

**U30**- Teacher manuals and planning aids (Teacher volumes, solutions, teaching aids)
**U40**- Problem books, student competitions, examination questions
**U50**- Programmed instruction, computer assisted instruction (CAI, intelligent tutor systems)
**U60**- Manipulative materials and their use in the
classroom (Visualizations, teaching aids, models, educational games,
worksheets. Teaching in laboratories)
- games see also A90

**U70**- Mathematical tables. Mathematical instruments, pocket calculators. Comments on their instructional use. Computer as a teaching medium
**U80**- Audiovisual media and their use in instruction (Transparencies, films, Broadcasting and television)
**U90**- Miscellaneous (Student publications, repetition
materials. Mathematical expositions)
- reference books see A10