- 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
- recreational mathematics see A20
- educational games see U60
(Educational research, educational reforms, pilot projects, official
documents, syllabuses)
- B10
- Educatioal research and planning
- B20
- General education
- B30
- Vocational education
- 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)
- concept teaching see E40
- teaching problem solving see D50
- social learning see C60
- learning with texts see C50
- teaching-learning-processes see C70
- C40
- Intelligence and aptitudes. Personality
(Talent, intelligence, abilities and skills, creativity. Behaviour.
Personality traits, personality development)
- learning difficulties and student errors see D70
- achievement control see D60
- special education see C90
- 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)
- mathematical language see E40
- readability of textbooks see U20
- C60
- Sociological aspects of learning (Group dynamics.
Interpersonal interaction. Social learning. Roles.
Social, economic and cultural influences)
- teaching methods see D40
- mathematics and society see A40
- 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)
- teacher-student-interaction see also C50,
C60
- learning see C30
- teaching methods see D40
- 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)
- mathematics teaching see D
- educational media and media research see U10
- media education see U
- 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
- history see A40
- learning theories see C30
- teaching-learning-research see C70
- 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)
- syllabuses and curricula see B70
- history of mathematics instruction see A30
- political education in the mathematics classroom see
A40
- socialisation in mathematics instruction see C60
- D40
- Teaching methods and classroom techniques.
Lesson preparation. Educational principles (E.g.: classroom conversation,
classroom organization, teaching approach, ability grouping)
- programmed instruction see U50
- interactions see C50,
C60, C70
- evaluation of instruction see C70
- language in mathematics instruction see C50
- preparation for examination see D60
- teacher resources for preparing lessons see U30
- interdisciplinary teaching see M10
- D50
- Teaching problem solving and heuristic strategies
(E.g.: methods of problem solving, classification of exercises, problem
solving in the curriculum)
- psychological aspects of problem solving see C30
- see also test theory C80
- exercise problems and student competitions see U40
- D60
- Achievement control and rating (Mathematics
achievement. Assessing pupils performance. Control and measurement of
knowledge, abilities and skills. Examinations, preparation for
examinations)
- student errors see D70
- problem books see U40
,
- abilities as personality traits see C40
- D70
- Diagnosis, analysis and remediation of learning
difficulties and student errors
- special education see C90
- achievement control and rating see D60
,
- 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
- E40
- Language of mathematics. Formalization. Defining.
Axiomatics and axiomatic methods. Acquisition of mathematical concepts
- psychological aspects of concept formation see C30
- verbal communications see C50
- number concept see F20
- mappings and functions see I20
- 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
- estimates see N20
- representation of numbers (numerical mathematics) see N20
- 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)
- 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)
- mathematical modelling and mathematical applications see M
- teaching problem solving see D50
- linguistic comprehension of word problems see C50
- 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)
- quantities and units see also F70
- word problems see F90
- 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
- technical drawing see M20
- cartography see M50
- G90
- Miscellaneous (E.g.: convex sets, packings,
coverings, tessellations, non-euclidean geometries, finite geometries)
- numerical methods see N30
- 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
- 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)
- H70
- Miscellaneous (E.g.: algebraic topology,
algebraic geometry)
- numerical analysis see N40
- 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)
- sequences see I30
- polynomials see H20
- 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
- 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
- discrete mathematics see N70
- finite geometries see G90
- 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
- probability and statistics see K
- numerical methods see N
- interactions with other subjects see D30
- M20
- Mathematics on vocational training and career
education
- 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)
- combinatorics see K20
- graph theory see K30
- finite geometries see G90
- difference equations see I70
- 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)
- comments on syllabuses and edicts see B70
- lesson preparation see D40
- draft lessons and teaching units see D80
- U40
- Problem books, student competitions,
examination questions
- preparation for examinations and achievement control see
D60
- teaching problem solving see D50
- 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)
- U70
- Mathematical tables. Mathematical instruments,
pocket calculators. Comments on their instructional use. Computer as
a teaching medium
- mathematical software see N80
- collections of computer programs see N80
- U80
- Audiovisual media and their use in instruction
(Transparencies, films, Broadcasting and television)
- U90
- Miscellaneous (Student publications, repetition
materials. Mathematical expositions)