General
comment to classification
A10
Comprehensive works on mathematics. Reference books, encyclopaedias and dictionaries

A20
Recreational mathematics

A30
Biographies. History of mathematics and of mathematics teaching

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

A50
Bibliographies. Information and documentation

A60
Proceedings. Conference reports

A70
Theses and postdoctoral theses

A80
Standards

A90
Picture stories. Cartoons. Fiction. Games




Educational policy and educational system

(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



Psychology of mathematics education. Research in mathematics education. Social aspects

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)



Education and instruction in mathematics

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



Foundations of mathematics

E10
Comprehensive works on the foundations of mathematics and their teaching. Methodology of mathematical research


E20
Metamathematics. Philosophical aspects of mathematical Epistemology

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

E50
Proof methods. Reasoning and proving in the mathematics classroom


E60
Sets. Relations. Set theory

E70
Miscellaneous



Arithmetic. Number theory. Quantities

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)

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

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



Geometry

G10
Comprehensive works on geometry and the teaching of geometry


G20
Informal geometry (Spatial orientation. Basic geometrical shapes)

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

G40
Plane and solid geometry. Geometry in multidimensional spaces

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)



Algebra

H10
Comprehensive works on algebra and the teaching of algebra


H20
Elementary algebra (Variables, manipulation of expressions. Binomial theorem. Polynomials. Finite sums)

H30
Theory of equations and inequalities

H40
Operations. Groups, rings, fields

H50
Ordered algebraic structures. Lattices. Boolean algebra

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

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



Analysis

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

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



Combinatorics and graph theory. Statistics and probability

K10
Comprehensive works on stochastics and the teaching of stochastics


K20
Combinatorics (Classical combinatorial theory, configurations, latin squares)

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)



Mathematical modelling, applications of mathematics

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

M20
Mathematics on vocational training and career education

M30
Financial mathematics. Insurance mathematics


M40
Operations research, economics

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)



Numerical mathematics. Discrete mathematics. Mathematical software

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)

N50
Approximation, interpolation, extrapolation


N60
Mathematical programming

N70
Discrete mathematics (Finite methods in various mathematical fields, especially used as theoretical foundations in other disciplines)

N80
Mathematical software. Collections of computer programs

N90
Miscellaneous (e.g. experimental mathematics)



Educational material and media. Educational technology

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

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)

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)