## MESC Classification

The Mathematics Education Subject Classification (MESC) was compiled by the Editorial Office of MathEduc with the kind support of numerous experts. It is reflected in the MSC2010 scheme in the area 97 – Mathematics education.

The MESC scheme consists of 16 main areas classified with two digits refined into over 1000 three-digit classifications. It serves as a compass to keep being informed about the developments in their areas of interest.

Searching the ever growing number of mathematical publications would not be possible without the help of this well organized scheme. Nearly all publications are classified according to this widely accepted tool.

## Last digit

The last digit refers to the educational level:**0**: General, difficult to classify in the third position**1**: Kindergarten, Pre-school education**2**: 1st to 4th year of school, primary education, elementary level**3**: 5th to 10th year of school, secondary level, lower and middle secondary (all types of school)**4**: 11th to 13th year of school, upper secondary**5**: Universities, Colleges, Polytechnics**6**: Special schools**7**: Vocational schools**8**: Extra mural institutes, Colleges of Further Education, Correspondence schools, Popular education etc.**9**: Teacher training, teacher in-service training

## Complete list

A | General |

A10 | Comprehensive works on mathematics. Reference books, encyclopaedias and dictionaries [textbooks see U20; material for repetition see U90; comprehensive works on special disciplines see each discipline] |

A20 | Recreational mathematics [educational games see U60] |

A30 | Biographies. History of mathematics and of mathematics teaching [sociological aspects of learning see C60; political education in the mathematics classroom see D30] |

A40 | Sociological and political issues. The profession of teaching. Careers in mathematics, labour market [sociological aspects of learning see C60; political education in the mathematics classroom see D30] |

A50 | Bibliographies. Information and documentation |

A60 | Proceedings. Conference reports. Collections of articles |

A70 | Theses and postdoctoral theses |

A80 | Popularization |

A90 | Picture stories. Cartoons. Fiction. Games [recreational mathematics see A20; educational games see U60] |

B | Educational policy and educational system (Educational research, educational reforms, pilot projects, official documents, syllabuses) |

B10 | Educational research and planning |

B20 | General education [syllabuses see B70] |

B30 | Vocational education [syllabuses see B70] |

B40 | Higher education |

B50 | Teacher education (Teacher preservice and inservice 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] |

C | 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) [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 communication (Teacher/student language styles. Language acquisition. Learning with texts. Language difficulties, multilingualism, teaching and learning mathematics in a second language. Communicative competence) [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] |

D | 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 [history see A30; 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; 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 examinations see D60; teacher resources for preparing lessons see U30; interdisciplinary teaching see M10] |

D50 | Investigating and problem solving (E.g.: teaching problem solving and heuristic strategies, methodology 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 competition questions see U40] |

D60 | Student assessment (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, misconceptions and student errors [special education see C90; achievement control and rating see D60] |

D80 | Teaching units, draft lessons and master lessons |

E | Foundations of mathematics |

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

E20 | Metamathematics. Philosophical and ethical aspects of mathematics. 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 [psychological aspects of concept formation see C30; verbal communication 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 |

F | 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 [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) [lengths, 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 in 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] |

G | Geometry |

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 [geometric transformations 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) [fractals see I90] |

H | Algebra[numerical method in algebra 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 [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 equations) [vector algebra see G70] |

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

I | Analysis[numerical method in analysis see N40] |

I10 | Comprehensive works on calculus and the teaching of calculus |

I20 | Mappings and functions. Elementary properties of functions. Special functions (Concept of function, representation of functions, graphs 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 [complex numbers see F50] |

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

K | 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) [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 theorems |

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) |

M | Mathematical modelling, applications of mathematics |

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 in 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) |

N | 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) [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 foundation 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) |

P | Computer science |

P10 | Comprehensive works on computer science [historical reflections see A30] |

P20 | Theory of computer science. Data (Information Theory, coding theory, automata theory, theory of formal languages, theory of algorithms, computational complexity, computability. Data acquisition, input, data structures, storage, coding, encryption) [data protection see P70; databases and information systems see R50] |

P30 | System software (Operating systems, tools, utilities [user programms see R70] |

P40 | Programming languages |

P50 | Programming techniques. Software engineering (Problem analysis, program design, flowcharting structured programming. Program verification, debugging, run-time estimation [psychology of computer programming see Q20, Q30] |

P60 | Hardware (Description of special computers, Computer architectures, network architectures) [software for networks see P30] |

P70 | Computer science and society. Computer Science and philosophy (Data protection. Impacts of computers on science and education) [impacts on mathematics teaching see D30; careers and labour market see A40; computer literacy see Q50] |

P80 | Miscellaneous |

Q | Psychology of computer science education. Computer science teaching[mathematics teaching and learning see C and D] |

Q10 | Comprehensive works |

Q20 | Affective behaviour. Personality (Motivation, attitudes, anxiety, feelings, self concept. Skills and abilities. Creativity. Personality traits) |

Q30 | Cognitive processes (Concept formation, thought processes, problem solving. Learning) [artificial intelligence see R40] |

Q40 | Sociological aspects of learning. Communication (Group dynamics. Roles. Social, economic and cultural influences. Social learning. [teaching-learning processes see Q60] |

Q50 | Objectives of computer science teaching. Computer literacy (Innovations and trends, curriculum development and research, testing of syllabuses in pilot classes) [syllabuses and curricula see B70; historical reflections see A30] |

Q60 | Lesson planning. Teaching methods and classroom techniques: evaluation of instruction (teaching-learning processes. Teaching principles. Classroom organization) [computer aided instruction (CAI) see U50] |

Q70 | Achievement control and rating. Diagnosis, analysis and remediation of learning difficulties and student errors |

Q80 | Teaching units, draft lesssons and master lessons |

Q90 | Miscellaneous |

R | Applications of computer science and computers |

R10 | Comprehensive works, collections of computer programs |

R20 | Applications in mathematics and mathematical education (e.g. : computer algebra) [computer aided instruction (CAI) see U50; user programs see R70] |

R30 | Applications in natural, behavioral and social sciences, engineering, economics, humanities, earth sciences. Computers in schools and universities. [computer aided instruction (CAI) see U50; user programs see R70] |

R40 | Artificial intelligence (Image processing. Language processing. Pattern recognition. Automatical theorem proving. Expert systems,. Knowledge engineering) [cognitive processes see C30, Q30; intelligent tutor systems see U50] |

R50 | Data base information systems. Telecommunication (e.g. Internet) [data see P20; data base managment systems R70] |

R60 | Graphical data processing, computer graphics |

R70 | User programs. Administrative uses in the educational system (e.g. word processing, spreadsheets) |

R80 | Recreational computing. Computer games |

R90 | Miscellaneous |

U | Educational material and media. Education 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 [textbooks for special disciplines see each discipline; learning with texts see also 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, competition and examination questions [student competitions see B60; preparation for examinations and achievement control see D60; teaching problem solving see D50] |

U50 | Programmed instruction, computer assisted instruction (CAI, intelligent tutor systems, courseware design, e-learning) [educational software see U70] |

U60 | Manipulative materials and their use in the classroom (visualizations, teaching aids, models, educational games, worksheets. Teaching in laboratories) [games see also A90] |

U70 | Technological tools (Computers, calculators, software, mathematical instruments, etc.) Comments on their instructional use [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) [reference books see A10] |