Bishop identifies six "universal" activities which can be characterized as mathematical activities. In addition, he also specifies for each activity some

"organisingconcepts" which should provide a "knowledge frame" for the mathematics curriculum. The six activities and their "organising concepts" specified by Bishop are:

## Counting

Quantifiers (each, some, many, none); Adjectival number names; Finger and body counting; Tallying; Numbers; Place value; Zero; Base 10; Operations on numbers; Combinatories; .Accuracy; Approximation; Erros; Fractions; Decimals; Positive, Negatives; Infinitely large, small; Limit; Number patterns; Powers; Number relationships; Arrow diagrams; Algebraic representation; Events; Probabilities; Frequency representations.

Locating:

Prepositions; Route descriptions; Environmental locations; N.S.E.W. Compass bearings; Up/down; Left/right; Forwards/Backwards; Journeys (distance); Straight and Curved lines; Angle as turning Rotations; Systems of location: Polar coordinates, 2D/3D coordinates, Mapping; Latitude / Longitude; Loci; Linkages; Circle; Ellipse; Vector; Spiral.

Measuring

Comparative quantifiers (faster, thinner); Ordering; Qualities; Development of units (heavy - heaviest - weight); Accuracy of units; Estimation; Length; Area; Volume; Time; Temperature; Weight; Conventional units; Standard units; System of units (metric); Money; Compound units.

Designing:

Design; Abstraction; Shape; Form; Aesthetics; Objects compared by properties of form; Large, small; Similarity; Congruence; Properties of shapes; Common geometric shapes, figures and solids; Nets; Surfaces; Tesselations; Symmetry; Proportion; Ratio; Scale-model Enlargements; Rigidity of shapes.

Playing

Games; Fun; Puzzles; Paradoxes; Modelling; Imagined reality; Rule-bound activity; Hypothetical reasoning; Procedures; Plans Strategies; Cooperative games; Competitive games; Solitaire games; Chance, prediction.

Explaining:

Similarities; Classifications; Conventions; Hierarchical classifying of objects; Story explanation; logical connectives; Linguistic explanations: Logical arguments, Proofs; Symbolic explanations: Graphs, Diagrams, Charts, Matrices; Mathematical modelling; Criteria: internal validity, external generalisability.

Bishop, A.J.: 1988 ( pp.100/103) Mathematical Enculturation: a cultural perspective on Mathematics Education, D. Reidel Publishing Company, Dordrecht, Holand.