estratto (p. 183-184) da
"Mathematics Education in its Cultural Context"
di Alan J. Bishop,
Educational Studies in Mathematics,
1988, p. 179-191

Non sono riportate due note ed è stata tolta una virgola dopo "sustained".
È stata modificata l'impaginazione.


[...]
Mathematics, as cultural knowledge,
derives from humans engaging in these six universal activities
in a sustained and conscious manner.
The activities can
either be performed in a mutually exclusive way
or, perhaps more significantly, by interacting together,
as in `playing with numbers'
which is likely to have developed number patterns
and magic squares,
and which arguably contributed to the development of algebra.

I would argue that,
in the mathematics which I and many others have learnt,
these activities have contributed at least
the following highly significant ideas:

Counting:
      Numbers. Number patterns. Number relationships.
      Developments of number systems.
      Algebraic representation.
      Infinitely large and small.
      Events, probabilities, frequencies.
      Numerical methods.
      Iteration.
      Combinatorics.
      Limits.

Locating:
      Position.
      Orientation.
      Development of coordinates - rectangular, polar, spherical.
      Latitude/longitude.
      Bearings.
      Angles.
      Lines. Networks. Journey.
      Change of position.
      Loci (circle, ellipse, polygon ...).
      Change of orientation. Rotation. Reflection.

Measuring:
      Comparing. Ordering.
      Length. Area. Volume.
      Time. Temperature. Weight.
      Development of units - conventional, standard, metric system.
      Measuring instruments.
      Estimation. Approximation. Error.

Designing:
      Properties of objects. Shape. Pattern.
      Design.
      Geometric shapes (figures and solids).
      Properties of shapes.
      Similarity.
      Congruence.
      Ratios (internal and external).

Playing:
      Puzzles. Paradoxes. Models. Games.
      Rules. Procedures. Strategies.
      Prediction. Guessing. Chance.
      Hypothetical reasoning.
      Games analysis.

Explaining:
      Classifications. Conventions. Generalisations.
      Linguistic explanations
          - arguments, logical connections, proof.
      Symbolic explanations
          - equations, formulae, algorithms, functions.
      Figural explanations
          - diagrams, graphs, charts, matrices.
      (Mathematical structure
          - axioms, theorems, analysis, consistency.)
      (Mathematical model
          - assumptions, analogies, generalisability, prediction.)

From these basic notions,
the rest of `Western' mathematical knowledge can be derived,
while in this structure can also be located
the evidence of the `other mathematics'
developed by other cultures.
Indeed we ought to re-examine labels such as
`Western Mathcmatics'
since we know that many different cultures
contributed to the knowledge encapsulated by that particular label.

[...]