"Mathematics Education in its Cultural Context"

di Alan J. Bishop,

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

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.

[...]