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Wykorzystanie prac Stanisława Drózdza jako srodków dydaktycznych w nauczaniu

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Hoffmann A.

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

2015

tom 7

45-58

As far as teaching practice in mathematics is concerned, we usedifferent methods, forms and tools, which enable pupils to acquire both theoreticalknowledge and practical skills more efficiently. Stanisław Drózdz(1939-2007) was a concrete poet, who, in his work, used not only words, butalso visual art. Poetry, art and mathematics are apparently distant domains,yet when I saw Drózdz‘s works, I noticed the opportunity to use them asoriginal tools in teaching mathematics. I will show his chosen works and differentways of using them in mathematical education. Some of them could beused as illustrations of various concepts (for example at early stages of mathseducation). Others could be starting points in discovering and exploringsome regularities. There are also some which could inspire pupils to look intocertain mathematical problems. Whilst creating his concept-shapes, StanisławDrózdz used similarities and differences of various situations.Searching for similarities and differences using analogies and contrast alsomakes it possible to build mathematical concepts in pupils‘ minds. Byputting together concept and shape, Drózdz worked in a way similar topractice in mathematical education - while defining concepts, we give thema name and (very often) a symbol, and we try to visualize them by givingthem a “shape”. Using Stanisław Drózdz‘s works, it is possible to build yetanother bridge between theory and practice, particularly for pupils to whommaths is not a life-long passion.

On Some Applied First-Order Theories which Can Be Represented by Definitions

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Shalack V., Section of Logic I. o. P., shalack@gmail.com

Bulletin of the Section of Logic

2015

tom 44

nr 1-2

In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this criterion such theories as the theory of equivalence relation, the theory of partial order and many theories based on the equality relation with finite set of functional and predicate symbols are represented by definitions in the first-order predicate calculus without equality.

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

1 Bulletin of the Section of Logic

1 Hoffmann A.

1 Section of Logic I. o. P.

1 Shalack V.

1 shalack@gmail.com

2 2015

Wyniki wyszukiwania

Wykorzystanie prac Stanisława Drózdza jako srodków dydaktycznych w nauczaniu

On Some Applied First-Order Theories which Can Be Represented by Definitions