Abstract
How do we teach children to express and communicate ideas in a formal and informal mode? What type of language do they need in a concrete context? How should they determine a proper level of formalization of their descriptions? In an attempt to explore these issues we carried out a pilot experiment in the frames of the DALEST European project whose goal was to create environment for stimulating the 3D geometry understanding of young students and to assist them in developing some fundamental mathematical skills including spatial visualization and articulating ideas. The pilot experiment was carried out with 5th graders from five Bulgarian schools by means of specially designed educational scenarios and the Cubix Editor (a Logo based application for manipulating unit-sized cubes). The children were given tasks to describe compositions of unit-sized cubes and to build such compositions by means of the Cubix Editor when given their descriptions by peers. The students experienced the whole process of generating a good description - becoming aware of the ambiguity, producing counterexamples, reducing the ambiguity, eliminating the redundancy. The pilot experiment aimed at specifying the structure, scope and methods behind the stereometry activities envisaged for 5th graders in the frames of the DALEST project. The first impressions confirm our belief that the language is playing significant role in the learning experiences of the students, that the relationship between thoughts and words involves back and forth reshaping process. While constructing and describing cubical structures they articulated their own ideas, developed concepts collaboratively with others, moved between everyday and mathematical terms, between procedural and declarative style, exploring the boundaries of understanding. Such interplay with the step-wise refinement of their descriptions of cubical structures would hopefully enhance students' skills for working with mathematical definitions, on one hand, and prepare them for writing, debugging and explaining programs, on the other.
Highlights
Such interplay with the step-wise refinement of their descriptions of cubical structures would hopefully enhance students’ skills for working with mathematical definitions, on one hand, and prepare them for writing, debugging and explaining programs, on the other
Experts in mathematics and informatics education find that the most important component of the mathematical way of thinking for workers in ICT is the ability to express their ideas in a rigorous language, where each word and expression has an unambiguous meaning (Khait, 2003)
The education should take care of enhancing the abilities of the students to translate their intuition to a formal language, to create definitions of new abstract objects, to write comprehensible descriptions of abstract and real structures and to understand those created by others
Summary
Such interplay with the step-wise refinement of their descriptions of cubical structures would hopefully enhance students’ skills for working with mathematical definitions, on one hand, and prepare them for writing, debugging and explaining programs, on the other. To use John Austin celebrated phrase, is learning how to do things with words – not what to say, but how, where, to whom, and under what circumstances (Bruner, 1990) It has been suggested (Truss, 1999; Khait, 2005) that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. The education should take care of enhancing the abilities of the students to translate their intuition to a formal language, to create definitions of new abstract objects, to write comprehensible descriptions of abstract and real structures and to understand those created by others. Since learning how to push the frontier of what we can express with words (Papert, 1980) has always been a very important and appealing educational goal
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