Transpondo obstáculos: da Aritmética para a Álgebra

Abstract

This work demonstrates difficulties of students on recognizing fractions asnumbers and how to overcome them. For this purpose, a strategy was developed to teachfractions taking as reference the number line. By relating the fraction to a well-defined objective concept, students proceed quickly to master more complex concepts. Theidentification of fractions as numbers is initially performed in the measurement of linesegments. From the number line the student transposes to other contexts in a process ofsuccessive generalizations. A sequence of activities involving, e.g., equivalence betweenfractions and order in the set of fractions, is here described and results of this methodologyapplication are presented. These results are evaluated from a global point of view and ofgroups with different levels of previous qualification. Results obtained demonstrate thatfamiliarization with the algebraic field is more easily reached when the concept of fraction isdealt in the proposed way.