Przyczynek do badań nad rozumieniem przez uczniów tekstu matematycznego

Abstract

In the paper is presented an investigation and its results that concern understanding the contents of a mathematical statement by pupils of grammar schools (15-18 years old). An atempt has been undertaken to formulate criteria of understanding as well as criteria for selecting such groups of pupils, which are equivalent in some view. The investigation was based on the example of one theorem, presented in three versions, due to an accepted hypothesis that formulation of a theorem influences understanding of its contents. Three kinds of formulation were singled out: indicative, conditional and conditional—funcional. The investigation concerned 633 pupils of 9th, 10th and 11th forms. Results were analised statistically and qualitatively. They confirm in principle the assumed hipoteses, while this confirmation is differentiated with regard to the atended by the investigated pupils. Among conclusions based on the investigation the following ones are primarily emphasized: 1. the need of teaching the pupils how to use a mathematical text, in particular the need of teaching them "to read" a mathematical statement, 2. the necessity of various formulations of mathematical statements, with particular consideration of the conditional-functional form, first of all in lower forms, 3. the need of search for various means of verifying the understanding of the contents of a statement. All conclusions are to be treated very carefully, and it is clearly suggested that further investigation is necessary for their fuller confirmation.