Rozumienie implikacji przez uczniów liceum (fragment badań)

Abstract

The paper presents part of larger investigation on "Formal and natural understanding by students the propositional connectors and quantifiers”. As the greatest difficulties met by students concern implication, which had been made apparent by an experimental research, a supplementary investigation was carried out with groups of persons that had already received a certain elementary logical education. Tests were differenciated with regard to formulation of problems in both conventional (everyday) language and formal language (i.e. with the use of logical symbols). The investigation was carried out on 694 2nd upper secondary form students, as well as on 73 students of the 1st year of mathematics and physics at the teachers training college. All those people were divided into three groups. The first group was given first a test in everyday language and then another one, analogical with regard to its logical structure, but formulated in formal language. The second group was given the tests in the inverted succession; students from the third one were allowed to choose the test which they preferred. Anoter differenciation consisted in picking out those experimental classes where logical knowledge was consolidated systematically during the whole year, and the comparative classes where this aspect was not particularly emphasised. The solutions were submitted to precise statistical as well as qualitative analyses. They provide arguments for the following conclusions: 1. Logical knowledge acquired by students remains unactive and is forgotten considerably if it is not applied systematically in the course of teaching. On the contrary, its continuous consolidation makes it more concrete. This follows from the essential differences between the scores of the experimental and the comparative classes. 2. Many students do not apply their logical knowledge in the course of reasoning consciously and spontaneously, do not submit the structure of the text to logical analysis. Scores in the formal test are considerably better than scores in the conventional one. 3. Using symbolic language by students brings advantages but at the same time may cause mistakes. A student often applies uncritically logical "rules" invented by himself, without any control of common sense, and without any interpretation in this logical insight. 4. Forcing students to excessive formalisation in logically simple situations is burdensome, painful and unnecessary. However in complicated situations logical knowledge and symbolic language help to avoid mistakes and in case where a mistake has been made facilitate its finding and correction.