The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences

Abstract

This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students’ use of relations between mathematical elements when solving a mathematical task. We use a qualitative methodology and the data collection instruments are a written questionnaire and a semi-structured interview. In this work we show the questionnaire task that provides analytical expressions and ask students to determine which of them numbers sequences are. We find that students’ use of logical implication when solving tasks related to number sequences is an indicator of the development of the scheme. This indicator helps to locate the transition mechanisms between the levels of development of the number sequence scheme. Moreover, our research shows that arithmetic and geometric progressions play a key role as an indicator of the development of the number sequence scheme.