The Teaching and Learning of Equations: Problems and Possibilities during the Transition from High School to Higher Education

Celia Finck Brandt,Ana Lúcia Pereira Baccon

doi:10.4236/ce.2015.610098

Abstract

The teaching of equations for elementary school students has been faced with many obstacles, as their difficulties to find the roots of equations of first or second degree. These difficulties are presented by the students in continuing their studies (high school) and also detected on the transition of students to higher education. According to Raymond Duval these difficulties come from the mathematical point of view which is incompatible with the cognitive point of view. In this research we aim to point out to what extent the meanings assigned to algebra by the students of the Bachelor in Mathematics are close among themselves or move away from the cognitive point of view. We developed two instruments to collect qualitative information: a questionnaire with two questions and interviews. The subjects were eighteen students of Degree in Mathematics of the UEPG. The data were analyzed in the light of the discourse functions mentioned by Duval (1995): apophantic, reference and discursive expansion and their cognitive operations: apophantic function and its illocutionary act of predication and operations; referential function and its pure designation of operations, simple categorization and determination; discursive expansion function and its operations narration, description, explanation and reasoning. The speech will be analyzed in terms of semiotic or semantic similarity, internal or external arranged in a double entry table. Empirical data will be entered in cells derived from the crossing of this categorization featuring differentiated discursive expansions: formal expansion, natural, cognitive and lexical. Research is in progress showing no results at this time.

Highlights

Contemporary society determines some assumptions and expects some attitudes with regard to education and educators
The apophantic function and discursive expansion function provide logical and epistemic value to the students’ responses
The above discussion and analysis allow us to infer about the social, logical or epistemic values that emerge from the teaching of Algebra, concerning the content of equations

Summary

Introduction

Contemporary society determines some assumptions and expects some attitudes with regard to education and educators. It is often expected that the school, besides providing the formal education, which is its main goal, could provide the psychological, emotional, ethical and human education in order to fulfill that aspects of education neglected by the parents, which are often so absorbed in their professional works that have less time to properly educate their children. As a result, it is expected from the school a role usually beyond its social function. L6 sum-subtraction-multiplicationfind the value of an unknown Equality-algebra-system balance-application

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Methods

Conclusion