Creative Education, 2015, 6, 961-975 Published Online June 2015 in SciRes. http://www.scirp.org/journal/ce http://dx.doi.org/10.4236/ce.2015.610098 How to cite this paper: Brandt, C. F., & Baccon, A. L. P. (2015). The Teaching and Learning of Equations: Problems and Pos- sibilities during the Transition from High School to Higher Education. Creative Education, 6, 961-975. http://dx.doi.org/10.4236/ce.2015.610098 The Teaching and Learning of Equations: Problems and Possibilities during the Transition from High School to Higher Education Celia Finck Brandt 1 , Ana Lúcia Pereira Baccon 2* 1 Department of Methods and Teaching Techniques, State University of Ponta Grossa (UEPG), Parana, Brazil 2 Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG), Parana, Brazi Email: * ana.baccon@hotmail.com Received 27 April 2015; accepted 15 June 2015; published 19 June 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ 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 pre- sented 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 ma- thematical 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 de- veloped 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 il- locutionary act of predication and operations; referential function and its pure designation of op- erations, simple categorization and determination; discursive expansion function and its opera- tions 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 differen- tiated discursive expansions: formal expansion, natural, cognitive and lexical. Research is in progress showing no results at this time. Keywords Algebra, Equations, Transition from High School to the Top, Functions and Discursive Operations * Corresponding author.