The Teaching and Learning of Equations: Problems and Possibilities during the Transition from High School to Higher Education
Affiliation(s)
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.
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.
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.
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.
KEYWORDS
Algebra, Equations, Transition from High School to the Top, Functions and Discursive Operations under Duval, Mathematics Education
Algebra, Equations, Transition from High School to the Top, Functions and Discursive Operations under Duval, Mathematics Education
Cite this paper
Brandt, C. and Baccon, A. (2015) The Teaching and Learning of Equations: Problems and Possibilities during the Transition from High School to Higher Education. Creative Education, 6, 961-975. doi: 10.4236/ce.2015.610098.
Brandt, C. and Baccon, A. (2015) The Teaching and Learning of Equations: Problems and Possibilities during the Transition from High School to Higher Education. Creative Education, 6, 961-975. doi: 10.4236/ce.2015.610098.
References
[1] Bogdan, R , & Biklen, S. (1994). Investigação qualitativa em educação: uma introdução à teoria e aos métodos. Porto: Porto Editora. [2] Brasil (1996). Lei 9394/96. Lei de Diretrizes e Bases da Educação Nacional. [3] Charlot, B. (2000). Da relação com o saber: elementos para uma teoria. São Paulo: Artmed. [4] Duval, R. (1995). Semiosis et pensée humaine: sémiotiques registres et apprentissages intellectuels. Berna: Peter Lang. [5] Duval, R. (2011). Deux regards sur les opposés points critiques sur l’enseignement de l’algèbre au collège (11-15 ans). Lecture given at the Graduate Program in Mathematics Education of Mato Grosso Federal University. [6] Fiorentini, D., Miorim, M. A., & Miguel, A. (1993). Contribuição para um repensar... A educação algébrica elementar. Pro-Posições, 4, 78-91. [7] Kuenzer, A. (2002). Ensino Médio: construindo uma proposta para os que vivem do trabalho. São Paulo: Cortez. [8] Marcozzi, A. M., & Dornelles, L. W., & Rêgo, M. V. B. S. (1976). Ensinando a criança: um guia para o professor (3rd ed.). Rio de Janeiro: Ao Livro Técnico. [9] Micotti, M. C. O. (1999). O ensino e as propostas pedagógicas. In: M. A. V. Bicudo (Ed.), Pesquisa em Educação Matemática: concepções & Perspectivas (pp. 153-167). São Paulo: Editora UNESP.
[1] Bogdan, R , & Biklen, S. (1994). Investigação qualitativa em educação: uma introdução à teoria e aos métodos. Porto: Porto Editora. [2] Brasil (1996). Lei 9394/96. Lei de Diretrizes e Bases da Educação Nacional. [3] Charlot, B. (2000). Da relação com o saber: elementos para uma teoria. São Paulo: Artmed. [4] Duval, R. (1995). Semiosis et pensée humaine: sémiotiques registres et apprentissages intellectuels. Berna: Peter Lang. [5] Duval, R. (2011). Deux regards sur les opposés points critiques sur l’enseignement de l’algèbre au collège (11-15 ans). Lecture given at the Graduate Program in Mathematics Education of Mato Grosso Federal University. [6] Fiorentini, D., Miorim, M. A., & Miguel, A. (1993). Contribuição para um repensar... A educação algébrica elementar. Pro-Posições, 4, 78-91. [7] Kuenzer, A. (2002). Ensino Médio: construindo uma proposta para os que vivem do trabalho. São Paulo: Cortez. [8] Marcozzi, A. M., & Dornelles, L. W., & Rêgo, M. V. B. S. (1976). Ensinando a criança: um guia para o professor (3rd ed.). Rio de Janeiro: Ao Livro Técnico. [9] Micotti, M. C. O. (1999). O ensino e as propostas pedagógicas. In: M. A. V. Bicudo (Ed.), Pesquisa em Educação Matemática: concepções & Perspectivas (pp. 153-167). São Paulo: Editora UNESP.