COGNITIVE PATTERNS AND SCHEMES IN MATHEMATICAL ASSESSMENT PROCEDURES
1 Universidad Autónoma de Puebla (MEXICO)
2 Universidad Nacional Autónoma de México (MEXICO)
3 Escuela fe Formación Docente, Universidad Autónoma de Puebla (MEXICO)
About this paper:
Appears in: ICERI2012 Proceedings
Publication year: 2012
Conference name: 5th International Conference of Education, Research and Innovation
Dates: 19-21 November, 2012
Location: Madrid, Spain
Abstract:Based on the analysis of the cognitive competencies that played a central role in solving problems and items from Mexican assessment procedures (Evaluación Nacional de Logro Académico en Centros Escolares, ENLACE; Examen Nacional de Ingreso a la Educación Superior, EXANI) and international assessment forms (PISA), we have designed a collaborative programme between university professors and high school teachers. In the first stage of this project, teachers analysed, identified and characterised central schemes, as well as meaningful and relational patterns, that underlie different kinds of problems and items found in the national and international assessment measures. The second step was to generate a pool of items derived from the original items analysed, for the first moment. The content of the new items reflected the identified schemes and relational patterns. Our cognitive framework considered knowledge organization as a social construction process; therefore the main objective is to make thinking patterns visible to students and teachers with the aim of improving achievement through the analysis of mistakes and misconceptions. The items developed were based on relational thinking and were designed in order to assess the following competencies: Identification and characterization of the essential elements involved in the problem; analysis of the relationships that play a role in the presented context; construction of a mathematical relation that expresses the analysed interaction; consistent and continuous use of mathematical terminology. Finally, after teachers have gathered the item responses of high school students, the last stage was to analyse and evaluate, qualitative and quantitative, the items.
Keywords: Cognitive competencies, assessment, relational thinking, schemes, patterns.