The problem-based learning for working on commercial factorization with 4th year secondary compulsory school students allows the application of practical knowledge in the mathematics classroom at an educational center in Bogotá, Colombia (South America).
Algebraic factor decomposition has been developed to describe the commercial management involved in the consumption of products, generating the process of buying and selling goods and services; in order to attract new concepts and experiences of useful, practical, creative, updated, competent knowledge and reflective challenges that are created among school work teams.
The core of this article lies in designing a didactic intervention to improve problem-solving through commercial factorization by applying technology and the collaborative learning wearing the basic economic equations and marketing measures to critical thinking training and assessment processes and analytical thinking in real cases of school learning.
Therefore, the theoretical framework explains the three categories based on the characteristics ranging from arithmetic factorization, algebraic, geometric and commercial with the problem-based learning and the manipulative-digital resources.
The methodology is based on the pedagogical techniques of the active-constructive learning, problem-based learning, commercial learning approach, collaborative learning and game-based learning of meaningful experiences, using
10 cases of algebraic decomposition, applying commercial and virtual learning with Geogebra and Python-Matplotlib which is synthesized in the games-contests.
Diagnostic, formative and summative assessments, as described in the rubric, were also carried out using the MAXQDA 2020 software program with qualitative data on cognitive tasks. The participants were eight heterogeneous and normal students of both sexes (four boys and four girls) without learning difficulties, grouped into four pairs for 24 work sessions in the library and computer lab.
The results indicate that students will solve applied problems using the heuristic method, generating knowledges and applying the analysis and use of graphs with business data. The effectiveness of the algebraic model, based on solving commercial factorization problems, is demonstrated, strengthening consume culture.
Keywords: Heuristic Method, Collaborative Learning, Algebraic Factorization, Problem-based Learning, Didactic Intervention, Compulsory Secondary Education, Commercial Management.
Abbreviations: STEM, AAC, PBL, BLA, CL, GBL, COPISI, LCM, GCD.
