Verbal Optimization Problems and The Importance of Their Writing

Objective: This study analyzes optimization word problems found in different sources of information and used in the teaching of differential calculus, with a specific focus on the ACF-0901 and ACF-2301 programs of the Minatitlán Technological Institute (ITM). ). The purpose is to identify and discuss deficiencies in these problem statements, such as insufficient data, errors in conditions, or poorly posed questions. Theoretical Framework: It is based on theories of mathematical problem solving, highlighting the importance of clarity in statements and the relationship between written language and the mathematical model, according to authors such as Kantowski, Gerofsky, Godino, Schoenfeld and Santos, among others. Method: An analytical approach was used to review 15 problems taken from three sources of information: textbooks, graduate theses, and online documents. The analysis included key components, such as the structure of the problem, clarity of language, relevance of the data, and whether the information can be used to formulate the mathematical model that solves the problem. Results and Discussion: Discrepancies were identified in the formulation of some of the problems analyzed. These inconsistencies make it difficult for students to learn and solve problems. In addition, corrections were proposed to the statements to align them with the competencies expected at the educational level of students taking the ACF-0901 or ACF-2301 programs and finally to seek the validity of the proposed statements through the collaboration of a group of experts. Research Implications: The findings highlight the need to select well-formulated and structured problems for teaching optimization in differential calculus. Appropriate writing and selection of problems can improve academic performance and facilitate the development of critical competencies in students. Originality/Value: This study contributes to the field of educational mathematics by proposing a detailed and systematic analysis of word problems in optimization proposed in different sources of information, and improving the use of these in the classroom. The results have direct applications in teaching practice and in the design of higher quality teaching materials.