Criteria That Guide the Professor's Practice to Explain Mathematics at Basic Sciences Courses in Engineering Degrees in Peru. A Case Study

Abstract

Background: Research on mathematics teaching in basic science classes within Peruvian engineering degrees was required prior to the identification of alternatives to improve the training of future engineers. Objective: To identify the criteria that guide the practice of professors in Peru when explaining mathematics in basic science classes within engineering degrees, with specific reference to derivatives. Design: Qualitative case-study research that seeks to understand current mathematics teaching through an analysis of and reflection on the participants' practices. Setting and participants: Professors who give classes within engineering faculties in Lima. One of these was selected as a case study. Data collection and analysis: The classes taught by these professors were filmed and the criteria they follow in the design and implementation of their classes were inferred by means of the didactic suitability criteria, which were also used to design a questionnaire to interview the teachers; triangulation was then performed between their words and their actions. Results: This professor was guided by ecological criteria (syllabus and profession) and mediational criteria (time available for classes), although he felt that his practice was based primarily on cognitive criteria (previous knowledge) and ecological criteria (future profession). Conclusion: The criteria that guided his practice help explain why basic science classes within engineering degrees are taught with a lecture-based and procedural approach, and why innovations are not included.

Evaluating problem-solving and procedural skills of first-year students in a Peruvian higher education institution

“…Additionally, engagement with mathematics promotes critical reasoning, decision-making, metacognition, among many other skills (Saha et al, 2020), all of which are imperative for success in today's rapidly changing world (Said et al, 2023). Particularly, two of the most important are procedural and problem-solving skills, and although efforts to enhance the teaching of mathematics are ongoing worldwide, including in Peru, where the existing mathematics education model in schools and universities is being examined for potential transformation and improvement (Garcés-Córdova & Font-Moll, 2022;Garcés Córdova et al, 2021;Maraví Zavaleta, 2021), recent studies revealed that the development of mathematical skills still requires a long process of improvement (Faulkner et al, 2020).…”

“…In Peruvian universities, the current state of mathematics education does not appear to be much better. While the continuous development of the Peruvian mathematics curriculum owes much to the efforts of educators and researchers engaged in scientific educational research (Maraví Zavaleta, 2021), there remains a noticeable lack of research in mathematics education within degree programs in Peru (Garcés Córdova et al, 2021). Additionally, Garcés Córdova et al (2021) have recently found that fundamental science courses are primarily delivered through a lecture-based and procedural approach, lacking innovations, realworld applications, and modeling.…”

“…Nevertheless, recent studies have revealed an overreliance on algebra and mechanization, with a noticeable absence of modeling processes in traditional mathematics teaching methods, which predominantly adopt a highly procedural approach (Garcés Córdova et al, 2021). Fortunately, procedural skills do not operate in isolation but are situated within a broader framework that encompasses other abilities; Applying the theory of George Pólya (as cited in Nasir & Syartina, 2021, p. 2), procedural skill, which encompass the process of implementing a planned strategy to find a solution, is part of problem-solving skills.…”

“…In many Peruvian schools, this has led to the overemphasis on algebraic and arithmetic aspects in mathematics subjects, resulting in students acquiring shallow knowledge without a deep understanding, thus encouraging students to seek mechanistic solutions without fostering creativity (Khalid et al, 2020) and leading them to prioritize procedural skills at the expense of important aspects like contextualization (Garcés-Córdova & Font-Moll, 2022;Garcés Córdova et al, 2021). Consequently, students pass through a learning process of mathematical concepts without gaining a profound understanding or a sense of practical application, ultimately resulting in a deficiency in problem-solving skills.…”

Theory of didactical suitability: An enlarged view of the quality of mathematics instruction

“…Several empirical research works have been conducted employing the didactic suitability criteria to analyze lesson design and teaching practices in mathematics teacher education courses (Breda et al, 2017;Garcés et al, 2021). These investigations reveal the usefulness of TDS to recognize that the value judgments issued by teachers on the quality of their practices correspond to TDS criteria in some facets, but do not mention systematically all its facets and components.…”