Abstract In this work, we expose and explain the elements of a theoretical construct called the interpretive field (IF), which is generated from a mathematical object called the IF core. To exemplify and demonstrate the construction process of an IF, we chose the Pythagorean Theorem (PT) as the core, given its relevance within mathematics and as a learning object in didactics. An IF is made up of conceptual networks that structure the mathematical objects immersed in the core, which are made explicit through hermeneutic tools, particularly analogy. During the construction process of the IF associated with the Pythagorean Theorem (IF-PT), the relevance of the tension between opposites (for example, particularization-generalization) is highlighted as a generator of relationships that articulate meanings and interpretations between mathematical objects. The purpose of generating an IF is to obtain a global vision of the relationships and articulations that emerge from the nucleus, in which the equivocal interpretations in different contexts are highlighted and made transparent. These relationships are useful to identify and design didactic trajectories, which are evidence of mathematical understanding, which can be achieved through a process of oriented reconstruction of knowledge. As a result of the work, we present a graphic representation of the partial network of constituent relationships of the IF-PT. This network is partial and incomplete, because the IC is a dynamic construct in permanent construction, whose structure is dialectically related to the knowledge of each person and to scientific advances at a certain historical moment. The previous ideas exemplify the inherent complexity of the mathematical objects that are placed in the didactic scenario, and which consideration is fundamental for the development of understanding.

Resumen En este trabajo exponemos y explicamos aquellos elementos que conforman un constructo teórico denominado campo interpretativo (CI), el cual se genera a partir de un objeto matemático llamado núcleo del CI. Para ejemplificar y evidenciar el proceso constructivo de un CI, elegimos al teorema de Pitágoras (TP) como núcleo, dada su relevancia dentro de la matemática y como objeto de aprendizaje en la didáctica. Un CI está integrado por redes conceptuales que estructuran los objetos matemáticos inmersos en el núcleo, las cuales se explicitan mediante herramientas hermenéuticas, particularmente la analogía. Durante el proceso constructivo del CI asociado al Teorema de Pitágoras (CI-TP) se destaca la relevancia de la tensión entre opuestos (por ejemplo, particularización-generalización) como generadora de relaciones que articulan significados e interpretaciones entre objetos matemáticos. La finalidad de generar un CI, es obtener una visión global de las relaciones y articulaciones que se desprenden del núcleo, en la que se destaca y transparenta la equivocidad de las interpretaciones en diferentes contextos. Estas relaciones son de utilidad para identificar y diseñar trayectorias didácticas, las cuales son evidencia de un entendimiento matemático, que se puede lograr a través de un proceso de reconstrucción orientada del conocimiento. Como resultado del trabajo, presentamos una representación gráfica de la red parcial de relaciones constituyentes del CI-TP. Dicha red es parcial e incompleta, porque el CI es un constructo dinámico en permanente construcción, cuya estructura se relaciona dialécticamente con los conocimientos de cada persona y de los avances científicos en un cierto momento histórico. Todo lo anterior es muestra de la complejidad inherente a los objetos matemáticos que son puestos en el escenario didáctico, y cuya consideración es fundamental para el desarrollo del entendimiento.

ABSTRACT The agri-food supply chain (AFSC) sets a series of challenges in the production, storage, distribution, and transportation processes, as the market's requirements for fresh food combine food quality and safety attributes. This research suggests a discrete event modeling to study the behavior of food quality in all supply chains (SCs) in terms of temperature and time variables in a stochastic manner. The ProModel software was used to simulate strawberry quality in the SC, considering a distribution route to export the fruit from Mexico to the United States. The suggested model together with a computer simulation analyzes the fruit quality from two perspectives: with and without a cold chain (CC). The obtained results revealed that in the case of CC usage, when consumed the strawberry's average quality was 85%. In the approach without CC, the results revealed that when the strawberry arrives and remains in the distribution center, it loses more than 40% of its quality. This proposal may help those involved in the AFSC to make decisions that allow them to maximize quality and profit, minimize waste, improve distribution routes, and control stock levels.

Abstract In this paper, we report the results of an exploratory research in which the interest was to identify how beliefs that support teachers in service about the Pythagorean Theorem are indicators of a didactical reductionism on this mathematical result. Questionnaires were applied to five public high school mathematics teachers and a semi-structured interview with a teacher who imparts courses of physics and mathematics in an engineering course at a public university. The collected data were analyzed based on six beliefs categories. One relevant result of the work is that teachers conceive the Pythagorean Theorem as an isolated fact and not as an integrated approach to a highly structured network of ideas, covering a wide variety of mathematics knowledge branches. However, it seems suitable that teachers think about their own beliefs and implications that those beliefs have in the teaching activity.

Resumen En este artículo reportamos los resultados de una investigación exploratoria, cuyo interés fue identificar cómo las creencias que sostienen profesores en servicio sobre el Teorema de Pitágoras, son indicadores de un reduccionismo didáctico relativo a este resultado matemático. Se aplicaron cuestionarios a cinco profesores de matemáticas que laboran en un bachillerato público y una entrevista semi-estructurada a un profesor quien imparte cursos de física y matemáticas en una carrera de ingeniería en una universidad pública. Los datos recolectados se analizaron con base en seis categorías de creencias. Un resultado relevante del trabajo es que los profesores conciben al Teorema de Pitágoras como un hecho aislado y no como un conocimiento integrado a una red altamente estructurada de ideas que abarcan una amplia variedad de ramas de la matemática. Por tanto, resulta conveniente que los profesores reflexionen acerca de sus propias creencias y las implicaciones que tienen sobre su actividad docente.