Intertwining cumulated and current mathematical problem-solving developments to frame and support teaching practices

The COVID-19 pandemic has modified social and school activities worldwide. The irruption of digital technologies to organize and carry out educational tasks not only shaped and marked the implementation of school activities during the critical period of the pandemic, but also, contributed to identify resources and new ways to interact with students to foster, monitor, and assess their learning. How could cumulated and current results and advances in problem-solving research be interpreted to frame teaching and learning scenarios to coordinate teachers and students’ online and face to face work? To address this question, a synthesis of problem-solving themes and research results is reviewed to sketch a route to frame a teaching/learning scenario for students to develop problem-solving competencies.The author received partial support from Plan Nacional del MICINN with reference EDU2017-84276-R

Framing the use of computational technology in problem solving approaches

Mathematical tasks are key ingredient to foster teachers and students’ development and construction of mathematical thinking. The use of distinct computational tools offers teachers a variety of ways to represent and explore mathematical tasks which often extends problem solving approaches based on the use of paper and pencil. We sketch a framework to characterize ways of reasoning that emerge as result of using computational technology to solve a task that involves dealing with variation phenomena

Introduction to International Perspectives on Problem Solving Research in Mathematics Education

Any field of research and innovation must be exposed to revisions, criticisms and to an intense scrutiny not only to discuss the state of the art but, hopefully, to identify prospective changes and new areas of study and exploration as well

High School Teachers use of Dynamic Software to generate serendipitous mathematical relations

In this study, we document and analyse problem-solving approaches that high school teachers exhibited as a result of using dynamic software (Cabri-Geometry) to construct and examine geometric configurations. What type of questions do teachers pose and pursue while representing and exploring mathematical tasks or objects dynamically? To what extent their initial problem solving strategies are enhanced with the use of the tools? Results indicate that the use of the tool offered the participants the opportunity of constructing geometric configuration (formed by simple mathematical objects) that led them to identify and explore key mathematical relations

Revisiting university students' knowledge that involves basic differential equation questions

This study documents the extent to which university students utilize diverse representations and mathematical processes to interpret and respond to a set of questions that involves fundamental concepts in the study of differential equations. Results indicate that students' idea to solve a differential equation is reduced to the application of proper solution methods to a certain type of equation differential expressions. Thus, instructional activities should promote the students' use of several representation systems in which they can reflect on the various aspects associated with the concept itself, the solution methods, procedures, and the corresponding meaning and connections among those representations

Procesos conceptuales y cognitivos en la introducción de las ecuaciones diferenciales ordinarias vía la resolución de problemas

En este artículo se identifican y analizan los procesos cognitivos que desarrollan un grupo de estudiantes de primer curso de la licenciatura en Química mientras resuelven un problema diseñado como parte de un Módulo de Enseñanza para la introducción de las Ecuaciones Diferenciales Ordinarias (EDO). La conjugación de un escenario de resolución de problemas, con el uso de tecnología (la calculadora VoyageTM200) y la interacción entre estudiantes se revelan como una combinación que promueve y favorece el uso de procesos que contribuyen a la construcción del concepto de Ecuación Diferencial.This study aims to analyze cognitive processes that a group of first year Chemistry students exhibit while working on a task that involves dealing with a variation phenomenon. The task is part of a teaching module to introduce the study of Ordinary Differential Equations. The implementation of the module was based on combining problem solving activities, the use of a hand-held calculator and fostering a collaboration work among students. Results indicate that the participants recognized and valued a problem solving approach that led them to use various representations and strategies to construct the concept of Differential Equation

Conceptual and cognitive processes in the introduction of ordinary differential equations through problem solving

En este artículo se identifican y analizan los procesos cognitivos que desarrollan un grupo de estudiantes de primer curso de la licenciatura en Química mientras resuelven un problema diseñado como parte de un Módulo de Enseñanza para la introducción de las Ecuaciones Diferenciales Ordinarias (EDO). La conjugación de un escenario de resolución de problemas, con el uso de tecnología (la calculadora VoyageTM200) y la interacción entre estudiantes se revelan como una combinación que promueve y favorece el uso de procesos que contribuyen a la construcción del concepto de Ecuación Diferencial.This study aims to analyze cognitive processes that a group of first year Chemistry students exhibit while working on a task that involves dealing with a variation phenomenon. The task is part of a teaching module to introduce the study of Ordinary Differential Equations. The implementation of the module was based on combining problem solving activities, the use of a hand-held calculator and fostering a collaboration work among students. Results indicate that the participants recognized and valued a problem solving approach that led them to use various representations and strategies to construct the concept of Differential Equation

The Merit-Order Effect of Energy Efficiency

The integration of certain amount of renewable generation in the wholesale market right-shifted the merit-order generation curve, which produces a noticeable reduction of the clearing price while slightly increases the traded energy (almost inelastic demand curve). The downward pressure on the clearing price is mainly due to the fact that the introduction of renewable generation bids with very low (even null) marginal cost, displaces to the right all kinds of conventional technologies (with higher marginal cost), including the technology which would otherwise have set the clearing market price. This right-shifted displacement of the merit-order generation curve leads to a lower wholesale clearing price, a small increment of the traded energy and a reduction of the total cost of the traded energy in the wholesale market. This is the key mechanism and its main effects on the market of the very well-known meritorder effect of the renewables. The promotion of energy-efficiency plans (industry and domestic) by policy-makers is expected to yield a reduction of the demand. As a result of the reduction of demand bids, the merit-order demand curve would experience a left-sifted displacement, which would produce a reduction of both the clearing price and the amount of traded energy. Consequently, the total cost of the traded energy also would diminish. As can be seen, the parallelism of the main effects on the market between the integration of renewable and energy efficiency evidences the existence of what can be called the merit-order effect of energy efficiency. To analyze the characteristics of this merit-order effect of the energy efficiency, a simplified model, based on the linearization of the market around the clearing point, is developed. This simplified model is also used to compare the merit-order effect of energy efficiency and renewables. A set of scenarios with energy efficiency and renewables have been generated in order to quantify the main effects on the Spanish/Iberian market for the year 2014

Renewables versus efficiency. A comparison for Spain

Along the last decades, renewable energy (especially wind) in Spain has undergone a significant development (lead by a small group of renewable promoters supported by institutional policies), contributing significantly to electric generation mix (42.8% renewable in 2014). On the contrary, the promotion of energy efficiency actions (accomplished by a large number of industrial and domestic consumers that are very poorly supported by energy policies), are still little explored. According to ODYSSEE-MURE, energy efficiency at the EU-28 level improved by 1.2%/year on average from 2000 to 2013, while for the case of Spain, the rate of improvement was only 0.6 %/year on average throughout that period (the lowest rate of energy efficiency improvement in the EU-28). This work seeks to compare the integration of renewable production with energy efficiency plans, in order to advance their potential economic impact in the wholesale market and consumers. To reach that goal, the hourly market data retrieved from the Spanish/Iberian Market Operator (OMIE) for 2014 will be used as a base. Then, a set of pseudoheuristic scenarios with integration of renewable production and energy efficiency (load saving) will be elaborated and analyzed to quantify what are expected to be the main effects on the Spanish electricity market and consumers. The results will show that energy efficiency exhibits the best performance in terms of economic efficiency (less cost of the traded energy) and environmental sustainability (greater replacement of fossil fuels).Ministerio de Economía y Competitividad PCIN-2015-043Ministerio de Economía y Competitividad ENE2015-69597-RMinisterio de Economía y Competitividad ENE2014-54115-