Hugo Caerols-Palma | Searcharxiv

arXiv2022

Learning Mathematics through incorrect Problems

In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures. These are problems that either their solutions do not make sense in a real life context and/or provide a contradiction during the solution process. In this article we call these problems incorrect problems. We show several examples that can be applied in undergraduate mathematics courses and provide possible ways these examples can be used to motivate critical mathematical thinking. We also discuss the results of exposing a group of 168 undergraduate engineering students to an incorrect problem in a Differential Equations course. This experience provided us with important insight on how well prepared our students are to "out of the box" thinking and on the importance of previous mathematical skills in order to master further mathematical analysis to solve such a problem.

math.HO↗

arXiv2019

Creating and experiencing Flipped Learning in Multivariable Calculus for Engineering

This article discusses the process of creating, implementing and experiencing Flipped Learning in a Multivariable Calculus course for second year engineering students. We describe the construction of the teaching material, consisting of short videos for pre-class preparation and aligned worksheets for in-class dynamics, and the activities that were conducted. We discuss difficulties and key aspects to be considered while creating this material and during implementation of Flipped Learning. We present how students reacted to pre-class preparation and how in-class dynamics developed during implementation. We show results on students performance and perception when enrolling in a flipped classroom section. We present comparative results on students performance of a section taught with Flipped Learning vs a parallel section thought in the traditional expository way. We could conclude that flipped courses show similar results in passing percentage than traditionally taught courses, that student's perceptions are generally mixed, and we perceived that students repeating the course preferably do not choose flipped classes. Finally, we discussed the methodological evolution of this course converging to a mixed methodology throughout a four year period, observing that the instructors evaluation decreases in classes that were flipped. Mixed methodologies on the other hand, increased the learning experience of students resulting in an increased instructors evaluation score and higher students enrollment in the course.

math.HO↗