Mathematics

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15 pages, 1445 KiB

Open AccessArticle

A Virus Infected Your Laptop. Let’s Play an Escape Game

by Araceli Queiruga-Dios, María Jesús Santos Sánchez, Marián Queiruga Dios, Víctor Gayoso Martínez and Ascensión Hernández Encinas

Mathematics 2020, 8(2), 166; https://doi.org/10.3390/math8020166 - 29 Jan 2020

Cited by 22 | Viewed by 7114

Abstract

Have you ever thought what would happen if a ransomware infected your laptop? This type of virus kidnaps files and encrypts them, and the only way to recover the data is by paying in bitcoin or some other cryptocurrency. This situation is undoubtedly [...] Read more.

Have you ever thought what would happen if a ransomware infected your laptop? This type of virus kidnaps files and encrypts them, and the only way to recover the data is by paying in bitcoin or some other cryptocurrency. This situation is undoubtedly terrible. All of your work, projects, and personal files will not be available (unless you pay the ransom). The first time students watched a video that contextualizes this stressful situation, they thought that they had been attacked by a computer virus. Fortunately, the panic only lasted a few seconds. This is the way to start a game called breakout or escape room. The difference between these two words is that, in the first case, the goal is to open a padlocked box, while the objective of an escape room is to find the key that allows to get out of a room. Both games are similar, containing riddles, puzzles, problems and some clues that would help the players to find the solution. This study analyses the use of a breakout game for educational purposes, more specifically in a university context. The experiment conducted mixes game–based learning methodologies with engineering students learning Linear Algebra, Calculus or Cryptography, which has allowed us to obtain promising results about the usage of this methodology. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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16 pages, 1007 KiB

Open AccessArticle

An Assessment of the Impact of Teachers’ Digital Competence on the Quality of Videos Developed for the Flipped Math Classroom

by Daniel Moreno, Alicia Palacios, Álvaro Barreras and Virginia Pascual

Mathematics 2020, 8(2), 148; https://doi.org/10.3390/math8020148 - 21 Jan 2020

Cited by 9 | Viewed by 5564

Abstract

The aim of this research is to determine the impact of perceived Teachers’ Digital Competence (TDC) on how well math teachers prepare the educational videos needed to put the flipped classroom model into practice. In preparing the videos, the teachers had to select [...] Read more.

The aim of this research is to determine the impact of perceived Teachers’ Digital Competence (TDC) on how well math teachers prepare the educational videos needed to put the flipped classroom model into practice. In preparing the videos, the teachers had to select pre-existing audiovisual material and then edit the content to adapt it to the flipped classroom. Described here is a non-experimental study of a sample of 50 teachers pursuing a Master’s degree in Secondary School Math Education in Spain. This is a preliminary univariate descriptive study of the relationship between TDC and the quality of videos prepared. Possible correlations between these two variables and between the characteristics of the sample are also explored. In general, the teachers had an intermediate level of TDC and prepared satisfactory videos. Nevertheless, the videos were deficient in the sections related to their pedagogical and math instructional components. No correlation was observed between TDC and the quality of the videos prepared. These results indicate that the integration of technological, pedagogical, and math instructional components is more important for developing quality instructional videos than the technological component alone. Teacher training should incorporate elements which emphasize the application of technology to the pedagogical process of math instruction. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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13 pages, 1101 KiB

Open AccessArticle

Modelling Dependency Structures Produced by the Introduction of a Flipped Classroom

by Ana D. Maldonado and María Morales

Mathematics 2020, 8(1), 19; https://doi.org/10.3390/math8010019 - 20 Dec 2019

Cited by 3 | Viewed by 2932

Abstract

Teaching processes have been changing in the lasts few decades from a traditional lecture-example-homework format to more active strategies to engage the students in the learning process. One of the most popular methodologies is the flipped classroom, where traditional structure of the course [...] Read more.

Teaching processes have been changing in the lasts few decades from a traditional lecture-example-homework format to more active strategies to engage the students in the learning process. One of the most popular methodologies is the flipped classroom, where traditional structure of the course is turned over by moving out of the classroom, most basic knowledge acquisition. However, due to the workload involved in this kind of methodology, an objective analysis of the results should be carried out to assess whether the lecturer’s workload is worth the effort or not. In this paper, we compare the results obtained from two different methodologies: traditional lecturing and flipped classroom methodology, in terms of some performance indicators and an attitudinal survey, in an introductory statistics course for engineering students. Finally, we analysed the changes in the relationships among variables of interest when the traditional teaching was moved to a flipped classroom by using Bayesian networks. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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17 pages, 496 KiB

Open AccessArticle

How Teacher’s Progressiveness in Using Digital Technologies Influences Levels of Pupils’ Metacognitive Knowledge in Mathematics

by Vlastimil Chytrý, Jaroslav Říčan and Janka Medová

Mathematics 2019, 7(12), 1245; https://doi.org/10.3390/math7121245 - 17 Dec 2019

Cited by 2 | Viewed by 3695

Abstract

The low efficiency of using appropriate strategies to solve problems in the classroom environment is not due to the lack of knowledge of how to classify concepts, but rather due to the failure to apply this knowledge strategically. Therefore, it is necessary to [...] Read more.

The low efficiency of using appropriate strategies to solve problems in the classroom environment is not due to the lack of knowledge of how to classify concepts, but rather due to the failure to apply this knowledge strategically. Therefore, it is necessary to find a balance between them, i.e., to let the pupils discuss the problems while supporting the teacher’s intervention. The aim of the presented study was to examine the influence of a teacher’s progressiveness on the level of metacognitive knowledge of the pupil. Altogether, 47 teachers and 278 pupils at grade 5 were participating in the study. It is shown that the approach of teachers to innovation itself has an influence on the pupil. When comparing all five groups of innovators, the difference among the categories of teachers was significant (

p = 0.044

) with the low effect (

d_{c o h e n} = 0.3)

. When considering only the two almost antagonistic poles of teachers, the innovators and the late majority according to Roger’s innovation diffusion theory, this influence was very strong (

p = 0.009

) and with medium effect (

d_{c o h e n} = 0.725

). Our research shows that it is necessary to address the teacher’s innovativeness, affecting the level of metacognitive knowledge of the pupil as an important prediction tool determining school success. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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13 pages, 948 KiB

Open AccessFeature PaperArticle

The Enhancement of Academic Performance in Online Environments

by Francisco I. Chicharro, Elena Giménez and Íñigo Sarría

Mathematics 2019, 7(12), 1219; https://doi.org/10.3390/math7121219 - 10 Dec 2019

Cited by 5 | Viewed by 6785

Abstract

Distance education has been gaining popularity for the last years. The proficiency in online environments of both learners and teachers explains the success of this methodology. An evaluation of graduate students’ performance within numerical analysis is discussed. In order to improve the marks [...] Read more.

Distance education has been gaining popularity for the last years. The proficiency in online environments of both learners and teachers explains the success of this methodology. An evaluation of graduate students’ performance within numerical analysis is discussed. In order to improve the marks obtained by the students, specific actions have been performed over the years and data from different classes has been analyzed using statistical tools. The results show that the actions proposed seemed to help the students in their learning process. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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14 pages, 2059 KiB

Open AccessArticle

Coordination between High School and University Teachers in Spain to Reduce Mistakes in Calculus

by Fernando Sánchez Lasheras, Manuel José Fernández Gutiérrez and Juan Cereijo Viña

Mathematics 2019, 7(9), 817; https://doi.org/10.3390/math7090817 - 4 Sep 2019

Cited by 3 | Viewed by 2839

Abstract

In level tests carried out in recent years to evaluate the competence acquired by calculus students enrolled in the Computer Software Engineering degree at the University of Oviedo, it has been observed that a significant percentage of students make very similar conceptual errors. [...] Read more.

In level tests carried out in recent years to evaluate the competence acquired by calculus students enrolled in the Computer Software Engineering degree at the University of Oviedo, it has been observed that a significant percentage of students make very similar conceptual errors. This article describes the research undertaken by a working group of teachers called BACUNIMAT, currently made up of two university professors and five high school professors. The name BACUNIMAT is the acronym in Spanish for the High School and University Teachers Working Group. The aim of this research group was to analyze the main deficiencies in mathematical knowledge that students possess upon arrival at university. The analysis was performed in order to propose solutions to alleviate these deficiencies. The research proposes how to focus mathematical teaching in secondary schools in order to better prepare students for university. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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20 pages, 2304 KiB

Open AccessArticle

3D Visualization through the Hologram for the Learning of Area and Volume Concepts

by Lara Orcos, Cristina Jordán and Alberto Magreñán

Mathematics 2019, 7(3), 247; https://doi.org/10.3390/math7030247 - 9 Mar 2019

Cited by 18 | Viewed by 8413

Abstract

This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in [...] Read more.

This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in the third year of secondary education from a privately-owned but state-funded school in Madrid. Thirty-five students who have been taught traditionally formed the control group, and 43 formed the experimental group in which the methodology was implemented. To evaluate its goodness, we have used the Student’s t-test to assess the existence of significant differences between both groups. The results reported by the test show that there is a difference of 3.9 points between the scores of both groups which is significant at the level of 0.05. In addition, the user experience in the experimental group has also been evaluated to assess the students’ opinions of the hologram in the learning process. The overall results have assisted us in corroborating the efficacy of the hologram as a teaching medium. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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17 pages, 2001 KiB

Open AccessArticle

The Kumon Method: Its Importance in the Improvement on the Teaching and Learning of Mathematics from the First Levels of Early Childhood and Primary Education

by L. Orcos, R. M. Hernández-Carrera, M. J. Espigares and Á. Alberto Magreñán

Mathematics 2019, 7(1), 109; https://doi.org/10.3390/math7010109 - 21 Jan 2019

Cited by 10 | Viewed by 76825

Abstract

The present work gathers an educational experience based on the application of the personalized Kumon Mathematics Method, carried out in the school year 2015–2016, in which 30,849 students and 230 teachers from several educational centers throughout Spain have participated. We start with a [...] Read more.

The present work gathers an educational experience based on the application of the personalized Kumon Mathematics Method, carried out in the school year 2015–2016, in which 30,849 students and 230 teachers from several educational centers throughout Spain have participated. We start with a theoretical foundation of the Kumon Method and continue with a description of the research methodology used. The empirical analysis carried out has been both in descriptive and correlational terms, using Spearman’s Rho statistic, between the levels at which the students of the sample have started and the Kumon level reached. The results show that the sooner students begin to learn Mathematics with the Kumon Method, the greater the chance of reaching a level of knowledge above their school level, which helps us to demonstrate the potential of this method in the teaching and learning process of Mathematics in the educational levels of Early Childhood and Primary Education. Full article

(This article belongs to the Special Issue New trends in Mathematics Learning)

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