Mathematics

Research

17 pages, 1456 KiB

Open AccessArticle

Rethinking the Teaching of University Statistics: Challenges and Opportunities Learned from the Colombia–UK Dialogue

by Rafael Alberto Méndez-Romero, Jackie Carter, Sofía Carrerá-Martínez, María Angélica Suavita-Ramírez and Vanessa Higgins

Mathematics 2023, 11(1), 52; https://doi.org/10.3390/math11010052 - 23 Dec 2022

Cited by 1 | Viewed by 2264

Abstract

The aim of this paper is first to examine, through a qualitative analysis of statistics syllabi, the current state of statistical education in a sample of universities in Colombia. The focus is on statistics teaching in degrees for economics and business administration students. [...] Read more.

The aim of this paper is first to examine, through a qualitative analysis of statistics syllabi, the current state of statistical education in a sample of universities in Colombia. The focus is on statistics teaching in degrees for economics and business administration students. The results from the qualitative analysis reflect a preponderance of traditional and didactic teaching methods centered on the teacher, not on the student. The second aim is to present findings from a case study that has developed an innovative pedagogical intervention, called a data fellows program, from the University of Manchester, United Kingdom, which evidences opportunities for how statistics can be taught effectively to non-STEM majors. Further, the data fellows model has also been explored in the context of developing statistical and data skills capacities in Latin America. We reflect on how the lessons from the UK case study could open up opportunities for rethinking the teaching of statistics in Colombia through developing data projects and experiential learning to practice statistics in the real world. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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21 pages, 1912 KiB

Open AccessArticle

Math Learning in a Science Museum—Proposal for a Workshop Design Based on STEAM Strategy to Learn Mathematics. The Case of the Cryptography Workshop

by Juan Roldán-Zafra and Carmen Perea

Mathematics 2022, 10(22), 4335; https://doi.org/10.3390/math10224335 - 18 Nov 2022

Cited by 1 | Viewed by 2026

Abstract

In mathematics teaching, great efforts are made, and diverse teaching strategies are employed in order to facilitate students’ learning process. Informal environments have proven to be conducive and motivating spaces for science learning. In particular, science museums can be used as a complement [...] Read more.

In mathematics teaching, great efforts are made, and diverse teaching strategies are employed in order to facilitate students’ learning process. Informal environments have proven to be conducive and motivating spaces for science learning. In particular, science museums can be used as a complement and collaborate in order to leverage each of their strengths to motivate mathematics learning. Educational models give a global explanation to the learning process. Taking into account all these aspects and considering van Hiele’s model as didactic reference, we propose the design of a general workshop that has among its objectives the learning of mathematics. To do this, we start from the three main elements and processes set forth in van Hiele’s model: insight, reasoning levels and learning phases. The insight or student’s competence are formulated through Hoffer’s abilities, and for the development of the activities of the learning phases, the STEAM (science, technology, engineering, art and maths) strategy. Once the general proposal has been made, we use it to design a scientific workshop for learning mathematics about cryptography. Our greatest challenge was in generating activities adapted to the established requirements. It would be interesting, for future works, to design research to evaluate the effectiveness of the proposal presented. Moreover, it would be interesting to develop a proposal for assessing student learning. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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20 pages, 3511 KiB

Open AccessArticle

Gamification for Maths and Physics in University Degrees through a Transportation Challenge

by Lucía Hilario, Marta Covadonga Mora, Nicolás Montés, Pantaleón David Romero and Sara Barquero

Mathematics 2022, 10(21), 4112; https://doi.org/10.3390/math10214112 - 4 Nov 2022

Cited by 3 | Viewed by 2452

Abstract

Our society is immersed in the Fourth Industrial Revolution due to the fast evolution of the new technologies that are modifying the labor market. In the near future, technologies related to Industry 4.0 will produce totally new goods and services. Therefore, the educational [...] Read more.

Our society is immersed in the Fourth Industrial Revolution due to the fast evolution of the new technologies that are modifying the labor market. In the near future, technologies related to Industry 4.0 will produce totally new goods and services. Therefore, the educational systems should adapt their programs to the future needs of an uncertain labor market. In particular, mathematics will play a key role in future jobs and there is a strong need to connect its teaching methodologies to the new technological scene. This work uses the STEAM approach (science, technology, engineering, arts and mathematics) along with active methodologies and educational robotics with the aim of developing a new strategy for the application of mathematics and physics in an engineering degree. In particular, a transportation challenge is posed to tackle the teaching–learning process of the Bézier curves and their applications in physics. A pilot project is developed using a LEGO EV3 robot and an active methodology, where students become the center of the learning process. The experimental results of the pilot study indicate an increase in the motivation due to the use of robots and the realistic context of the challenge. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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26 pages, 3150 KiB

Open AccessArticle

The Mathematical Culture in Test Items of National College Entrance Examination in China from 1978 to 2021

by Peiyao Lei, Wenqing Kong, Su Han, Sunzhong Lv and Xiaoqin Wang

Mathematics 2022, 10(21), 3987; https://doi.org/10.3390/math10213987 - 27 Oct 2022

Cited by 1 | Viewed by 3875

Abstract

As one of the most important examinations in China, the National College Entrance Examination (commonly known as the Gaokao, hereafter denoted Gaokao) has a long history and has attracted attention from the Chinese educational community, among others. This study focused on [...] Read more.

As one of the most important examinations in China, the National College Entrance Examination (commonly known as the Gaokao, hereafter denoted Gaokao) has a long history and has attracted attention from the Chinese educational community, among others. This study focused on mathematics test items of the Gaokao from the perspective of mathematical culture and examined the national papers (drafted by the Ministry of Education of the People’s Republic of China) of tests from 1978 to 2021 in order to investigate the content and time variation characteristics of mathematics test items reflecting mathematical culture since its restoration. A mathematical culture categorization conceptual framework was established based on previous studies and was applied to test item analysis. Mathematical culture in test items was classified using four categories: Historical Topics, Interdisciplinary Connections, Social Roles, and Aesthetics & Recreation. These were used for data coding and analysis. The results showed that mathematical culture in the mathematics test items of the Gaokao over a 44-year period, in terms of content categories, was diverse but uneven in distribution, with greater focus on demonstrating the social roles of mathematics and less on the historical development of mathematical knowledge. Moreover, the average number of items with mathematical culture during this period was small and fluctuated over time. The content of topics related to social context and technology also changed over time with the distinct characteristics of the times and changes in society. This study provides empirical evidence on how mathematical culture is integrated into test items and how they have changed over time. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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21 pages, 7160 KiB

Open AccessArticle

Design of 3D Metric Geometry Study and Research Activities within a BIM Framework

by José M. Olmos-Noguera, Eduardo J. Renard-Julián and María Socorro García-Cascales

Mathematics 2022, 10(9), 1358; https://doi.org/10.3390/math10091358 - 19 Apr 2022

Cited by 2 | Viewed by 2605

Abstract

This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of [...] Read more.

This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices and is framed in the Didactic Situations Theory and in the Anthropological Theory of the Didactic. Although the mentioned theories, which the French school has developed since the seventies, are widely known and studied by secondary school mathematics teachers during their training in pedagogy, especially in Spanish- and French-speaking countries, their innovative approach has not been fully implemented in the field of algebraic geometry. Mathematics textbooks follow the traditional approach in which the teacher simply provides the contents and instructs the student, who captures these concepts and reproduces them as they have been supplied. In the presented didactic proposal, the approach proposed by Brousseau is followed, in which three fundamental elements take part: student, teacher, and the didactic environment. The teacher is the one who facilitates the environment in which the student builds his knowledge. In the proposal the didactic contract is stablished, the didactic situations are designed, and the means and didactic variables for the study of 3D metric geometry are chosen. The methodology followed in this study consisted of identifying educational problems; describing the theoretical framework; developing the didactic proposal; and analysis, reflection, and criticism of this training product. The contextualization of the geometry workshop in the field of the construction of structures and the use of deductive reasoning techniques that are applied in synthetic geometry and also in the building information modeling (BIM) methodology may be a way of showing the use of analytical geometry in the industries of engineering and architecture; they also serve as an opportunity for students to better understand this mathematical work. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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14 pages, 738 KiB

Open AccessArticle

Encouraging Students’ Motivation and Involvement in STEM Degrees by the Execution of Real Applications in Mathematical Subjects: The Population Migration Problem

by María Teresa López-Díaz and Marta Peña

Mathematics 2022, 10(8), 1228; https://doi.org/10.3390/math10081228 - 8 Apr 2022

Cited by 2 | Viewed by 1762

Abstract

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining [...] Read more.

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining the city population equilibrium point, and making a sociological interpretation of population flows. This practical problem is part of the seminar “Applications of Linear Algebra in Engineering”, which is being held at the Universitat Politècnica de Catalunya-BarcelonaTech (UPC). This seminar consists in the learning of linear algebra by the implementation of real applications where mathematical tools are required to resolve them. This paper presents an application of linear algebra to the population migration problem and analyses students’ appreciation through anonymous surveys and personal interviews. The surveys assessed students’ motivation towards the subject of linear algebra and their learning of mathematical concepts. Personal interviews were conducted for students in order to let them express in detail their opinion about the seminar. The results confirm that the introduction of real applications in the learning of mathematics increases students’ motivation and involvement, which implies an improvement in students’ performance in the first courses of STEM degrees. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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27 pages, 1034 KiB

Open AccessArticle

Supporting Preservice Mathematics Teachers’ Culturally Responsive Teaching: A Focus on Teaching for Social Justice

by Jordan Register, Anthony Fernandes and David Pugalee

Mathematics 2022, 10(6), 896; https://doi.org/10.3390/math10060896 - 11 Mar 2022

Cited by 3 | Viewed by 3453

Abstract

This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social [...] Read more.

This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social justice topics, though not all the PSTs integrated mathematics and social justice throughout their lessons. The results show that most of the PSTs need more experience with mathematization, handling controversial discussions, and developing transformative student action. Our work also led to a modification of the tool (CRMT-M). We discuss the implications of the study for mathematics teacher preparation. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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10 pages, 373 KiB

Open AccessArticle

The STEM Methodology and Graph Theory: Some Practical Examples

by Cristina Jordán, Marina Murillo-Arcila and Juan R. Torregrosa

Mathematics 2021, 9(23), 3110; https://doi.org/10.3390/math9233110 - 2 Dec 2021

Cited by 4 | Viewed by 2884

Abstract

In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at [...] Read more.

In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at STEM undergraduate students to be solved by using shortest path algorithms from Graph Theory after previous modeling. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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32 pages, 8209 KiB

Open AccessArticle

Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates

by Ana Laura Pérez-Martínez, Maria del Pilar Aguilar-Del-Valle and Arturo Rodríguez-Gomez

Mathematics 2021, 9(22), 2943; https://doi.org/10.3390/math9222943 - 18 Nov 2021

Viewed by 6191

Abstract

For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding, and [...] Read more.

For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding, and manipulating the Laplacian operator allows us to tackle complex and exciting physics, chemistry, and engineering problems. In this paper, contained in the Special Issue “Mathematics as the M in STEM Education”, we present an instructional derivation of the Laplacian operator in spherical coordinates. Our derivation is self-contained and employs well-known mathematical concepts used in all science, technology, engineering, and mathematics (STEM) disciplines. Our lengthy but straightforward procedure shows that this fundamental tool in mathematics is not intractable but accessible to anyone who studies any of the STEM disciplines. We consider that this work may be helpful for students and teachers who wish to discuss the derivation of this vital tool from an elementary approach in their courses. Full article

(This article belongs to the Special Issue Mathematics as the M in STEM Education)

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