# EXPLORIA, STEAM Education at University Level as a New Way to Teach Engineering Mechanics in an Integrated Learning Process

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Active Methodologies

#### 1.1.1. Project-Based Learning

#### 1.1.2. Challenge-Based Learning

## 2. The EXPLORIA Project, a New Learning Approach for University Students

#### 2.1. Integrating STEAM Projects in Bachelor Degrees

#### 2.2. University Students’ Attitudes towards Maths

#### 2.3. University Students’ Attitudes towards Maths and Their Effect in Physics

#### 2.4. Basic Subjects vs. Engineering Subjects

#### 2.5. The EXPLORIA Project

## 3. Research Objectives

## 4. Materials and Methods

#### 4.1. Participants

#### 4.2. Scope of Application

#### 4.3. Tools

## 5. Design and Implementation of the EXPLORIA Pilot Project

- Act I: Shape
- Act II: Volume
- Act III: Color

- Act IV: Space
- Act V: Structure
- Act VI: Project

## 6. Physics (Mechanical Engineering) in EXPLORIA

#### 6.1. Description of Sessions and Timing

#### 6.1.1. The Transportation Challenge

- Session 1. The project begins with a motivational session explaining the problem to be solved from the point of view of mobile robotics, AGVs (Automated Guided Vehicle), AMR (Autonomous Mobile Robot), autonomous robots used to transport materials in industry and society.
- Session 2. A theory session is held in which Newton’s 3 laws are explained. Inertial frames of reference are defined and the limitations of Newton’s laws are explained.
- Session 3. A math session is held in which students work on the vector and scalar product.
- Session 4. A Physics session is carried out in which the force moment (M = D × F) is explained and a practical exercise is carried out on how to calculate it on a bottle of water.
- A mathematics session is held in which parametric curves, Bézier’s curves, Frenet’s Diedro, etc., are explained.
- Session 5. A physics session is carried out in which kinematics is explained, the accelerations suffered by a moving object when it follows a curved path and centripetal/centrifugal acceleration. After, all this is linked to the reference frames in which the centrifugal force is a fictitious force found in the non-inertial frames. Here, we explain how to calculate the limit centrifugal acceleration when an object is transported. The ability of parametric curves to approximate any curve, circle or clothoid is also explained, the latter being explained in depth given its mathematical properties and therefore its application in road design and in the generation of mobile robot trajectories [41]. Students select an object and calculate the centripetal acceleration limit. The condition of moment equilibrium and the centroid are indirectly introduced for their calculation.
- Session 6. A mathematics session is carried out in which the developed Geogebra applet is explained and the students design the path the robot will follow, with the centripetal acceleration limit calculated in the previous session, moving the control points of the Bézier curve and simulating it to verify that the restriction of centripetal acceleration limit is met.
- Session 7. A test session of the trajectories designed by the students is carried out in which they verify whether the designed trajectory manages to transport the object to the destination. Otherwise, the students will redesign the trajectory until the selected object is transported to the destination.

#### 6.1.2. The Equilibrium Challenge

- Session 1. A physics session is held in which the centroid and gravity center are explained. We explain how to calculate the centroid and gravity center both analytically and experimentally in irregular objects, by finding the equilibrium point. Finally, we explain how to calculate the gravity center of composite objects and tests are carried out.
- Session 2. The students bring objects from home to make the sculpture and firstly they calculate the gravity center of each object and their weight. Later, they make their sculpture in equilibrium, measure it and calculate the composite center of gravity of the composition.

#### 6.1.3. The Pringles Ring Challenge

- Session 1. A descriptive geometry session is carried out explaining the warped surfaces, including the hyperbolic paraboloid, its mathematical formulation and its properties.
- Session 2. The concept of friction is introduced and exercises are carried out in class with different objects using a ramp and throwing different objects over it to demonstrate that the challenge is met.
- Session 3. The students bring at least 2 Pringles cans and the basic concepts are explained to them to be able to carry them out. These include:
- 1.
- Object stacking: we explain to them what happens when objects are stacked, how much space can protrude from an object to another and how it affects the gravity center of composites.
- 2.
- Friction: The side walls of the ring are supported by friction between the Pringles and the normal force they exert on each other.
- 3.
- Gravity center of composites: One of the keys to overcoming the challenge is to generate a good base of the ring and force the gravity center of composites to remain in that area.

#### 6.1.4. The Letters Challenge

- 1.
- The letter must include at least 3 different joints (from an initial list provided by the teachers), in this challenge the use of one of the joints will be mandatory and assigned through a first draw.
- 2.
- The letter must be self-supporting, that is, it must be able to stand upright and must be able to be transported, by grabbing it from a higher point and moving it from one point to another without dismounting.
- 3.
- The use of glue or any other element to anchor or fix the joints is not allowed.

- •
- Session 1. A basic design extension session is held in which the concept of structure is explained from the design point of view and real objects and sculptures are analyzed.
- •
- Session 2. A physics session is carried out in which the equations of equilibrium and the calculation of the free-body diagram are introduced. The same real objects and sculptures from session 1 are used for analysis from the physical point of view.
- •
- Session 3. Students are proposed to do research and analysis. They must check the websites of famous designers, select a product and obtain:
- 1.
- The free-body diagram of the selected product.
- 2.
- Dimensions and information from their designer.
- 3.
- Proposal for design improvements, both from a physical and design point of view.

- •
- Session 4. Combined session with the Design and Physics teachers in which an elevator pitch is held: a 2-min short presentation in which each student explains his/her results from session 3 to the rest of their peers. This session is used to share the results but also used as an evaluation for the teacher.
- •
- Session 5. Basic design extension session in which the different types of joints used in design are explained, the challenge is defined and the draw for the mandatory joint to be used is carried out for each student.
- •
- Session 6. Physics session in which the equations of equilibrium are explained and their calculation from the free body diagram.
- •
- Sessions 7 and 8. Work session in the combined classroom with design and physics teachers in which students design their letters, calculate their free body diagram and equilibrium equations to guarantee the viability of the challenge.
- •
- Session 9 and 10. Workshop session. The students go to the workshop and mechanize their letters. Figure 4 shows the students working in the workshop.
- •
- Session 11. Combined session with the Design and Physics teachers in which an elevator pitch is held: a 2 min short presentation in which each student presents his/her letter design, calculations, manufacturing problems and they perform the self-support test on-site, moving the letter from a table to the center of the classroom. Figure 5 shows the resulting letters placed in a vertical position on a table. In the elevator pitch session, each student takes his/her letter with one hand from a point chosen by him/her and moves it to the central table where the student will explain his/her design and manufacturing process. Figure 6 shows details of some designs in which we can see how the student, in the case of the letter “P”, has used the calculation of the center of gravity to calculate the angle at which the base should be cut in order to keep the P in balance.

#### 6.1.5. Milestones

## 7. Results

- “These are exercises that help you understand the syllabus in a very dynamic way. It’s a good way to learn theory while putting it into practice”.
- “When we carry out this type of projects, we are learning and understanding the lesson explanations”.
- “The most interesting exercise is the Pringles ring since with common food you can realize the importance of shape for calculating balance. On the other hand, the balancing exercise was more about calculation of structure. Finally, the letter seems to me a very complete exercise to bring together all the subjects in the same work”.
- “When it comes to doing it in a practical way, you learn better”.
- “They are examples that perfectly convey the theory taught”.
- “They help us to really realize the usefulness of physics in any type of project”.
- “I think it was an exercise that allowed us to understand in a practical way how friction and gravity act and how to use these factors to our advantage”.
- “These exercises are a very good way to learn, since you understand what you are studying because you can check it at the same time”.
- “Very useful exercises, since you can see how to apply physics and mathematics in specific things such as for example the pringles exercise, this helps you see how the content taught in class is reflected in reality and helps you understand the contents much better”.

## 8. Discussion

## 9. Conclusions and Further Developments

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

STEM | Science Technology Engineering Mathsi |

STEAM | Science Technology Engineering Art Maths |

AGV | Automated Guided Vehicle |

AMR | Autonomous Mobile Robot |

ESET | Technical School of Engineering |

## References

- Irwanto, I.; Saputro, A.D.; Ramadhan, W.M.F.; Lukman, I.R. Research Trends in STEM Education from 2011 to 2020: A Systematic Review of Publications in Selected Journals. Int. J. Interact. Mob. Technol.
**2022**, 16, 19–32. [Google Scholar] [CrossRef] - Pisa, Programa para la Evaluación Internacional de los Alumnos. Spanish Report. Informe Español. Ministerio de Educacion, Cultura y Deporte. 2018. Available online: https://www.oecd.org/pisa/aboutpisa/ebook%20-%20PISA-D%20Framework_PRELIMINARY%20version_SPANISH.pdf (accessed on 26 May 2021).
- Sanders, M. STEM, STEM education, STEM mania. In Technology Teacher; Association Drive Suite 201; International Technology Education Association (ITEA): Reston, VA, USA, 2009. [Google Scholar]
- Ludeña, E.S. La educación STEAM y la cultura maker. Padres y Maestros. J. Parents Teach.
**2019**, 379, 45–51. [Google Scholar] - Yakman, G. ST ∑@M Education: An overview of creating a model of integrative education. In PATT-17 and PATT-19 Proceedings; de Vries, M.J., Ed.; ITEEA: Reston VA, USA, 2008; pp. 335–358. [Google Scholar]
- Williams, J. STEM Education: Proceed with caution. Des. Technol. Educ. Int. J. Spec. Ed.-Stem-Underpinned Res.
**2011**, 16, 26–35. [Google Scholar] - Wells, J.G. STEM education: The potential of technology education. Counc. Technol. Eng. Teach. Educ.
**2019**, 16, 195–229. [Google Scholar] - Pitt, J. Blurring the boundaries—STEM education and education for sustainable development. Des. Technol. Educ. Int. J.
**2009**, 14, 37–48. [Google Scholar] - Yakman, G.; Lee, Y. Exploring the exemplary STEAM education in the U.S. as a practical educational framework for Korea. J. Korea Assoc. Sci. Educ.
**2012**, 32, 1072–1086. [Google Scholar] [CrossRef][Green Version] - Kim, E.; Kim, S.; Nam, D.; Lee, T. Development of STEAM program Math centered for Middle School Students. Des. Technol. Educ. Int. J.
**2012**, 1, 1–5. [Google Scholar] - Parlamento Europeo, Consejo de la Unión Europea. Recomendación 2006/962/CE del Parlamento Europeo y del Consejo, de 18 de Diciembre de 2006, Sobre las Competencias Clave Para el Aprendizaje Permanente. 2006. Available online: https://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2006:394:0010:0018:ES:PDF (accessed on 26 May 2021).
- Sousa, D.A.; Pilecki, T. From STEAM to STEAM: Using Brain-Compatible Strategies to Integrate the Arts; Corwin: Thousand Oaks, CA, USA, 2013. [Google Scholar]
- Vergara, D.; Paredes-Velasco, M.; Chivite, C.; Fernandez-Arias, P. The Challenge of Increasing the Effectiveness of Learning by Using Active Methodologies. Sustainability
**2020**, 12, 8702. [Google Scholar] [CrossRef] - Ugras, M. The Effects of STEM Activities on STEM Attitudes, Scientific Creativity and Motivation Beliefs of the Students and Their Views on STEM Education. Int. Online J. Educ. Sci.
**2018**, 10, 165–182. [Google Scholar] - Konopka, C.L.; Adaime, M.B.; Mosele, P.H. Active Teaching and Learning Methodologies: Some Considerations. Creat. Educ.
**2015**, 6, 1536–1545. [Google Scholar] [CrossRef][Green Version] - Abou-Hayt, I.; Dahl, B.; Rump, C. A Problem-Based Approach to Teaching a Course in Engineering Mechanics. In Educate for the Future: PBL, Sustainability and Digitalisation; Guerra, A., Chen, J., Winther, M., Kolmos, A., Eds.; Aalborg Universitetsforlag: Aalborg, Denmark, 2020; pp. 499–509. [Google Scholar]
- Santyasa, I.W.; Rapi, N.K.; Sara, I.W.W. Project Based Learning and Academic Procrastination of Students in Learning Physics. Int. J. Instr.
**2020**, 13, 489–508. [Google Scholar] [CrossRef] - Zavala, G. Integration of physics, mathematics and computer tools using challenge-based learning. In Proceedings of the 2020 IEEE Global Engineering Education Conference (EDUCON), Porto, Portugal, 27–30 April 2020; pp. 1387–1391. [Google Scholar]
- Mills, J.E.; Treagust, D. Engineering education—Is problem-based or project-based learning the answer. Australas J. Eng. Educ.
**2003**, 3, 2–16. [Google Scholar] - Pospiech, G.; Eylon, B.S.; Bagno, E.; Lehavi, Y. Role of Teachers as Facilitators of the Interplay Physics and Mathematics. In Mathematics in Physics Education; Pospiech, G., Michelini, M., Eylon, B.S., Eds.; Springer: Cham, Switzerland, 2019; Volume 12, pp. 269–291. [Google Scholar]
- UNESCO. Engineering: Issues Challenges and Opportunities for Development; UNESCO: Paris, France, 2010. [Google Scholar]
- Hidalgo, S.; Maroto, A.; Palacios, A. ¿ Por Qué se Rechazan las Matemáticas? Análisis Evolutivo y Multivariante de Actitudes Relevantes Hacia las Matemáticas; Revista de Educación: Madrid, Spain, 2004; Volume 334, pp. 75–95. [Google Scholar]
- Pedrosa, C. Actitudes Hacia las Matemáticas en Estudiantes Universitarios. Ph.D. Thesis, Universidad de Cordoba, Córdoba, Sapin, 2020. [Google Scholar]
- Espinosa, E.O.C.; Mercado, M.T.C.; Mendoza, J.R.R. Actitudes hacia las matemáticas de los estudiantes de posgrado en administración: Un estudio diagnóstico. REXE Rev. Estud. Exp. Educ.
**2012**, 11, 81–98. [Google Scholar] - Hill, D.; Bilgin, A.A. Pre-Service Primary Teachers’ Attitudes towards Mathematics in an Australian University. Creat. Educ.
**2018**, 9, 597. [Google Scholar] [CrossRef][Green Version] - Mato-Vázquez, D.; Soneira, C.; Muñoz, M. Estudio de las actitudes hacia las Matemáticas en estudiantes universitarios. Números Rev. didáCtica Mat.
**2018**, 97, 7–20. [Google Scholar] - Ataide, A.R.P.D.; Greca, I.M. Epistemic views of the relationship between physics and mathematics: Its influence on the approach of undergraduate students to problem solving. Sci. Educ.
**2013**, 22, 1405–1421. [Google Scholar] [CrossRef] - Bishof, G.; Zwolfer, A.; Rubesas, D. Correlation between engineering students’ performance in mathematics and academic success. In Proceedings of the 122nd ASEE Anual Conference & Exposition Seattle, Seattle, WA, USA, 14–17 June 2015. [Google Scholar]
- Adebisi, A.; Olanrewaju, O. Mathematics Skills as Predictors of Physics Students’ Performance in Senior Secondary Schools. Int. J. Sci. Res.
**2013**, 2, 391–394. [Google Scholar] - Kamal, N.; Rahman, N.N.S.A.; Husain, H.; Nopiah, Z.M. The Correlation Between Electrical Engineering Course Performance and Mathematics and Prerequisite Course Achievement. Soc. Sci. Humanit.
**2016**, 24, 97–110. [Google Scholar] - Rossdy, M.; Michael, R.; Janteng, J.; Andrew, S.A. The Role of Physics and Mathematics in Influencing Science Students’ Performance. In Proceedings of the Second International Conference on the Future of ASEAN (ICoFA); Mat Noor, A., Mohd Zakuan, Z., Muhamad Noor, S., Eds.; Springer: Cham, Switzerland, 2017; Volume 1, pp. 399–406. [Google Scholar]
- Ojonugwa, T.; Umaru, R.; Sujaru, K.O.; Ajah, A.O. Investigation of the Role of Mathematics on Students’Performance in Physics. J. Res. Educ. Sci. Technol.
**2020**, 5, 101–108. [Google Scholar] - Pospiech, G. Framework of Mathematization in Physics from a Teaching Perspective. In Physical Review Special Topics—Physics Education Research; Springer: Cham, Switzerland, 2019; Volume 1, pp. 1–33. [Google Scholar]
- Imran, A.; Nasor, M.; Hayati, F. Relating grades of maths and science courses with students’ performance in a multidisciplinary engineering program. A gender inclusive case study. Procedia Soc. Behav. Sci.
**2012**, 46, 3989–3992. [Google Scholar] [CrossRef][Green Version] - Perdigones, A.; Gallego, E.; Garcia, N.; Fernandez, P.; Perez, E.; del Cerro, J. Physics and Mathematics in the Engineering Curriculum: Correlation with Applied Subjects. Int. J. Eng. Educ.
**2014**, 30, 1509–1521. [Google Scholar] - Jose, J. An Exploration of the Effective Use of Bloom’s Taxonomy in Teaching and Learning. In Proceedings of the International Conference on Business and Information (ICBI), Virtual, 16 November 2021; p. 100. [Google Scholar]
- Romero, P.D.; Montés, N.; Barquero, S.; Aloy, P.; Ferrer, T.; Granell, M.; Millán, M. EXPLORIA, a new way to teach maths at university level as part of everything. Mathematics
**2021**, 9, 1082. [Google Scholar] [CrossRef] - Makrakis, V.; Kostoulas-Makrakis, N. Bridging the qualitative–quantitative divide: Experiences from conducting a mixed methods evaluation in the RUCAS programme. Eval. Program Plan.
**2016**, 54, 144–151. [Google Scholar] [CrossRef] [PubMed] - Jebb, A.T.; Ng, V.; Tay, L. A Review of Key Likert Scale Development Advances: 1995–2019. Front. Psychol.
**2021**, 12, 1590. [Google Scholar] [CrossRef] - Hilario, L.; Mora, M.C.; Montés, N.; Pantaleon, D.; Barquero, S. The transport challenge. A new way to learn Mathematics through physics in university studies. Comput. Educ. 2022; under review. [Google Scholar]
- Montes, N.; Herraez, A.; Armesto, L.; Tornero, J. Real-time clothoid approximation by Rational Bezier curves. In Proceedings of the IEEE International Conference on Robotics and Automation, Pasadena, CA, USA, 19–23 May 2008; Volume 1, pp. 2246–2251. [Google Scholar]
- Vrontissi, M.; Castellón, J.J.; D’Acunto, P.; Monzó, L.E.; Schwartz, J. Constructing equilibrium: A methodological approach to teach structural design in architecture. In Proceedings of the IV International Conference on Structural Engineering Education, Madrid, Spain, 20–22 June 2018; pp. 1–10. [Google Scholar]
- Hibbeler, R.C. Engineering Mechanics, 14th ed.; Pearson Prentice Hall: Hoboken, NJ, USA, 2016. [Google Scholar]
- Sumiyoshi, T.; Matsui, G. Wood Joints in Classical Japanese Architecture; Kajima Institute: Tokyo, Japan, 1991. [Google Scholar]

**Table 1.**First-year subjects of bachelor of engineering in design and their classification into STEAM categories (Science, Technology, Engineering, Art, Math).

Semester 1 | STEAM Classification | Semester 2 | STEAM Classification |
---|---|---|---|

Physics | S, T, M | Physics Extension | S, T, M |

Maths | M | Maths Extension | M |

Art History | A | Anthropology | S |

Basic design | A, S, T | Design Extension | A, S, T |

Shape representation | A | Descriptive geometry | A, S, T |

Item | Contents |
---|---|

1 | Newton’s laws |

2 | Moment of forces. |

3 | Kinematics |

4 | Friction |

5 | Centroid and center of gravity |

6 | Free body diagram |

7 | Equilibrium of a particle |

8 | Equilibrium of a rigid body |

ID | Question |
---|---|

1 | I know what the center of gravity is and how to apply it in product design |

2 | I know Newton’s laws and how to apply them in product design |

3 | I know what the moment of a force is and how it affects product design |

4 | I know what friction is and how it affects product design. |

5 | I know what the free-body diagram is and its usefulness in product design |

6 | I know what equilibrium equations are and their usefulness in product design |

7 | I know the usefulness of integral calculus in product design |

8 | I know the types of traditional wood joints applied in the design of products and their physical restrictions. |

9 | I understand that the decision to cut a product determines it, both from the physical/functional point of view, as from the aesthetic one. |

10 | I recognize the aesthetic impact and the added value, in detail, that can determine the choice of any traditional wood joint applied in the product design. |

11 | The Pringles ring exercise helped me understand how the gravity center of friction works |

12 | The “Equilibrium challenge” exercise helped me understand how the center of gravity works and is calculated |

13 | The letter design exercise helped me understand how joints work |

14 | The letter design exercise helped me understand the usefulness of equilibrium equations |

15 | The letter design exercise helped me understand the importance of integral calculusl of several variables applied to design. |

16 | The letter design exercise helped me model mathematically and visualize the triple volume concept |

17 | The letter design exercise helped me relate the concepts of transversal section and volume |

18 | The letter design exercise helped me understand the importance of the center of gravity. |

19 | The letter design exercise helped me understand the importance of the value of detail incorporated into the design. |

20 | The letter design exercise helped me understand which graphic system/s to use to render them according to the required objective. |

21 | What do you think about the physics, Pringles ring, Equilibrium challenge and letter design exercises? |

Question | SD | D | N | A | SA |
---|---|---|---|---|---|

1 | 0 | 0 | 0 | 8 | 15 |

2 | 0 | 0 | 2 | 12 | 9 |

3 | 0 | 0 | 2 | 13 | 8 |

4 | 0 | 0 | 1 | 11 | 11 |

5 | 0 | 0 | 4 | 9 | 10 |

6 | 0 | 0 | 4 | 15 | 4 |

7 | 0 | 2 | 5 | 9 | 7 |

8 | 0 | 0 | 0 | 4 | 19 |

9 | 0 | 0 | 1 | 6 | 16 |

10 | 0 | 0 | 1 | 5 | 16 |

11 | 0 | 1 | 3 | 12 | 7 |

12 | 0 | 0 | 5 | 8 | 10 |

13 | 0 | 0 | 0 | 5 | 18 |

14 | 0 | 0 | 4 | 15 | 4 |

15 | 0 | 0 | 5 | 12 | 5 |

16 | 0 | 0 | 6 | 9 | 8 |

17 | 0 | 0 | 3 | 13 | 7 |

18 | 0 | 0 | 0 | 10 | 13 |

19 | 0 | 0 | 0 | 9 | 14 |

20 | 0 | 0 | 3 | 9 | 11 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Montés, N.; Aloy, P.; Ferrer, T.; Romero, P.D.; Barquero, S.; Carbonell, A.M. EXPLORIA, STEAM Education at University Level as a New Way to Teach Engineering Mechanics in an Integrated Learning Process. *Appl. Sci.* **2022**, *12*, 5105.
https://doi.org/10.3390/app12105105

**AMA Style**

Montés N, Aloy P, Ferrer T, Romero PD, Barquero S, Carbonell AM. EXPLORIA, STEAM Education at University Level as a New Way to Teach Engineering Mechanics in an Integrated Learning Process. *Applied Sciences*. 2022; 12(10):5105.
https://doi.org/10.3390/app12105105

**Chicago/Turabian Style**

Montés, Nicolás, Paula Aloy, Teresa Ferrer, Pantaleon D. Romero, Sara Barquero, and Alfonso Martinez Carbonell. 2022. "EXPLORIA, STEAM Education at University Level as a New Way to Teach Engineering Mechanics in an Integrated Learning Process" *Applied Sciences* 12, no. 10: 5105.
https://doi.org/10.3390/app12105105