Open Education Studies 2024; 6: 20240051
Research Article
Lurdes Babo*, Jorge Mendonça, Carla Pinto
Students’ Perceptions of PBL Usefulness
https://doi.org/10.1515/edu-2024-0051 Railienė, & Cruz, 2019; Schwab & Samans, 2016; Stevens &
received July 04, 2023; accepted November 14, 2024 Norman, 2016; Suleman, 2016).
Abstract: Problem-based learning (PBL) is a teaching tech- The development of problem-solving skills is an essen-
nique in which students’ learning is conveyed using real- tial aspect of education as they are linked with the devel-
world problems. However, the implementation of PBL is opment of critical thinking and analytical skills necessary
confronted with several challenges, namely the involve- for academic, professional, and personal success. Effective
ment of students, the definition of the teacher’s role, and problem-solving techniques help students avoid conflict,
the development of effective assessment mechanisms. This learn self-regulation, and improve academic performance.
paper describes and analyses a teaching framework based In addition, collaboration, communication, and creativity,
on PBL followed in the Differential and Integral Calculus essential skills for twenty-first-century students, are also
and Statistical Models courses in a Biomedical Engineering developed. In general, problem-solving skills are vital in
Bachelor, at the School of Engineering, Polytechnic of education as they equip students with tools that enable
Porto. In order to assess students’ points of view about them to face complex challenges and succeed in their aca-
the effectiveness of this PBL approach with regard to demic and personal lives.
knowledge acquisition, development of soft skills, and assess- Critical thinking empowers learners to objectively evaluate
ment methods, a questionnaire was administered at the ter- situations, make logical decisions, and tackle complex problems.
minus of the semester. Data analysis revealed that newcomers It enables students to effectively process information, ques-
are more likely to use PBL, while second-year students feel tioning assumptions, and identifying biases, resulting in better
more pressure and report more workload with this type of decision-making and problem-solving. Critical thinking is there-
assessment. In this regard, we consider that factors such as fore an essential skill for success in many aspects of life and can
maturity, education level, workload in other courses, and lead to better outcomes for individuals, organizations, and
prior PBL experience may influence students’ willingness to society as a whole (Dumitru et al., 2018). Critical thinking has
adhere to PBL. been identified as a planned outcome of education in 2050
(UNESCO, 2022).
Keywords: problem-based learning, soft skills, students’ Therefore, many higher education institutions are
perceptions reflecting on pedagogical practices and seeking to imple-
ment teaching methods able to equip students with these
personal qualities and skills desired by future employers
(McGunagle & Zizka, 2020).
1 Introduction Approaches that prioritize active involvement from
the learner and are centered around their needs have
Nowadays, the labor market requires competent people been proven to be more successful in boosting the devel-
who possess problem-solving skills as well as creative opment of essential skills for twenty-first-century students
and critical thinking to deal with rapidly changing business (Deep et al., 2020). One such approach that has been incor-
circumstances (Bierema, 2019; Hayes, 2020; Penkauskienė, porated into teaching in a wide range of areas is problem-
based learning (PBL). PBL is a student-oriented learning
method that emphasizes self-directed learning and small
* Corresponding author: Lurdes Babo, CEOS.PP, ISCAP & SIIS, group work, where students learn through hands-on experi-
Polytechnic of Porto, Porto, Portugal, e-mail: lbabo@iscap.ipp.pt ences, identify and solve problems, and engage collabora-
Jorge Mendonça: ISEP & SIIS, Polytechnic of Porto, Porto, Portugal, tively with real-world issues.
e-mail: jpm@isep.ipp.pt
The effectiveness of this approach has been investi-
Carla Pinto: ISEP, Polytechnic of Porto & Centre of Mathematics,
University of Porto, Porto, Portugal, e-mail: cap@isep.ipp.pt
gated over decades, and several studies demonstrate that
ORCID: Lurdes Babo 0000-0001-5090-8736; Jorge Mendonça 0000-0002- PBL enables better academic outcomes, greater student
8359-139X; Carla Pinto 0000-0002-0729-1133 engagement, and improved critical thinking skills (Mursid,
Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License.
2 Lurdes Babo et al.
Saragih, & Hartono, 2022; Pinho, Mota, Conde, Alves, & Real-world problems and teamwork are the core around
Lopes, 2015). which students develop knowledge, and learning outcomes
Thus, the purpose of this article is to explore engi- are achieved by the team actively working on these unstruc-
neering students’ experiences working in two math courses, tured problems. In PBL classrooms, teachers provide a chal-
Differential and Integral Calculus (CALCL), and Statistical lenging problem for their students to solve together through
Models (SM), which involve solving real-world problems to collaborative discussion and research activities. Students
deepen their knowledge of the syllabus. CALCL students work together to identify relevant facts related to the issue
were first-semester freshmen, while SM students were at hand while developing strategies for finding solutions or
second-semester sophomores. The article aims to assess making decisions about how best to proceed with the given
students’ points of view about the effectiveness of PBL as task. Summarizing, the process involves identifying the
a teaching approach on various aspects such as knowl- problem, gathering information, analyzing the data, and
edge acquisition, development of soft skills, and assess- coming up with a solution. During this process, teachers
ment methods. act as facilitators who guide student inquiry by asking
The following set of research questions guided the open-ended questions that encourage deeper exploration
investigation: into potential answers or approaches towards resolution
RQ1: How do students perceive their skill levels on of the issue presented before them. Students decide their
teamwork and communication? own way of finding the solution to the problem they have
RQ2: How do students perceive their knowledge to solve.
acquisition? This type of learning encourages students to become
RQ3: How do students perceive the assessment methods? active participants in their own education, rather than
RQ4: Are there any differences in the views of freshman passive recipients of information that comes from the tea-
and sophomore students regarding the PBL experience? cher. By taking a central role in their own learning, stu-
Overall, this article contributes to the understanding dents are better prepared for higher education and are more
of how PBL can be implemented in specific courses in empowered in their educational experiences (UNESCO, 2022).
Biomedical Engineering and sheds light on the factors It has been argued that by using real-life problems as a
that may influence students’ engagement with PBL. focus, students would effectively learn how to learn (Tan,
The article is structured in four sections following the 2003). This type of problem challenges students to think
present introduction. Section 2 presents the background of about new situations and to integrate previous knowledge
the study, Section 3 describes the methodology adopted, creatively. In addition, they represent an opportunity to
and Section 4 shows the statistical analysis performed introduce diversified topics of interest into the curriculum.
and the main results. Finally, the main conclusions and Goti, Akyazi, de la Calle, Oyarbide-Zubillaga, and Alberdi
limitations of the study are presented in the closing section. (2020) found that students solving real-world problems
using PBL achieved better results when compared to tradi-
tional teaching methods.
Additionally, PBL fosters teamwork among classmates
and encourages students to ask questions and explain
2 Background to the Study topics in their own words, which helps to build a deeper
understanding of the material.
2.1 Literature Review According to Nilson (2016), a well-designed PBL pro-
vides students with the opportunity to develop skills related
PBL is an educational approach that has been used for to teamwork, management, leadership, oral and written
decades in a variety of disciplines to foster critical thinking communication, self-awareness, working independently,
and problem-solving skills (Liu & Pásztor, 2022). PBL is a critical thinking and analysis, explaining concepts, self-
student-centered method in which students are exposed to directed learning, applying course content to real-world
complex real-world problems to construct learning about a examples, researching and information literacy, problem-
subject. This strategy is implemented in a self-learning solving across disciplines.
environment where the “trigger” is given by a proposed These generic skills are commonly referred to as soft
problem that must be solved. Students have to conduct skills or emotional intelligence. Their importance lies in
research, learn new information, integrate theory and their transferability across disciplines and situations. They
practice, and apply knowledge and skills in order to develop prepare students to respond to the challenges of society,
a solution to the problem at hand. fostering the entrepreneurship and adaptability needed in
Students’ Perceptions of PBL Usefulness 3
the labor market. These competencies enable individuals to
effectively navigate diverse work environments and contri-
bute to the overall success of organizations (Suryanti &
Supeni, 2019).
Some authors have also noted that PBL encourages
life-long learning and language acquisition by developing
self-directed learning skills through group brainstorming,
problem definition, and clarification of knowledge about
the material (Razak et al., 2022).
As stated by Seibert (2021), a key role of tutors in PBL is
Figure 1: Problem complexity and multiplicity steps (adapted from
to facilitate the learning process.
Tan, 2003).
The tutor acts as a guide, providing support and gui-
dance to students throughout the learning journey, helping
them develop problem-solving strategies, and encouraging PBL variations must include a focus on teamwork and
independent learning. To guarantee the successful imple- presentation skills, as it is an opportunity for students to
mentation of this student-centered approach and optimize develop their ability to listen to others, communicate their
the learning outcomes, it is imperative to adapt the role of ideas clearly, and assume leadership responsibilities through
the tutor in PBL. collaborative work (Figure 1) (Tan, 2003).
Instead of lecturing, the instructor in PBL adopts the In the meta-analysis performed by Liu & Pásztor (2022),
position of facilitator. By providing scaffolding, guiding the authors summarize the Problem-based Learning steps in
inquiry, reiterating comprehension of challenging topics, Figure 2.
and presenting resources, the facilitator aids the groups in The implementation of PBL presents several chal-
creating understanding and making connections between lenges. Chen et al. (2021) categorized three levels of chal-
ideas. Furthermore, the facilitator encourages reflection on lenges faced in PBL implementation at the individual level,
the group’s procedures and results. institutional level, and culture level. Challenges at the indi-
Facilitators play a crucial role in guiding groups through vidual level include issues faced by students and teachers.
PBL sessions, providing support, criticism, and motivation. Teachers frequently refer to challenges in how to design
They help students overcome setbacks and foster resilience, the course activities, how to play the role of learning facil-
while also helping them understand complex ideas. Facilitators itator rather than lecturer, and how to balance between
also offer supplementary materials and encourage reflection helping and influencing the students’ work. Some studies
on group activities, ultimately creating a positive and produc- have focused specifically on the role of the teacher in this
tive PBL environment. context (Hmelo-Silver, Bridges, & McKeown, 2019).
PBL problems that are too simple or too complex may One of the goals of PBL is to enhance students’ trans-
not engage students effectively, so it’s important to strike a ferable skills, including communication, collaboration, cri-
balance. A good problem challenges students to think cri- tical thinking, and independent learning. To measure the
tically and creatively, encourages collaboration and com- development of these skills and learning outcomes, effec-
munication, and fosters a deeper understanding of the tive assessment methods are needed combining traditional
subject matter. It can inspire curiosity and motivate stu- and new methods, namely self-assessment, peer review,
dents to pursue further inquiry beyond the classroom. presentations, observation, joint with quizzes, exams, lab
The key components of a typical PBL process include reports, attendance, etc. (Chen et al., 2021). Teachers must
(a) identifying the problem or scenario, (b) researching and also figure out how to encourage students to be truthful in
gathering information, (c) analyzing the information, (d) the self and peer assessment. It is important to establish
proposing solutions, and (e) evaluating the outcomes clear guidelines and expectations for the assessment pro-
(Tan, 2003). cess, as well as providing training and support for students
PBL activities and duration can be designed in a to develop their assessment skills and ethical values. Incor-
variety of ways, depending on the objectives and goals of porating technology and anonymous evaluations can also
the curriculum. A problem could be on a particular topic, help advance accuracy and fairness in the evaluation
or it could be interdisciplinary, requiring students to draw process.
on knowledge and skills from multiple subjects. The dura- The PBL environment requires students to transfer from
tion can also vary, from a short-term project to a semester- traditional learning methods to PBL methods. Without rich
long endeavor (Chen, Kolmos, & Du, 2021). However, all teamwork and PBL experiences, students may struggle to
4 Lurdes Babo et al.
Figure 2: PBL steps (adapted from Liu & Pásztor, 2022).
identify problems and translate knowledge into practical pro- engineers to apply their technical knowledge and skills to
blem solutions. Teachers and facilitators can support this solve complex problems and design innovative solutions.
development by providing ongoing guidance and incorpor- Additionally, engineers must possess strong communica-
ating relevant skills training into the PBL curriculum. PBL tion and teamwork skills to effectively collaborate with
practice has created new challenges for both teachers and colleagues and stakeholders. As technology continues to
students in devoting more time and effort. Teachers face a advance, engineering students must also stay updated
heavier workload in PBL courses by providing guidance, with the latest tools and techniques to remain competitive
practical experiences, and teamwork facilitation. Students in the ever-evolving job market. The integration of PBL
have to devote more effort to overcoming expected and unex- into engineering education not only enhances students’
pected issues, which can lead to anxiety or depression. In problem-solving abilities but also prepares them for real-
their study, Chen et al. (2021) found that teachers have world scenarios. For these reasons, PBL is a suitable
expressed the need for more PBL-supportive materials, approach for engineering students.
resources, and policies at the faculty or university level. In this study, the PBL approach was followed in two math
Also, the high number of students and a lack of infrastruc- courses, CALCL and SM. Both courses are from the Bachelor's
ture for teamwork can limit the PBL application. degree in Biomedical Engineering, from the first year, first
At the culture level, Chen et al. (2021) refer to the lan- semester (CALCL), and second year, second semester (SM).
guage barriers arising for participants in international
PBL. This aspect carries less weight when PBL is developed
at a more restricted level.
2.2.1 Differential and Integral Calculus (CALCL)
Trends in PBL research emphasize the use of technology
to improve learning outcomes. This involves establishing
The Differential and Integral Calculus (CALCL) aims to pro-
dynamic and captivating settings for problem-solving
vide students with (a) a basic scientific knowledge and
through the use of virtual platforms (Sistermans, 2020),
techniques by consolidating and complementing students’
simulations (Reilly, Kang, Grotzer, Joyal, & Oriol, 2019),
mathematics training, gained during the third level of educa-
cooperative online tools (Hursen, 2021), or augmented
tion; (b) developing students’ ability to reason and abstrac-
reality (Fidan & Tuncel, 2019).
tion; and (c) encouraging the development of a mathematical
language and the acquisition of critical thinking. These are
crucial to developing a strong engineer profile and laying
2.2 Teaching Framework the groundwork for later comprehension and interpretation
of other courses in the bachelor’s program in biomedical
Engineering students are expected to seamlessly transition engineering.
into professional roles that demand problem-solving, ana- The course’s syllabus started with a brief chapter on
lytical thinking, innovation, and the application of theore- differential calculus, followed by a chapter on indefinite
tical concepts to real-world problems. These roles require integrals. The next chapter was devoted to definite
Students’ Perceptions of PBL Usefulness 5
integrals. The penultimate chapter was about a numerical may not have a statistical background. This also helps stu-
series of non-negative terms. The last chapter consisted of dents develop their presentation and communication skills.
case studies on sustainable mathematics. The case studies
were proposed by the teacher on a PBL model and consisted
of the application of differential and integral calculus to 3 Methodology
solve real-world problems, namely studying information
from epidemic outbreaks and analyzing data from rainfall To ascertain students’ opinion, a questionnaire was distrib-
in certain areas of the globe, amongst others. uted in the Moodle platform to all students enrolled in the
The lectures were delivered by the students in the courses of CALCL and SM, after the semester’s end for the
course’s final weeks, with reference to the final chapter academic year 2021–2022.
of the syllabus. They presented their solution to the PBL The questionnaire aimed to gather valuable insights from
problems. The students were actively engaged in this teaching participants regarding their PBL experiences in the two courses
framework, working autonomously. To encourage their class- considered. It consisted of 16 questions replied on a 5-point
mates’ active participation in class, they created slides and Likert scale, ranging from strongly disagree to strongly agree.
searched the internet for math and other educational resources. The same set of questions were answered by the CALCL
They used PollEv, Kahoot, EclipseCrossword, among others. freshmen and the SM sophomores about teamwork, communi-
Some groups prepared leaflets on climate change to distribute cation, learning outcomes, and assessment. Continuous feedback
among their peers. Each group complemented their work with a is essential to identify areas for improvement and enhance the
poster and a written assignment. The students created the poster overall quality of education. The feedback collected will be used
using a variety of tools, including Canvas and Piktochart, as well to improve the learning experience and ensure that students
as Microsoft Publisher and PowerPoint. The written assignment receive the best possible education.
had a series of tips to help structure and organize the contents. In total, 36 validated responses from CALCL and 41
from SM courses were obtained.
A quantitative approach was adopted in this paper.
2.2.2 SM Using exploratory descriptive statistics and nonparametric
Mann-Whitney tests, the statistical analysis sought to under-
The syllabus of the SM course is designed to provide stu- stand the differences or similarities in the feedback from
dents with a) a solid base of mathematics and b) statistical students in the two courses CALCL and SM regarding their
knowledge to solve medium-complex problems in the field learning experience using PBL.
of Biomedical Engineering, particularly those involving In the annexes, it is shown an example of a proposed
data analysis and interpretation, forecasting, and deci- PBL given to students of the SM course. The overall assess-
sion-making. The course comprises topics of Probability Theory ment is done using the following weighted formula:
and Discrete and Continuous Distributions, the Central Limit
Theorem, Confidence Intervals and Hypothesis Testing, and CF = 0.35 M1 + 0.3 M2 + 0.35 EG,
Linear Regression. The final chapter addresses real-world appli-
where:
cations of statistical methods in a PBL format.
• M1 includes the grade of the group report, the poster and
The SM course is delivered mainly by lectures and prac-
the oral presentation grade, with weights: 60, 20, and
tical classes, supported by active-learning strategies such as
20%, respectively;
Think-Pair-Share, Buzz, Q&A sessions (Pinto, Mendonça, &
• M2 is the assessment of each student individual report on
Babo, 2020; Zimmermann, Stallings, Pierce, & Largent, 2018),
a scientific paper, on the application of Probabilities and
and a modified version of eduScrum (Wijnands & Stolze, 2019).
Statistics in Engineering;
The last chapter of the SM course included the stu-
• EG is the grade of the individual written test, assessing
dents’ public presentation of the solutions to the previously
students’ knowledge of all syllabus.
assigned PBL. Each team had to “sell” their solution and
respond to audience questions in a scientifically rigorous
manner. Moreover, they also had to present a written report
of up to 20 pages and make a scientific poster. Peer assess- 4 Data Analysis and Results
ment, flipped learning, and brainstorming were the primary
active learning reflections at this point. This activity pre- This section aims to present and discuss the results derived
pares students for real-world scenarios where they would from a statistical analysis conducted on the responses
need to communicate their findings to stakeholders who obtained from the questionnaire described above.
6 Lurdes Babo et al.
The detailed results of the analysis are listed in Table 1. although they felt that the effort and workload were
Mean scores and standard deviations were calculated, and higher.
nonparametric Mann–Whitney tests were employed to
identify significant distinctions between freshman (CALCL)
and sophomore (SM) students.
Significant differences were observed in three specific 5 Conclusions/Final Considerations
questions among the student groups. These questions include
“The PBL approach enhanced my learning under pressure” In this article, we analyze and discuss four main research
(sig. <0.01), “I would like to see this evaluation method used in questions related to students’ perceptiveness of the devel-
other Curricular Units” (sig. <0.001), and “This evaluation opment of soft skills, knowledge acquisition, and assessment
method required more effort on my part” (sig. <0.001). methods in a PBL teaching framework. Were enrolled in two
Sophomore students acknowledged that this approach is groups of students, freshmen, and sophomore, attending
more demanding, although they expressed hesitance in two Math courses, CALCL and SM, respectively.
applying it to other curricular units. The differences high- Generically, the study’s findings revealed that the
lighted in the radar chart (Figure 3) of the means obtained in majority of participants felt positively about their learning
each question are visually illustrated and provide a clear experience. They claimed it enabled them to acquire knowl-
representation of these distinctions. edge more effectively and develop important soft skills such
It is noteworthy that all questions received positive as critical thinking, communication, and collaboration. These
evaluations, with average scores higher than 3. Scores findings are consistent with those previously reported by
higher than 3 indicate a positive overall perception of Suryanti & Supeni (2019) who concluded that PBL is an effec-
PBL among students including the recognition of PBL’s tive instructional model for fostering essential soft skills in
effectiveness in developing crucial soft skills, fostering higher education. Furthermore, the students who partici-
enhanced learning opportunities, and a nuanced under- pated in the present study highlighted that the applied assess-
standing of the practical trade-off involving increased ment methods were more engaging, when compared to those
effort and workload. This suggests that students perceive of traditional courses. The main evidence presented to justify
tangible benefits in terms of skills development and learning this claim was that they could apply what they learned
outcomes, coupled with a practical awareness of the chal- directly in real-life scenarios, rather than just taking tests or
lenges associated with the PBL approach. Students also con- writing papers with no practical application, a finding echoed
sidered that the PBL approach allowed them to learn more, by other studies (Rézio, Andrade, & Teodoro, 2022).
Table 1: Descriptive statistics and Mann–Whitney test
CALCL SM U M-Whit Sig.
Mean SD Mean SD
I properly managed the tasks attributed to me by my workgroup 4.25 0.65 4.05 0.55 608 0.123
As a member of my group, I made a positive impact on the learning process of my colleagues 4.11 0.67 4.05 0.63 700 0.661
My workgroup had a positive impact on my learning 4.14 0.72 4.07 0.69 695.5 0.623
I was anxious during oral presentation 3.61 1.10 3.85 1.13 633.5 0.266
I developed my public speaking skills 3.75 0.87 3.46 0.98 610.5 0.156
I was pleased with my presentation 3.81 0.79 3.66 0.91 687.5 0.564
I managed to properly convey the concepts to the public (colleagues from other groups and the 4.08 0.55 3.93 0.61 653 0.281
lecturer)
The PBL approach allowed me to learn more about the course than if I studied exclusively for 3.61 1.13 3.39 1.00 645 0.312
the written tests
The PBL allowed me to apply knowledge of the course in the area of engineering 3.89 0.71 3.88 0.95 705 0.71
The PBL promoted my learning under pressure. 3.50 0.97 4.12 0.84 481.5 0.006
The PBL developed my time management skill. 3.50 0.97 3.61 1.02 686 0.572
I would like this assessment method to be used in other Curricular Units 3.78 1.05 3.07 0.88 429 <0.001
This assessment method required more effort on my part 3.50 1.00 4.27 0.55 407.5 <0.001
With this assessment method I had a more active role in the classes 3.56 1.16 3.54 0.95 698.5 0.672
With this approach I received more feedback from the teacher about my learning 3.22 1.10 3.61 1.07 572 0.074
This approach allowed me to better understand my learning difficulties 3.58 0.87 3.32 0.99 652.5 0.343
Students’ Perceptions of PBL Usefulness 7
CALCL SM
I properly managed the tasks
atributed to me by my
workgroup
This approach allowed me to As a member of my group, I
5
better understand my learning made a positive impact on the
difficulties learning process of my…
With this approach I received 4 My workgroup had a positive
more feedback from the
impact on my learning
teacher about my learning
3
With this assessment method
I was anxious during oral
I had a more active role in the 2
presentation
classes
1
This assessment method
I developed my public
required more effort on my 0
speaking skills
part
I would like this assessment
I was pleased with my
method to be used in other
presentation
Curricular Units
I managed to properly convey
The PBL developed my time
the concepts to the public
management skill
(colleagues from other…
The PBL approach allowed
The PBL promoted my
me to learn more about the
learning under pressure
course than if I studied…
The PBL allowed me to apply
knowledge of course in the
area of Engineering
Figure 3: Radar chart of the means of each question from CALCL and SM students.
This study revealed some disparities in the percep- successful educational experiences, for teachers and students
tions of the students attending the CALCL and SM courses. alike, and on the other hand, students achieve higher academic
Newcomers (CALCL course) are more prone to have PBL in goals and better preparation to cope with the rapidly changing
other courses, whereas second-year students (SM course) labor market.
felt more pressure and reported more workload with this This article can contribute to the body of knowledge on
type of assessment. PBL and provides some practical ideas for its implementa-
Students’ maturity, level of education, workload in tion. It also emphasizes that the students’ responses can be
other courses, and no prior PBL experience may induce different depending on some internal or external factors
differences and willingness to adhere to PBL. such as maturity and workload. For a more comprehensive
According to Liu & Pásztor (2022), the maturity of the insight, the study would need to be extended to encompass
students, type of instruction, and group size are factors a larger and more diverse sample size that we are consid-
that may affect the effectiveness of PBL. ering as future work.
Overall, the obtained results suggest that PBL can ben-
efit students’ academic growth by providing opportunities Acknowledgements: The authors are grateful for the reviewer’s
for active engagement, while developing twenty-first-cen- valuable comments that improved the manuscript.
tury essential skills needed outside of the classroom. As for
educators, PBL helps them to engage different learners in Funding information: All authors would like to thank
mathematics classrooms, by utilizing different approaches Erasmus + through the PYTHAGORAS project, No 2021-1-
beyond traditional methods. The later are often less appealing, RO01-KA220-HED-000032258, and through the MATH-DIGGER
universally across all types or groups of students and do not project – MATHematics DIGital Escape Rooms, No. 2021-1-PT01-
always yield desired outcomes for everyone involved. New KA220-HED-000032234. The author C.P. was partially sup-
educational settings are win–win situations, on the one hand, ported by CMUP, which is financed by national funds through
teachers gain more insights into what works best and where FCT – Fundação para a Ciência e a Tecnologia, I.P., under the
improvements should be made in their classes, to achieve project with reference UIDB/00144/2020.
8 Lurdes Babo et al.
Author contributions: All authors have accepted responsi- Nilson, L. B. (2016). Teaching at its best: A research-based resource for
bility for the entire content of this manuscript and con- college instructors (3rd ed.). San Francisco: John Wiley & Sons, Inc.
sented to its submission to the journal, reviewed all the http://writeprofessionally.org/how-teach-tpc/files/2018/01/2014-
05-02Teaching-at-its-best.pdf.
results, and approved the final version of the manuscript.
Penkauskienė, D., Railienė, A., & Cruz, G. (2019). How is critical thinking
All the authors L.B., J.M., and C.P. have equal contributions. valued by the labour market? Employer perspectives from different
European countries. Studies in Higher Education, 44(5), 804–815.
Conflict of interest: The authors state no conflict of interest. doi: 10.1080/03075079.2019.1586323.
Pinho, L. A., Mota, F. B., Conde, M. V. F., Alves, L. A., & Lopes, R. M. (2015).
Mapping knowledge produced on problem-based learning between
1945 and 2014: A bibliometric analysis. Creative Education, 6(6),
576–584. doi: 10.4236/ce.2015.66057.
References Pinto, C., Mendonça, J. M., & Babo, L. (2020). Trends of active-learning
teaching practices among engineering students. INTED2020
Bierema, L. L. (2019). Enhancing employability through developing Proceedings, 1(March), 8580–8589. doi: 10.21125/inted.2020.2338.
T-shaped professionals. New Directions for Adult and Continuing Razak, A. A., Ramdan, M. R., Mahjom, N., Zabit, M. N. M., Muhammad, F.,
Education, 2019(163), 67–81. doi: 10.1002/ace.20342. Hussin, M. Y. M., & Abdullah, N. L. (2022). Improving critical thinking
Chen, J., Kolmos, A., & Du, X. (2021). Forms of implementation and chal- skills in teaching through problem-based learning for students: A
lenges of PBL in engineering education: A review of literature. scoping review. International Journal of Learning, Teaching and
European Journal of Engineering Education, 46(1), 90–115. doi: 10. Educational Research, 21(2), 342–362.
1080/03043797.2020.1718615. Reilly, C. M., Kang, S. Y., Grotzer, T. A., Joyal, J. A., & Oriol, N. E. (2019).
Deep, S., Ahmed, A., Suleman, N., Abbas, M. Z., Nazar, U., & Razzaq, H. S. A. Pedagogical moves and student thinking in technology-mediated
(2020). The problem-based learning approach towards developing medical problem-based learning: Supporting novice-expert shift.
soft skills: A systematic review. Qualitative Report, 25(11), 4029–4054. British Journal of Educational Technology, 50, 2234–2250. doi: 10.1111/
Peace and Conflict Studies. doi: 10.46743/2160-3715/2020.4114. bjet.12843.
Dumitru, D., Bigu, D., Jan, E., Jiang, L., Railiene, A., Penkauskiene, D., … Rézio, S., Andrade, M. P., & Teodoro, M. F. (2022). Problem-based
Fradelos, E. C. (2018). A European collection of the Critical Thinking learning and applied mathematics. Mathematics, 10(16), 2862.
skills and dispositions needed in different professional fields for the 21st doi: 10.3390/math10162862.
century. https://drive.google.com/file/d/ Schwab, K., & Samans, R. (2016). The future of jobs: Employment, skills
1G6qBNWmX1GRsfu8SPuOacV4viQJSXHpS/view. and workforce strategy for the fourth industrial revolution. In World
Fidan, M., & Tuncel, M. (2019). Integrating augmented reality into pro- economic forum.
blem based learning: The effects on learning achievement and Seibert, S. S. (2021). Problem-based learning: A strategy to foster gen-
attitude in physics education. Computers & Education, 142, 103635. eration Z’s critical thinking and perseverance. Teaching and Learning
Goti, A., Akyazi, T., de la Calle, A., Oyarbide-Zubillaga, A., & Alberdi, E. in Nursing, 16(1), 85–88. doi: 10.1016/j.teln.2020.09.002.
(2020). Validation of real case solving (RCS) methodology as an Sistermans, I. J. (2020). Integrating competency-based education with a
efficient engineering learning tool. Journal of Open Innovation: case-based or problem-based learning approach in online health
Technology, Market, and Complexity, 6(4), 198. doi: 10.3390/ sciences. Asia Pacific Education Review, 21(4), 683–696.
joitmc6040198. Stevens, M., & Norman, R. (2016). Industry expectations of soft skills
Hayes, R. M. (2020). Employability skills. Library Acquisitions: Practice and in IT graduates. CEUR Workshop Proceedings, 1828, 53–59.
Theory, 14(4), 359–370. doi: 10.1016/0364-6408(90)90007. doi: 10.1145/1235.
Hmelo-Silver, C. E., Bridges, S. M., & McKeown, J. M. (2019). Facilitating Suleman, F. (2016). Employability skills of higher education graduates:
problem-based learning. In The Wiley handbook of problem-based Little consensus on a much-discussed subject. Procedia – Social and
learning (pp. 297–319). New York: John Wiley & Sons, Inc. doi: 10. Behavioral Sciences, 228, 169–174. doi: 10.1016/j.sbspro.2016.07.025.
1002/9781119173243.ch13. Suryanti, H. H., & Supeni, S. (2019). A problem based learning (PBL) model
Hursen, C. (2021). The effect of problem-based learning method sup- in developing students’ soft skills aspect. International Journal of
ported by web 2.0 tools on academic achievement and critical Higher Education, 8(8), 62–69. doi: 10.5430/ijhe.v8n8p62.
thinking skills in teacher education. Technology, Knowledge and Tan, O. S. (2003). Problem-based learning innovation: Using problems to
Learning, 26, 515–533. power learning in the 21st century. Singapore: Cengage Learning Asia.
Liu, Y., & Pásztor, A. (2022). Effects of problem-based learning instructional UNESCO. (2022). Reimagining our futures together: A new social contract for
intervention on critical thinking in higher education: A meta-analysis. education. Paris, France: United Nations Educational, Scientific and
Thinking Skills and Creativity, 45, 101069. doi: 10.1016/j.tsc.2022.101069. Cultural Organization.
McGunagle, D., & Zizka, L. (2020). Employability skills for 21st-century Wijnands, W., & Stolze, A. (2019). Transforming education with eduScrum.
STEM students: The employers’ perspective. Higher Education, Skills In D. Parsons & K. MacCallum (Eds.), Agile and lean concepts for
and Work-Based Learning, 10(3), 591–606. doi: 10.1108/HESWBL-10- teaching and learning: Bringing methodologies from industry to the
2019-0148. classroom (pp. 95–114). Singapore: Springer. doi: 10.1007/978-981-
Mursid, R., Saragih, A. H., & Hartono, R. (2022). The effect of the blended 13-2751-3_5.
project-based learning model and creative thinking ability on Zimmermann, P., Stallings, L., Pierce, R., & Largent, D. (2018). Classroom
engineering students’ learning outcomes. International Journal of interaction redefined: Multidisciplinary perspectives on moving
Education in Mathematics, Science and Technology, 10(1), 218–235. beyond traditional classroom spaces to promote student engage-
doi: 10.46328/ijemst.2244. ment. Journal of Learning Spaces, 7(1), 45–61.
Students’ Perceptions of PBL Usefulness 9
ANNEXES
Example of a proposed PBL in the Statistical Models • The presentation must be active, that is, it must create
course 2021/2022 class situations in which other classmates actively par-
Consider the file data_case_study_IV.csv, which con- ticipate. Tools you can use (examples): Mentimeter;
tains the weight variation of young patients with anorexia, AhaSlides; Quizizz, Kahoot, GpConqr, Padlet, Genially,
in 3 different treatment groups. etc.
a. Describe the statistical distribution of the data.
b. Present boxplots of weight differences before and after https://learninginnovation.duke.edu/faculty-
treatment and calculate outliers. opportunities/art-and-science-of-teaching/active-learning-
c. Test the hypothesis that there was an increase in weight techniques-classroom/.
in the young women after treatment (use a left-sided test). https://eduscrum.org/about-us-and-how-we-try-to-
d. Discuss the p-value of question c. in terms of the pro- make-it-happen/.
blem at hands. https://www.scrumalliance.org/
e. Repeat question c. for a two-sided test. ScrumRedesignDEVSite/media/ScrumAllianceMedia/
f. Compare the results from questions c. and e. from the Certification/Guide_to_Agile_K-12_Education.pdf.
perspective of the problem at hands. https://www.techlearning.com/tl-advisor-blog/tech-
g. Use linear regression to find the function that relates the tools-for-active-learning-classrooms.
two weights for each young person. Approximate the https://www.prodigygame.com/blog/active-learning-
value of the weights after treatment for 3 young patients strategies-examples/.
per treatment. Compute the approximation errors and https://sites.google.com/site/jhdou363/.
comment on the obtained results.
Creating slides
Written report Your slides should be created with a purpose of con-
The written report must comply with the following veying your work in an effective and clear way to your
requirements: teacher and colleagues. Read the following tips:
(a) Cover – which must include the title, authors and date; • The content should be straightforward, brief, and cen-
(b) Index; tered on essential details;
(c) Introduction – identification of the subject covered, • The visuals should include graphs, charts and tables;
paragraph with the structure of the work; • Include essential formulas and provide oral explanation
(d) Methods used in the resolution – briefly present the to them.
theoretical foundations of the work, the methodologies • The Design and color scheme should be consistent. The
applied and the tools used; font size should be readable;
(e) Solution of the proposed problem and discussion of the • Interpret and explain the statistical results, in the scope
results obtained. It must be done in R. of the proposed problem;
(f) Conclusion – summary of the results obtained; • The slides need to have a coherent and logical structure,
(g) Bibliographic references – presentation of the biblio- with Introduction.
graphy used in the development of the work; • Limit text, use keywords and brief phrases;
(h) Annexes – additional information, if justified; • Limit the number of animations;
(i) Written report must be presented in Times New • Check your slides for data, grammar and spelling errors;
Roman format, 12, with a maximum of 20 pages. • Engage the audience, encourage interaction and discus-
sion of topics;
Oral presentation • Do not forget to practice your presentation time;
The oral presentation must comply with the following
assumptions: http://www.garrreynolds.com/preso-tips/design/.
• All group members must present a part of the work; https://www.slideshare.net/edahn/10-tips-for-making-
• Duration is 10 min presentation and 5 min questions. beautiful-slideshow-presentations-9210564∼.
• The number of slides must be at most 10 http://www.garrreynolds.com/preso-tips/design/.
• Every team member has to answer questions from their https://www.slideshare.net/edahn/10-tips-for-making-
classmates, if applicable, and the teacher; beautiful-slideshow-presentations-9210564.
10 Lurdes Babo et al.
Scientific poster • Include references and acknowledgements.
The scientific poster should be written in English. It • During poster presentation, be ready to explain your
should be effective, clear, concise in conveying the infor- work, and engage with the audience to answer questions
mation, and visually engaging. and discuss your findings.
• The title should be coherent with the work and the goals
must be stated in a comprehensible way; Deliverables
• The organization of the poster should have a logical At the deadline for completion of the PBL, you should
sequence and suggest the reading path to the readers. submit, at Moodle, the following files:
• Focus on transmitting the most important information. Use – The written report, in pdf format;
visuals (graphs, charts, tables), bullet points, short sentences. – The scientific poster, in pdf format;
• The visual elements should be easily understandable. – The slides.
Avoid immoderate detail and too few or too many visuals.
• The letter fonts should be consistent and readable. Good job!
• The design and color framework should be as to ensure The teacher
readability and spot the most important information.
