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Can I Eat Melted-Frozen-Melted Bread?: Use of Practical Assignments to Harmonize Mathematics and STEM Courses and as a Measure for Future Technology Studies
Abstract
In the domain of engineering education, the crucial role of mathematics, especially Calculus, cannot be overstated, as it lays the foundational groundwork for numerous sciences, technology, engineering and mathematics (STEM) courses. The integration of mathematics into STEM disciplines is achieved through the practical application of mathematical concepts in real-world scenarios or in conjunction with other STEM subjects, thereby enhancing the coherence of engineering studies and acting as a significant motivational catalyst for students. This paper presents an analytical narrative of a practical mathematics assignment, woven into the Calculus curriculum and other STEM courses from 2013 to 2018. It delves into the potential impacts of these practical assignments on student performance and attitudes by evaluating data sourced from final exam scores and anonymous course surveys, both before and after the intervention period. Through the analysis of an extensive dataset comprising 1526 final exam scores, this study endeavors to make a substantive contribution to Future Technology Studies (FTS), focusing on the strategic harmonization of mathematics and STEM courses to enrich the educational experience and foster a more cohesive and applied learning framework in these disciplines.
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This study investigated the influence of phenomenon-based learning videos (PhBLVs) on students' mathematics self-efficacy, problem-solving skills, reasoning skills, and mathematics achievement using mixed methods experimental embedded design. The participants of this study were the two intact classes both mathematics education students enrolled in Calculus class at USTP-CDO Philippines. The study used an adapted instrument on mathematics self-efficacy scale and four researcher-made instruments on problem solving, reasoning, mathematics achievement, and in-depth interview subjected to validity and reliability tests. The quantitative aspect utilized quasi-experimental pretest-posttest control group design with one control group exposed to conventional short-video lectures from YouTube and one experimental group exposed to PhBLVs during asynchronous online classes. An in-depth interview followed with 11 participants from the experimental group chosen as informants. The quantitative data were analyzed using mean, standard deviation, and ANCOVA, while the qualitative data were analyzed using thematic analysis technique. Quantitative data analysis revealed that students exposed to PhBLVs had significantly higher mathematics self-efficacy, problem-solving and reasoning skills as compared to students exposed to non-phenomenon-based videos. However, the result showed that students' mathematics achievement under control and experimental groups are comparable. This was supported by the results of qualitative data analysis which revealed that students exposed to PhBLVs had remarkable experiences with five key themes emerged: difficulty with problem construction, enhancement of reasoning and problem-solving skills, solving real-world problems relevant to social issues, relating math to real-life contexts, and confusing yet enjoyable activities. This implies that PhBLVs can increase students' mathematics achievement and can significantly influence the mathematics self-efficacy, problem-solving and reasoning skills of students. Hence, the researcher recommends to tertiary mathematics educators to use PhBLVs for Calculus and its related mathematics courses as students are engaged in an inquiry or discovery form of learning cultivating their higher-order thinking skills.
After experiencing years of procedural teaching in K-12 mathematics classrooms, many students arrive at college with ideas about, and approaches towards, mathematics that are not helpful to their learning. Students’ prior experiences and misconceptions can then negatively impact their experiences in university STEM courses. This paper describes a short course in the “big ideas” of calculus, that offered students an approach of problem-based learning, combined with mindset messages, otherwise known as a “mathematical mindset approach”. The mixed-method study considered how a ‘mathematical mindset’ teaching intervention impacted the learning, achievement, and beliefs of incoming college students, finding that the intervention significantly changed students’ ideas about mathematics, their own potential, and the value of collaboration. At the end of the course students also significantly improved their achievement on assessments of problem solving and collaboration. Importantly the course allowed students to believe in their own potential and to approach mathematics with a growth mindset, suggesting a role for such courses in students’ mathematics pathways.
The purpose of this experimental study was to examine the creative constructs of students enrolled in Differential Calculus at the University of Science and Technology of Southern Philippines, Cagayan de Oro City, Philippines. This study was composed of 132 engineering and mathematics education students enrolled in two different semesters. The experimental group was chosen randomly, exposed to the problem-based HALP model teaching approach and problem posing while the control group was taught using Polya’s problem-solving heuristics. Multiple Solution Tasks (MST) test in Calculus was administered to determine their creative constructs which can be measured in terms of their level of mathematical fluency, flexibility and novelty of solutions before and after the experiment. Results indicated that the experimental group exhibited a remarkable improvement of their mathematical fluency and flexibility but still in the developing level when they are required to posit novel solutions to problems as influenced by the problem-based HALP and problem posing activities. Hence, it is recommended that mathematics teachers may utilize these methods to successfully develop students’ mathematical creativity and future research may also be explored on integrating technology and how it can influence developing student’s mathematical creativeness as well as the mediating role of their affective domains and IQ (intelligent quotient).
The focus of this study is the effectiveness of the Problem Based Learning (PBL) model assisted by hypermedia-based e-books on the results of integral calculus learning. The objectives of the study are (1) to describe the students’ learning outcomes of integral calculus which are taught through problem-based learning model with the help of a hypermedia-based e-book, and (2) to find out the effectiveness of the Problem Based Learning model with the help of a Hypermedia-Based e-book on integral calculus learning outcomes. This research employed an experiment with a posttest only control design. The study population was all students from the Department of Mathematics Education, Halu Oleo University in the 2017-2018 academic year. The study sample consisted of 60 students distributed equally in two classes namely the experimental class (30) and the control class (30). The Problem Based Learning model with the help of a hypermedia-based e-book was applied in the experimental class while the traditional learning model with the help of printed teaching materials was applied in the control class. The PBL learning model steps consist of (1) presenting contextual problems, (2) forming cooperative groups, (3) analyzing problems cooperatively, (4) presenting the results of group discussions, (5) reflections. Data were collected using the test of integral calculus learning. Then the data were analyzed descriptively and inferentially. The descriptive analysis included the mean value, variance, and standard deviation, while the inferential analysis included the data normality test, the data homogeneity test, and the average difference test. The results showed that the students' integral calculus learning outcomes taught with Problem Based Learning model was categorized well, and the PBL learning model effectively improved the integral calculus learning outcomes.
The research was carried out through research and development to produce an innovative chemistry laboratory workbook (InoChemLaW) followed by the implementation of the learning package in the teaching of chemistry. The result showed that a standard InoChemLaW has successfully been developed on the topic of Colligative Properties of solutions. The implementation of InoChemLaW was carried out onto the experimental class compared to the existing laboratory workbooks (ConChemLaW) in the control class. An InoChemLaW package helps the students to learn chemistry independently so that the learning stages are carried out systematically, the students are actively completed the projects, thereby increasing their knowledge and skills. Students' knowledge and skills respectively in experimental groups were found higher than that in control group, and both groups are significantly different. The developed InoChemLaw package is highly very good. It is recommended that innovative laboratory workbooks integrated with project-based learning can be developed and implemented for teaching of other chemistry subjects and science studies.
Subjects related to fluid mechanics for hydraulic engineers ought to be delivered in interesting and active modes. New methods should be introduced to improve the learning students’ abilities in the different courses of the Bachelor’s and Master’s degree. Related to active learning methods, a continuous project-based learning experience is described in this research. This manuscript shows the developed learning methodology, which was included on different levels at Universitat Politècnica de València. The main research goal is to show the active learning methods used to evaluate both skills competences (e.g., “Design and Project”) and specific competences of the students. The research shows a particular developed innovation teaching project, which was developed by lecturers and professors of the Hydraulic Engineering Department, since 2016. This project proposed coordination in different subjects that were taught in different courses of the Bachelor’s and Master’s degrees, in which 2200 students participated. This coordination improved the acquisition of the learning results, as well as the new teaching methods increased the student’s satisfaction index.
Science, Technology, Engineering and Mathematics (STEM) Project-Based Learning (PjBL) is increase effectiveness, create meaningful learning and influence student attitudes in future career pursuit. There are several studies in the literature reporting different aspects of STEM into a PjBL pedagogy. However, the effect of implementing STEM PjBL in terms of improving students’ skills in self-efficacy levels in physics mechanics at high school level has not been demonstrated as expected in the previous literature. This study followed a quasi-experimental research method. Bandura’s social cognitive theory is used to assess and compare the effect of STEM PjBL with conventional teaching method on students’ self-efficacy level in learning physics among over 100 high school students. The result illustrated that STEM PjBL improve students’ self-efficacy to solve physics problem. Also, the study proposes a guideline for future research.
Guiding students how to think critically and creatively is a crucial part of the educational process in order to meet the required skills to face the 21st century. In addition, attention to the local culture especially that is closely related to the scientific concepts needs to be strongly emphasized. Due to those two aspects i.e. creative and critical thinking as well as attention to local culture, the ethno-STEM project-based learning for high school students has been implemented and its impact to students’ critical and creative thinking skills has been investigated. This study involved 230 students from seven high schools in Central Java Indonesia. The data collection was carried out through a set of instruments to reveal the students’ critical and creative thinking skills. The instruments were declared as valid based on the experts’ judgment and showed an Alpha Cronbach score of 0.79 prior to use. The results showed that the ethno-STEM project-based learning was able to improve the average critical and creative thinking skills of students in all indicators varying from low to medium categories. The improvement of students' critical thinking skills was observed by the achievement of the N-gain score, i.e. 52 students (22.6%) achieved a high category, 102 students (44.4%) achieved a medium category, and 76 students (33.0%) achieved a low category. Moreover, an increase in the creative thinking skills was also observed, indicated by the N-gain score, i.e. 63 students (27.4%) were at a high category, 109 students (47.4%) were at a medium category, and 58 students (25.2%) were at a low category. In conclusion, the ethno-STEM project-based learning showed a significant effect on the improvement of students' critical and creative thinking skills.
Science, Technology, Engineering and Mathematics (STEM) Project-Based Learning (PjBL) is increase effectiveness, create meaningful learning and influence student attitudes in future career pursuit. There are several studies in the literature reporting different aspects of STEM into a PjBL pedagogy. However, the effect of implementing STEM PjBL in terms of improving students' skills in self-efficacy levels in physics mechanics at high school level has not been demonstrated as expected in the previous literature. This study followed a quasi-experimental research method. Bandura's social cognitive theory is used to assess and compare the effect of STEM PjBL with conventional teaching method on students' self-efficacy level in learning physics among over 100 high school students. The result illustrated that STEM PjBL improve students' self-efficacy to solve physics problem. Also, the study proposes a guideline for future research.
The aim of the research presented in this work is to investigate how innovative teaching formats, based on student-centred activities, may help first year university students to deal with the difficulties in the transition from the mathematics they are used to in high school, to the one they meet at university, which requires a significant shift to conceptual understanding, especially in Calculus courses. As part of this overarching goal, this presentation investigates the case of Taylor series, a topic that is taught in all calculus courses at university. This work shows the efficacy of a blended learning approach, highlighting the main difficulties concerning the deep understanding of functions by students. We discuss possible limitations, and we provide suggestions for best practices in university math classes.
Power electronics is a fast-developing technology within the electrical engineering field. This paper presents the results and experiences gained from applying design-oriented project-based learning to switch-mode power supply design in a power electronics course at the Technical University of Denmark (DTU). Project-based learning (PBL) is known to be a motivating problem-centered teaching method that not only places students at the core of teaching and learning activities but also gives them the ability to transfer their acquired scientific knowledge into industrial practice. Students choose a specification to implement from various power converter application projects, such as a fuel cell power conditioning converter, a light-emitting diode (LED) driver or a battery charger. The students select the topology, design magnetic components, calculate input/output filters and design closed-loop controllers necessary to fulfill the requirements listed in the chosen specification and thus meet the project's goals. This paper presents the course teaching plan and teaching methods, assessment method and student feedback.
Design-based research (DBR) evolved near the beginning of the 21st century and was heralded as a practical research methodology that could effectively bridge the chasm between research and practice in formal education. In this article, the authors review the characteristics of DBR and analyze the five most cited DBR articles from each year of this past decade. They illustrate the context, publications, and most popular interventions utilized. They conclude that interest in DBR is increasing and that results provide limited evidence for guarded optimism that the methodology is meeting its promised benefits.
This article describes the characteristics and aims of problem-based learning (PBL), a successful strategy for higher education. PBL has been implemented as an overall strategy for several programmes at Maastricht University, for example medicine. The suitability of PBL as an innovation in engineering education is analysed, given the characteristics of this particular domain. Project work and guided small group work also present themselves as alternatives for conventional engineering education. PBL has been implemented as a partial strategy for Mechanical Engineering and Biomedical Engineering at Technische Universiteit Eindhoven. The differences between the medical and the engineering implementation are analysed. PBL offers good prospects in the first few years of a programme, especially if group work tutorials and some directive teaching are added. In later phases project work offers a strong alternative. The conclusion is that PBL has certain limitations, which make it less suitable as an overall strategy for engineering education.
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.
Problem-based learning (PBL) has swept the world of medical education since its introduction 40 years ago, leaving a trail of unanswered or partially answered questions about its benefits. The literature is replete with systematic reviews and meta-analyses, all of which have identified some common themes; however, heterogeneity in the definition of a 'problem-based learning curriculum' and its delivery, coupled with different outcome measurements, has produced divergent opinions. Proponents and detractors continue to dispute the merits of the cognitive foundation of a PBL approach, but, despite this, there is evidence that graduates of PBL curricula demonstrate equivalent or superior professional competencies compared with graduates of more traditional curricula.
Problem-based learning in mathematics (ED482725)
- K H Roh
Roh, K. H. (2003). Problem-based learning in mathematics (ED482725). ERIC. https://eric.ed.gov/?id=ED482725