The Effects of Blended Learning on the Performance of Engineering Students in Mathematical Modeling
Abstract
:1. Introduction
1.1. The B-Learning Approach
1.2. Taxonomy of the Cognitive Domain
1.3. Application of ODEs to Mathematical Modeling
1.4. Theoretical Basis
2. Methodology
2.1. Research Question
2.2. Hypothesis
2.3. Goal
2.4. Implementation of the Didactic Proposal
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Session | Type | Learning Activities |
---|---|---|
1 | Synchronous remote | Presentation of subject, purpose, and support materials. Diagnostic evaluation. Formation of work teams. |
2 | Asynchronous remote | Readings, videos, and activities focused on the principles of ODEs. Matlab R2022a tutorials (algebra, graphs, calculus, and ODEs). Readings, videos, and exercises to solve ODEs analytically. |
3 | Synchronous remote | Advice regarding analytical method procedures to solve ODEs. |
4 | Asynchronous remote | Administration of Questionnaire 1. Readings and videos of exponential growth systems modeling. |
5 | Synchronous remote | Development of a mathematical model for a system and its analytical solution. Numerical solution of a system’s mathematical model on the online software platform. |
6 | Face-to-face | Analytical and numerical comparison of solutions to the system’s dynamics. Random assignment of exercises from different situations to build a mathematical model using first-order ODEs. |
7 | Asynchronous remote | Construction of a mathematical model and an analytical solution. Obtention of the numerical solution. |
8 | Face-to-face | Drafting of a written report. Presentation and discussion of results. Administration of the rubric. |
9 | Asynchronous remote | Administration of Questionnaire 2. Administration of the survey. |
Instrument | Contents | Purpose |
---|---|---|
Diagnostic Evaluation | Items/questions regarding the definition, domain, differentiation, and integration of one-variable functions. | Verify the homogeneity of prior knowledge possessed by the sample using converging questions (multiple choice). |
Questionnaire 1 (Pre-test) | Items related to ODE definitions, symbols, classification, use, structure, and solution methods. | Measuring the extent of ODE knowledge and understanding (cognitive domain levels 1 and 2). |
Questionnaire 2 (Post-test) | Items related to the meaning of ODE terms, rules, and procedures for a mathematical model. | Measuring how effectively ODEs are applied and used to analyze a system (cognitive domain levels 3 and 4). |
Rubric | Five criteria with four levels. | Qualitative evaluation of hard and soft skills development. |
Survey | Items with responses on a six-point Likert scale. | Qualitative evaluation of student satisfaction with the b-learning approach adopted in the activities. |
Shapiro–Wilk Test for a Sample | |||
---|---|---|---|
DF | Statistic | p-value | Decision at level (5%) |
19 | 0.91865 | 0.10684 | Normality cannot be rejected |
Descriptive Statistics | |||||||
---|---|---|---|---|---|---|---|
N | Mean | Standard Deviation | Variance | Minimum | Median | Maximum | |
Pre-test | 19 | 6.15789 | 2.33959 | 5.47368 | 2 | 7 | 10 |
Post-test | 19 | 8.84211 | 1.70825 | 2.91813 | 4 | 9 | 10 |
Paired Sample Student’s t-Test | |||
---|---|---|---|
t0 statistic | DF | t0.05,18 | p-value |
−3.69885 | 18 | −1.73406 | 8.21435 × 10−4 |
Item | Sample Responses |
---|---|
Describe the interaction or collaboration in your team when carrying out these activities. | Collaboration was very good, each person did what they had to do, and there was a lot of chemistry since my partner and I have known each other for a long time; that is why I feel that everything went just fine. There was adequate cooperation and collaboration when we carried out the tasks; we agreed on ideas and made everybody’s work easier. The communication with my partner was very good; we both contributed equally to the task. |
What do you think about the material (text, software, etc.,) you used to solve your task? | Very useful to solve the problem and acquire the right solution with the right tools to better understand the subject. After researching different sources, we could completely satisfy our doubts and clear up any issues that came our way. As far as the problem was concerned, it was very clear, we also relied on the book, and we had all of Matlab’s support materials. |
Describe the difficulties you had during this activity. | In my opinion, the most difficult thing was that I could not fully understand the difference between the numerical and the analytical solution. Better understand the relationship between the variables. Implementing the script in Matlab for it to provide a numerical solution. |
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López-Reyes, L.J.; Jiménez-Gutiérrez, A.L.; Costilla-López, D. The Effects of Blended Learning on the Performance of Engineering Students in Mathematical Modeling. Educ. Sci. 2022, 12, 931. https://0-doi-org.brum.beds.ac.uk/10.3390/educsci12120931
López-Reyes LJ, Jiménez-Gutiérrez AL, Costilla-López D. The Effects of Blended Learning on the Performance of Engineering Students in Mathematical Modeling. Education Sciences. 2022; 12(12):931. https://0-doi-org.brum.beds.ac.uk/10.3390/educsci12120931
Chicago/Turabian StyleLópez-Reyes, Luis Javier, Auria Lucia Jiménez-Gutiérrez, and Diana Costilla-López. 2022. "The Effects of Blended Learning on the Performance of Engineering Students in Mathematical Modeling" Education Sciences 12, no. 12: 931. https://0-doi-org.brum.beds.ac.uk/10.3390/educsci12120931