Investigation of Progressive Learning within a Statics Course: An Analysis of Performance Retention, Critical Topics, and Active Participation
2. Objective and Scope
3. Background of Statics
3.1. Statics Topics and Their Interrelations
4. Data Collection
4.1. Data Source and Attributes
4.2. Data Preparation
- Highly similar sequence between the solution manual and student homework while there are multiple possible sequences to be taken.
- Equation/solution details (e.g., order of values in equations, use of notations).
- High similarity of FBD and/or figures between solution manual and homework.
- Skipping steps covered in class to solve the problem.
- Different notation and sign conventions compared to the instructor’s teaching.
5. Analysis, Results, and Discussion
5.1. Performance Retention
5.1.1. Exam Performance Retention
- High scores on exam 1: Out of the 80 students in this group, 65 (81.2%) maintained a high score on exam 2; and of these 65 students, 50 (76.9%) maintained a high score in exam 3. Not a single student in this group failed the course; 70% obtained a final grade of A; and 90% obtained a final grade of B or better. These findings demonstrate that a high proportion of students who developed a good understanding early on are more likely to retain the same level of high performance and successfully complete the course without failing. This indicates that performance retention is clearly found among students who build a good understanding from the beginning. In other words, early-on understanding is critical in this course for knowledge progression and retention.
- Medium scores on exam 1: Out of the 55 students in this group, 46 (83.6%) achieved the same or better levels (i.e., medium or high) of performance on exam 2; out of these 46 students, 39 (84.7%) achieved a medium or high score on the final exam 89% of the students in this group successfully passed the course, with 11% of the students in this group failing. More specifically, 16% obtained a final grade of A, which is significantly less than that of the students who received high scores on exam 1 while 61.8% of the students in this group received a grade of B or better for the final grade. These results indicate that students who develop an acceptable level of understanding early on either maintained or improved on that performance. Most of them achieved acceptable final grades and successfully completed the course without failing. However, depending on their follow-up progression, some students in this group may still fail the course or achieve a high final grade.
- Low scores on exam 1: Out of the 60 students in this group, 37 (61.6%) obtained a low score on exam 2; out of these 37 students, 35 (94.5%) maintained the low score in exam 3. Moreover, 67% of the students in this group failed the course, and only 3% obtained a final grade of A. From exam 1 to exam 2, about 30% of the students improved their performance. However, from exam 2 to exam 3, only 5% improved their performance. This indicates that low performance on exam 1 is strongly associated with the continuous low performance, and low performance on exam 2 is extremely strongly associated with the continuous low performance. This suggests that building a weak understanding from the beginning makes it difficult for them to recover or properly learn. Although some students may overturn low performance on exam 1 and achieve satisfactory or high final grades, the number of such students is insignificant.
5.1.2. Homework Performance Retention
- High scores on homework set 1: From the 128 students in this group, 82 (64.1%) maintained a high score on homework set 2; from these 82 students, 64 (78.1%) maintained a high score on homework set 3. Approximately 80% of the students in this group passed the course, and 42% obtained a final grade of A. These findings demonstrate that students who develop a good understanding from the beginning retain the same level of high performance till the end, and most of them successfully complete the course without failing. This result generally corroborates our findings related to exam performance retention that performance retention is clearly found among students who build a good understanding from the beginning. However, there is a notable number of students, worth noting, who had a significant drop in performance to low homework performance from homework set 2. An additional, separate analysis indicates that many students from this group performed poorly on exam 1. Although we are unable to prove this with hard evidence or data, these students may have learned completion of homework without a proper understanding of the material is not helpful for their exam performance and overall knowledge retention, and stopped using extra resources (e.g., solutions’ manual) to complete their homework.
- Medium scores on homework set 1: In total, 44 students were identified to initially be in this group. As this is the medium performing group, the spread of the performance on the next homework sets covers more broadly than the other groups. Considering the performance in homework set 2, the 44 students are distributed to 24, 14, and 6 in low, medium and high groups (L2, M2, and H2), respectively. A larger proportion is found in the low performance (L2) group from M1. The same true considering the third homework set: there are more students in L3 than the other groups, M3 and H3. From this student distribution in subsequent homework sets, we claim a medium level performance presents challenges to improve performance in subsequent learning; however, it is not impossible to improve as a small portion of students were able to improve their performance while majority struggled with lower performance. From this group (M1), 22% of the students received an A grade, 32% failed the course, and 68% passed the course. Given the importance of initial topics of statics serving the fundamental basis of later topics, these results are deemed reasonable.
- Low scores on homework set 1: From the 23 students in this group, 20 (86.9%) maintained the same level of performance at a low score on homework set 2; from these 20 students, 17 (85%) maintained a low score on homework set 3. Moreover, 44% of students in this group—a significant portion—failed the course and only 19% obtained a final grade of A. These findings demonstrate that on homework, almost all students who develop a poor understanding early on retain the same level of low performance on subsequent assessments, and almost half of the students fail to pass the course. This corroborates exam retention findings that performance retention negatively builds among students who attain a poor understanding from the beginning.
5.2. Critical Topics
5.2.1. Critical Topics for All Failing Students
- Based on Figure 7, from homework 4 to homework 5, the gap in scores for the failing students experienced the most drastic increase.
- Based on Figure 6, from homework 5 to the following homework assignments, there is no significant increase in performance, which implies that the students continue to suffer at a low grade.
- The failing students maintained a constantly low performance on homework 5 to 9 at 62.0, 49.6, 49.6, 56.3, and 47.3, respectively.
- On homework 8, their performance improved; however, on homework 9, again, a significant drop in performance occurs.
5.2.2. Critical Topics for Continuously Low-Performing Students
5.3. Progressive Course Interaction
5.3.1. Active Participation
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|Topic||Homework||Exam 1||Exam 2||Exam 3|
|Free-body Diagram, Equilibrium||2||✓||✓||✓|
|Moment, Varignon’s Theorem, Couple||3||✓||✓||✓|
|Load Simplification, Distributed loads||4||✓||✓||✓|
|FBD, Equilibrium, Two Force Member, Support||5||✓||✓|
|Truss, Frames, Friction||6||✓||✓|
|Internal Forces: Shear and Moment||7||✓|
|Moment of Inertia||9||✓|
|Performance Category||Performance Score (S)|
|High||S ≥ 85|
|Medium||70 ≤ S < 85|
|Low||S < 70|
|All Failing Students vs. H1-H2-H3||p-Value||Significant|
|Homework 1||p = 0.078||No|
|Homework 2||p < 0.01||Yes|
|Homework 3||p < 0.01||Yes|
|Homework 4||p < 0.001||Yes|
|Homework 5||p < 0.001||Yes|
|Homework 6||p < 0.001||Yes|
|Homework 7||p < 0.001||Yes|
|Homework 8||p < 0.001||Yes|
|Homework 9||p < 0.001||Yes|
|L1-L2-L3 vs. H1-H2-H3||p-Value||Significant|
|Homework 1||p = 0.072||No|
|Homework 2||p < 0.001||Yes|
|Homework 3||p < 0.001||Yes|
|Homework 4||p < 0.001||Yes|
|Homework 5||p < 0.001||Yes|
|Homework 6||p < 0.001||Yes|
|Homework 7||p < 0.001||Yes|
|Homework 8||p < 0.001||Yes|
|Homework 9||p < 0.001||Yes|
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Ahmed, N.; Park, J.; Arteaga, C.; Stephen, H. Investigation of Progressive Learning within a Statics Course: An Analysis of Performance Retention, Critical Topics, and Active Participation. Educ. Sci. 2023, 13, 576. https://doi.org/10.3390/educsci13060576
Ahmed N, Park J, Arteaga C, Stephen H. Investigation of Progressive Learning within a Statics Course: An Analysis of Performance Retention, Critical Topics, and Active Participation. Education Sciences. 2023; 13(6):576. https://doi.org/10.3390/educsci13060576Chicago/Turabian Style
Ahmed, Naveed, JeeWoong Park, Cristian Arteaga, and Haroon Stephen. 2023. "Investigation of Progressive Learning within a Statics Course: An Analysis of Performance Retention, Critical Topics, and Active Participation" Education Sciences 13, no. 6: 576. https://doi.org/10.3390/educsci13060576