Improving Student Learning of Impulse and Momentum in Particle Dynamics Through Computer Simulation and Animation

Abstract

Computer simulation and animation (CSA) is educational technology in which computer programs are employed to simulate and animate real-world physical phenomena and processes. CSA has attracted growing attention and received an increasing number of applications in the international science, technology, engineering, and mathematics education community in recent years. The present study focuses on developing and assessing two CSA learning modules for improving student learning and problem-solving related to impulse and momentum in particle dynamics. Both CSA learning modules integrate mathematical problem-solving procedures into computer simulation and animation. They have interactive computer graphical user interfaces, which enable students to change input variables and visualize how output variables change accordingly. A quasi-experimental, quantitative research study was performed, involving 285 undergraduate engineering students divided into a comparison group that did not use CSA and an intervention group that used CSA. The results of statistical non-parametric analysis on the data collected from pre- and post-tests on the two groups show that, on average, the intervention group achieved more learning gains than the comparison group by 44% and 40% from two CSA learning modules, respectively. The difference in learning gains between the two groups of student participants was statistically significant.

Keywords

Computer simulation and animation impulse momentum particle dynamics quasi-experimental quantitative study

Introduction

Advantages of Computer Simulation and Animation

Computer-based educational technology has been widely recognized as an effective and critical intervention to improve student learning in a variety of academic disciplines in science, technology, engineering, and mathematics (STEM) (Moore, 2021; Sanders & George, 2017; Schindler et al., 2017; Wang et al., 2018). An important computer-based educational technology is computer simulation and animation (CSA), where real-world physical phenomena and processes are simulated and animated with computer programs and shown on computer screens.

The history of CSA can be traced back to World War II when the earliest form of computers was employed in military projects, such as the Manhattan Project, to model the process of a nuclear detonation. Since then, CSA has received growing attention and widespread applications in a variety of STEM and non-STEM disciplinary areas (Brom et al., 2018; D’Angelo et al., 2014; Harrison & Hummell, 2010; Kaushal et al., 2020; Rivera-Ortega, 2021; Taylor & Chi, 2006). For example, Newell and Simon (1956) are widely recognized as pioneers who employed computers to simulate human action to understand the psychology of human cognition. Forrester (1968) is widely regarded as a pioneer of computer animation. He developed a naval flight simulator, which eventually evolved into the SAGE (Semi-Automatic Ground Environment) air defense system for North America.

Compared to physical experiments that typically require real-world equipment, devices, and instruments, CSA has three advantages, among others. First, CSA is cost-effective. Except for needing a desktop computer or a laptop, CSA typically does not require highly expensive real-world equipment, devices, and instruments, which significantly reduces experimental and maintenance costs. Purchasing and maintaining physical equipment, devices, and instruments, especially those expensive ones, has been a significant financial challenge to many higher education institutions worldwide (Gustavsson, 2002; Lasica et al., 2016). If students bring their own mobile devices, such as smart phones or tablets, to the classroom, they can run CSA on their own mobile devices, which further offsets CSA costs.

Second, as long as students have access to a computer, they can conduct CSA anywhere, not necessarily in a brick-and-mortar teaching laboratory (Sans-Cope et al., 2021; Tsai, 2017). The instructor can integrate CSA into online teaching and learning activities. CSA is critical and meaningful in the context of the COVID-19 pandemic, as the situation continuously evolves and requires students to social distance and wear face coverings when they conduct experiments in a brick-and-mortar teaching laboratory.

Third, some phenomena and processes can be easily demonstrated with CSA, but are very difficult, or even impossible, to be shown with physical experiments due to many practical and environmental constraints (Kozma, 2003). For instance, CSA can be used to simulate how the Solar System in the universe evolves and how black holes are developed (Ruphy, 2015). It is highly challenging to design and create physical experiments to demonstrate these processes without significant time and labor investments.

Applications of Computer Simulation and Animation in Science, Technology, Engineering, and Mathematics Education

Computer simulation and animation has attracted growing attention and received an increasing number of applications in the international STEM education community in recent years. Raymond & Maxwell (2015) examined the role of computer simulation in enhancing the learning experience and satisfaction of electronics technology students. They concluded that computer simulation helps students understand concepts in electronics technology faster than using conventional laboratory equipment. Tseng et al. (2020) incorporated computer simulation into classroom activities to enhance manufacturing systems’ learning experience. On the first page of their paper (Tseng et al., 2020), they stated that computer simulation not only “provides an effective way [for students] to evaluate the design and operational performance of manufacturing systems” but also “motivates the students to be engaged in the classroom activities besides learning the theoretical knowledge.” Sehgal (2019) examined the role of computer animation in teaching technical courses, such as computer-aided design, computer-aided manufacturing, and engineering graphics. He concluded that computer animation enhanced student memory and provided students a different perspective for understanding and solving technical problems.

Computer simulation and animation has also been employed in teaching and learning engineering dynamics, a foundational second-year undergraduate course required in many engineering programs, such as mechanical, aerospace, civil, environmental, and biomedical engineering programs. This course covers numerous fundamental concepts and problem-solving procedures requiring solid spatial visualization and mathematical modeling skills (Beer et al., 2015; Hibbeler, 2015; Lane et al., 2005).

Importance of the Present Study

The present study is important as it addresses two research gaps in existing literature. First, the majority of CSA programs developed to date for engineering dynamics focus on improving students’ conceptual understanding only, rather than their problem-solving skills (Flori et al., 1996; Stanley, 2008; Wieman et al., 2008). Flori et al. (1996) developed Basic Engineering Software for Teaching (BEST) Dynamics for use in the classroom. Their software focuses on improving students’ conceptual understanding though computer animations. Stanley (2008) developed a computer animation program to improve students’ conceptual understanding of particle dynamics through the animation of the motion of particles. Several learning topics covered in engineering dynamics, such as projectile motion and collision, were also included in the well-known Physics Education Technology (PhET) Simulations software (Wieman et al., 2008).

While conceptual understanding is essential, solving technical problems is the ultimate purpose of learning engineering dynamics (le Roux & Kloot, 2020). In engineering dynamics, students are often required to solve dynamics problems using Newton’s second law, the principle of work and energy, the principle of linear impulse and momentum, etc. CSA can be used to animate a variety of phenomena in engineering dynamics, such as how an object moves in a 2-D or 3-D space, to help students understand these phenomena. However, conceptual understanding of various phenomena is insufficient for students to solve problems in engineering dynamics. Students must also be able to translate their conceptual understanding into correct mathematical models to eventually solve those problems. In the present study, two computer simulation and animation learning modules were developed to improve student learning as well as problem-solving related to impulse and momentum in particle dynamics.

A significant amount of research has shown that many students have difficulty in understanding the concepts of impulse and momentum, as well as associated problem-solving procedures (Adimayuda et al., 2021; Rosa, Carl, Aminah, & Handhika, 2018; Wirjawan, Pratama, Pratidhina, Wijaya, Untung, & Herwinarso, 2020). In a recent study conducted by the first author of this paper (Fang, 2014), engineering undergraduates were asked to identify, from a list of 50 concepts in engineering dynamics, those concepts that were difficult for them to understand or difficult to apply in problem-solving. Students identified the top three most difficult concepts: the Principle of Angular Impulse and Momentum for a rigid body, the Conservation of Angular Momentum for a rigid body (or a system of rigid bodies), and the angular impulse of a rigid body. All three of the most difficult concepts were focused on impulse and momentum. The CSA learning modules developed in the present study directly concentrate on student learning of impulse and momentum. With an interactive set of computer graphic user interfaces (GUIs), these CSA learning modules have the following features:

1) Providing step-by-step instructions to solve technical problems involved in CSA learning modules mathematically.

2) Enabling students to observe the motion of relevant objects to understand better technical problems involved.

3) Enabling students to change the values of input variables of CSA learning modules and observe how output variables change accordingly.

Integrating mathematical problem-solving procedures into computer simulation and animation is the most critical feature of the CSA learning modules developed in the present study. It is this important feature that sets the CSA learning modules developed in the present study from other CSA programs developed by other researchers. This feature not only enables students to understand better the technical problems involved, but also helps students develop mathematical problem-solving skills.

Second, the majority of research associated with CSA programs involved single-group questionnaire surveys, student interviews, and/or expert interviews only (Kaniawati et al., 2016; Serevina & Luthfi, 2021; Stanley, 2008). These surveys and interviews are subjective and cannot provide objective assessments and evaluations. Single-group pre- and post-tests were utilized in some studies (Triyani et al., 2019). A quantitative research study including a comparison or control group is lacking. In the present study, quasi-experimental research was performed, involving pre- and post-tests on two groups of student participants: a comparison group that did not use two CSA learning modules and an intervention group that used two CSA learning modules. Statistical and quantitative comparison described in the Results section of this paper will show that, on average, the intervention group achieved more learning gains than the comparison group by 44% and 40% from two CSA learning modules, respectively. The difference in learning gains between the two groups of student participants was statistically significant.

In the remaining sections of this paper, the development of CSA learning modules is described first. Then, research design and data collection methods are introduced, followed by a description of the results. The purpose and limitations of the present study are discussed. Conclusions are made at the end of the paper.

Development of Computer Simulation and Animation Learning Modules

Two computer simulation and animation learning modules were developed in the present study. The development work involved the following four steps:

Step 1: Design a specific set of learning objectives for each CSA learning module.

Step 2: Design technical problems for use in each CSA learning module to meet the learning objectives.

Step 3: Design interactive computer graphical user interfaces (GUIs) for each CSA learning module.

Step 4: Develop, test, and debug computer codes for each CSA learning module to ensure they are fully functional.

The following subsections describe details of each step.

Step 1: Design a Specific Set of Learning Objectives for Each CSA Learning Module

The learning objectives for CSA learning module I included:

1. Apply the Principle of Conservation of Linear Momentum to determine velocity for a system of particles.

2. Apply the Principle of Linear Impulse and Momentum to determine impulsive forces.

3. Understand how the coefficient of restitution plays a role in velocity changes.

The learning objectives for CSA learning module II included:

1. Determine angular impulse and angular momentum.

2. Apply the Principle of Angular Impulse and Momentum to determine the velocity of a particle.

Step 2: Design Technical Problems for Use in Each CSA Learning Module

Figures 1 and 2 show two technical problems designed for CSA learning modules I and II, respectively. In Figure 1, two bumper cars collide with each other. The mass of each bumper car is given. The initial velocity of each bumper car, as well as the coefficient of restitution between the two bumper cars, are variables. Students need to determine the velocity of each bumper car after the collision and the average impulsive force between the two cars when the collision occurs.

In Figure 2, a block is placed on a round platform. Moment M_p is applied to the platform. Force F is applied to the block at angle θ. Both moment M_p and Force F are functions of time t. The initial velocity of the block, as well as angle θ, are variables. Students need to determine the velocity of the block at time t = 4 seconds.

Figure 1.

Technical problem designed for CSA learning module I.

Figure 2.

Technical problem designed for CSA learning module II.

Step 3: Design Interactive Computer Graphical User Interfaces for Each CSA Learning Module

A series of interactive computer graphical user interfaces (GUIs) were designed for each CSA learning module. These interactive GUIs allow students 1) to change input variables to see how outputs change accordingly and 2) to observe how objects move based on specific values of input variables.

Figure 3 shows how three input variables involved in CSA learning module I can be changed. Students can move three bars at the top-right corner to change the values of each bumper car’s initial velocity and the coefficient of restitution. The values of output variables simultaneously vary when the values of input variables are changed.

Figure 4 shows how two input variables involved in CSA learning module II can be changed. Students can move two bars at the top-right corner to change the values of the initial velocity of the block as well as angle θ. The values of output variables also simultaneously vary when the values of input variables are changed.

Figures 5 and 6 show the animation function of CSA learning modules, i.e., how objects move based on specific values of input variables. Figure 5 shows the initial positions of two bumper cars and their positions before and after the collision. Figure 6 shows the initial position of the block as well as its position after a specific time.

Figure 3.

Change Input variables in CSA learning module I.

Figure 4.

Change Input variables in CSA learning module II.

Figure 5.

Animations in CSA learning Module I: (a) Initial positions, (b) before the collision, and (c) after the collision.

Figure 6.

Animations in CSA learning module II: (a) Initial position and (b) after a specific time.

Step 4: Develop, Test, and Debug Computer Codes for Each CSA Learning Module

Adobe Flash was employed to code each CSA learning module. Several users were involved in the testing and debugging of code. The process of Step 4 was both time- and labor-intensive.

Research Design and Data Collection Method

Research Question and Quasi-Experimental Research Design

The research question of the present study was: To what extent, if any, did the interactive computer simulation and animation learning modules improve student learning of impulse and momentum in particle dynamics? To answer this question, quasi-experimental research design was employed in the present study. It involved pre- and post-tests on two groups of student participants: a comparison group that did not use two CSA learning modules and an intervention group that used two CSA learning modules. Each group completed both pre- and post-tests using the same assessment instrument. A quantitative comparison in terms of student learning gains was made between the two groups.

Student Participants

A total of 285 sophomore-year undergraduate engineering students participated in the present study. The vast majority were from two engineering departments at the authors’ institution: the Department of Mechanical and Aerospace Engineering (MAE) and the Department of Civil and Environmental Engineering (CEE). The authors’ institution is a public research university in the Mountain West region of the United States of America. Before conducting pre-tests, all student participants signed on an Informed Consent form approved by an Institutional Review Board.

Table 1 shows the number of student participants in the comparison and intervention groups for each CSA learning module. The students in the comparison group took an engineering dynamics course in Semester A (Spring). Those in the intervention group took an engineering dynamics course in Semester B (Fall). Student participants in both semesters followed the same course sequence of their undergraduate study. In other words, student participants in both semesters were comparable as none of them took extra courses to prepare them for the engineering dynamics course. Both semesters also had the same time period (16 weeks).

Table 1.

The Number of Student Participants.

Computer simulation and animation learning modules	Comparison group	Intervention group	Two-group total
I	64	82	146
II	56	83	139

The first author of this paper was the instructor for the engineering dynamics course in both semesters, using the same syllabus and the same textbook. It was highly challenging to conduct the present study in one single semester. This is because it was not feasible to assign students in the same semester into two groups while allowing one group to use CSA learning modules and not allowing another group to use CSA learning modules.

In summary, the convenience sampling technique was employed in the present study. All student participants completed their pre- and post-tests within a certain time period. Due to convenience sampling and time constraints, the present study is a quasi-experimental study rather than an experimental study with randomly assigned student participants.

Data Collection and Statistical Analysis Methods

Each student participant in the comparison and intervention groups completed both pre- and post-tests using the same assessment instrument. The assessment instrument includes 10 multiple-choice questions: five for CSA learning module I and five for CSA learning module II. The face and content validity of the assessment instrument was verified by an experienced senior instructor and his PhD students. This senior instructor has taught engineering dynamics for more than 20 years. The internal consistency reliability of the assessment instrument was also examined to ensure it is acceptable. A pilot study that included a small number of student participants was also conducted before the assessment instrument was finally administered to all student participants.

Student participants completed pre- and post-tests at their own pace without the presence of the researchers of the present study. Based on their answers to these assessment questions, each student participant earned a score (%) in the pre-test and the post-test for each CSA learning module. Based on student scores in the pre- and post-test, normalized learning gains were calculated. Normalized learning gains were calculated as (Hake, 1998):

Normalized learning gain = [Post-test score (%) – Pre-test score (%)] / [100% - Pre-test score (%)]

It should be noted that the above equation may result in an undefined score. For example, a student participant may earn a full score (100%) in the pre-test, which means the student participant possesses knowledge or skills beyond what the assessment instrument can measure. In this case, the data collected from the student participant is removed from the present study.

The group-average normalized learning gain for each CSA learning module was also calculated based on each student’s normalized learning gains. Statistical analysis was subsequently performed involving normality tests, descriptive analysis, correlation analysis, median tests, and Mann-Whitney U tests.

Results

Normality Tests

Normality tests were performed on the data collected from the present study, including each student’s pre-test scores, post-test scores, and normalized learning gains. The purpose was to determine if parametric or non-parametric statistical analysis should be employed. If the collected data does not have a normal distribution, non-parametric statistical analysis should be used (Kaufhold, 2013). Otherwise, parametric statistical analysis should be employed.

Tables 2 and 3 summarize the results of normality tests for CSA learning modules I and II, respectively. Two types of normality tests were performed: the Kolmogorov-Smirnova test and the Shapiro-Wilk test. The fifth and eighth columns in Tables 2 and 3 list the significance level (p-value). A p-value of less than 0.05 indicates a non-normal distribution of data. As can be seen from Tables 2 and 3, the data collected from the present study have a non-normal distribution. Therefore, non-parametric statistical analysis was employed for both CSA learning modules I and II. The results of non-parametric statistical analysis are described in the following sections, including descriptive statistical analysis, correlation analysis, median tests, and Mann-Whitney U tests.

Table 2.

Normality Test Results for Computer Simulation and Animation Learning Module I.

Variables	Student groups	Kolmogorov-Smirnov^a			Shapiro-Wilk
Variables	Student groups	Statistic	df	Sig^b	Statistic	df	Sig^b
Pre-test scores	Comparison group	0.235	64	0.000	0.861	64	0.000
Pre-test scores	Intervention group	0.195	82	0.000	0.887	82	0.000
Post-test scores	Comparison group	0.204	64	0.000	0.915	64	0.000
Post-test scores	Intervention group	0.227	82	0.000	0.856	82	0.000
Normalized learning gains	Comparison group	0.173	64	0.000	0.956	64	0.024
Normalized learning gains	Intervention group	0.160	82	0.000	0.877	82	0.000

^aLilliefors significance correction.

^bThe significance level (p-value) less than 0.05 indicates a non-normal distribution of data.

Table 3.

Normality Test Results for Computer Simulation and Animation Learning Module II.

Variables	Student groups	Kolmogorov-Smirnov^a			Shapiro-Wilk
Variables	Student groups	Statistic	df	Sig^b	Statistic	df	Sig^b
Pre-test scores	Comparison group	0.243	56	0.000	0.873	56	0.000
Pre-test scores	Intervention group	0.246	83	0.000	0.867	83	0.000
Post-test scores	Comparison group	0.303	56	0.000	0.795	56	0.000
Post-test scores	Intervention group	0.278	83	0.000	0.782	83	0.000
Normalized learning gains	Comparison group	0.135	56	0.012	0.933	56	0.004
Normalized learning gains	Intervention group	0.277	83	0.000	0.799	83	0.000

^aLilliefors significance correction.

^bThe significance level (p-value) less than 0.05 indicates a non-normal distribution of data.

Descriptive Statistical Analysis

Tables 4 and 5 show the descriptive statistical analysis results for CSA learning modules I and II, respectively. Although mean values (i.e., average values) and standard deviations are typically not included in non-parametric statistical analysis (Cohen, 1988), they are still included in Tables 4 and 5 because they are widely employed in educational research and readily understood in the research community.

Table 4.

Descriptive Statistical Analysis for Computer Simulation and Animation Learning Module I.

Variables	Student groups	Mean	Median	Standard deviation	Min	Max	Interquartile range	Skewness	Kurtosis
Pre-test scores	Comparison group	0.23	0.20	0.18	0.00	0.80	0.35	0.56	0.43
Pre-test scores	Intervention group	0.30	0.20	0.22	0.00	0.80	0.20	0.53	-0.07
Post-test scores	Comparison group	0.35	0.40	0.25	0.00	1.00	0.40	0.43	-0.53
Post-test scores	Intervention group	0.72	0.80	0.28	0.00	1.00	0.40	-0.95	0.26
Normalized learning gains	Comparison group	0.13	0.20	0.37	-1.00	1.00	0.33	-0.53	1.05
Normalized learning gains	Intervention group	0.57	0.67	0.43	-1.00	1.00	0.75	-0.98	0.84

Table 5.

Descriptive Statistical Analysis for Computer Simulation and Animation Learning Module II.

Variables	Student groups	Mean	Median	Standard deviation	Min	Max	Interquartile range	Skewness	Kurtosis
Pre-test scores	Comparison group	0.25	0.20	0.18	0.00	0.80	0.20	0.55	0.35
Pre-test scores	Intervention group	0.25	0.20	0.22	0.00	0.80	0.40	0.77	0.08
Post-test scores	Comparison group	0.44	0.40	0.29	0.00	1.00	0.35	1.00	-0.11
Post-test scores	Intervention group	0.72	0.80	0.34	0.00	1.00	0.60	-0.83	-0.78
Normalized learning gains	Comparison group	0.22	0.25	0.48	-1.00	1.00	0.48	0.07	-0.24
Normalized learning gains	Intervention group	0.62	0.80	0.46	-1.00	1.00	0.75	-1.02	0.38

From Table 4, it can be seen that for CSA learning module I, the average normalized learning gain is only 13% (0.13) for the comparison group, but as high as 57% (0.57) for the intervention group. In other words, the intervention group achieved more learning gain than the comparison group by 44%, on average. The median value of normalized learning gains is only 20% (0.20) for the comparison group but as high as 67% (0.67) for the intervention group.

From Table 5, it can be seen that for CSA learning module II, the average normalized learning gain is only 22% (0.22) for the comparison group, but as high as 62% (0.62) for the intervention group. In other words, the intervention group achieved more learning gains than the comparison group by 40% on average. The median value of normalized learning gains is only 25% (0.25) for the comparison group but as high as 80% (0.80) for the intervention group.

Correlation Analysis

Non-parametric correlation analysis was performed to calculate Spearman’s correlation coefficients between student groups (i.e., comparison and intervention groups) and pre-test scores, post-test scores, and normalized learning gains for both CSA learning modules I and II. The results are summarized in Table 6.

Table 6.

Spearmen’s Correlation Coefficients Between Student Groups and Other Variables.

Computer simulation and animation learning modules	Computation results	Pre-test scores	Post-test scores	Normalized learning gains
I	Correlation coefficients	0.172^a	0.575^b	0.501^b
	Sig. (2-tailed)	0.038	0.000	0.000
	N	146	146	146
II	Correlation coefficients	-0.014	0.371^b	0.382^b
	Sig. (2-tailed)	0.873	0.000	0.000
	N	139	139	139

^aCorrelation is statistically significant at the 0.05 level (2-tailed).

^bCorrelation is statistically significant at the 0.01 level (2-tailed).

As can be seen clearly from Table 6, for CSA learning module I, a statistically significant correlation exists between student groups and pre-test scores (p = 0.038), post-test scores (p = 0.000), and normalized learning gains (p = 0.000). A statistically significant correlation exists between student groups and post-test scores (p = 0.000) and normalized learning gains (p = 0.000) for CSA learning module II.

Median Tests and Mann-Whitney U tests

Median and Mann-Whitney U tests were performed to determine if a statistically significant difference between the intervention and comparison groups exists for CSA learning modules I and II. The results are summarized in Tables 7 and 8.

Table 7.

Median Test Results.

Computer Simulation and Animation learning modules	Variables	Median	Test statistic	Asymptotic sig^a
I	Pre-test scores	0.200	3.768	0.052
	Post-test scores	0.600	40.479	0.000
	Normalized learning gains	0.333	33.199	0.000
II	Pre-test scores	0.200	0.009	0.925
	Post-test scores	0.600	28.550	0.000
	Normalized learning gains	0.400	21.475	0.000

^aA p-value less than 0.05 indicates the statistically significant difference between the intervention and comparison groups.

Table 8.

Mann-Whitney U Test Results.

Computer Simulation and Animation learning modules	Variables	Mann-Whitney U	Standardized test statistic (Z value)	Asymptotic sig^a
I	Pre-test scores	3125.500	2.075	0.038
	Post-test scores	4353.000	6.925	0.000
	Normalized learning gains	4142.500	6.035	0.000
II	Pre-test scores	2288.500	-0.160	0.873
	Post-test scores	3305.500	4.363	0.000
	Normalized learning gains	3340.000	4.483	0.000

^aA p-value less than 0.05 indicates the statistically significant difference between the intervention and comparison groups.

The p-values listed in the last columns in Tables 7 and 8 show a statistically significant difference between the intervention and comparison groups in post-test scores (p = 0.000) and normalized learning gains (p = 0.000) for both CSA learning modules I and II. The asymptotic significance (p-value) 0.052 indicated in Table 7 means that there exists no statistically significant difference between the intervention and comparison groups in pre-test scores for CSA learning module I. However, Table 8 shows a statistically significant difference between the intervention and comparison groups in pre-test scores (p = 0.038) for CSA learning module I. Apparently, median test and Mann-Whitney U tests caused different p-values. This data discrepancy is common in statistical analysis. The significant differences at the post-test between two student groups are more pronounced during and after the intervention.

Based on the normalized learning gains shown in Table 8, effect size was calculated as:

Effect size = Z value / square root of N

where Z value is the standardized test statistic listed in Table 8, and N is the number of student participants (146 for CSA learning module I and 139 for CSA learning module II). The results show that the effect size is 0.50 for CSA learning module I and 0.38 for CSA learning module II, representing a medium effect of CSA learning modules on student learning (Cohen, 1988).

Discussions

The results of quantitative comparisons summarized in Tables 4 and 5 demonstrate that CSA learning modules I and II are effective in improving student learning of linear impulse and linear momentum as well as angular impulse and angular momentum in particle dynamics. The results summarized in Tables 6, 7, and 8 further imply that it did matter if a student was in the comparison group or the intervention group due to the statistically significant correlation between student groups, pre-test scores, post-test scores, and normalized learning gains. All these results clearly demonstrate the effectiveness of the CSA learning modules developed in the present study. As these results were generated from objective quantitative research, the researchers of the present study have no bias toward the effectiveness of the CSA learning modules.

In addition, it should be noted that the purpose of the present study was to demonstrate that the CSA learning modules developed from the present study could be used to improve student learning and more importantly, problem-solving as well. The purpose of the present study was not to compare CSA with other STEM pedagogy, such as hands-on demonstrations, in-class real-time assessments, and collaborative learning. Each STEM pedagogy has its own strengths and weaknesses. Students also have diverse preferences toward different pedagogy. No pedagogy should be abandoned simply because there is another pedagogy that can provide a better advantage in a certain aspect of teaching and learning.

The present study has two primary limitations. First, all 285 student participants in the present study were from the same institution, a public research university in the Mountain West region of the United States of America. The research findings reported in this paper were generated from these students only. Students at different types of institutions, such as research universities, teaching universities, and community colleges, have different backgrounds and experiences. Future research is needed to study how the CSA learning modules developed in the present study affect student learning at other institutions.

Second, the scope of the present study is limited in studying the extent to which our CSA learning modules improved student learning of impulse and momentum in particle dynamics. Although the research findings demonstrate that our CSA learning modules effectively enhance student learning and problem-solving, the present study does not answer why these CSA learning modules are effective. Given the diverse backgrounds and experiences of each student, qualitative or mixed-methods studies are needed in the future to find out why our CSA learning modules are effective. In addition, more complex objectives will be considered in future research to assess specific problem-solving skills of students, such as analysis, synthesis, interpretation, and creation.

Conclusions

This paper has described the four-step development of two CSA learning modules (I and II) for improving student learning and problem-solving related to impulse and momentum in particle dynamics. Both CSA learning modules integrate mathematical problem-solving procedures into computer simulation and animation. A quasi-experimental, quantitative research study was performed, involving 285 engineering undergraduates in a comparison group and an intervention group. The following paragraphs summarize the major research findings of the present study.

• Compared to the comparison group, the intervention group achieved a higher average normalized learning gain: 44% more for CSA learning module I and 40% more for CSA learning module II.

• A statistically significant correlation exists between student groups and pre-test scores, post-test scores, and normalized learning gains.

• The effect size is 0.50 for CSA learning module I and 0.38 for CSA learning module II, which represents a medium effect for CSA learning modules.

Therefore, it can be concluded that both CSA learning modules I and II developed from the present study are effective in improving student learning and problem-solving related to impulse and momentum in particle dynamics. Future research will be focusing on more quantitative, qualitative, or mixed-methods studies to find out why these CSA learning modules are effective and how they affect student learning at other institutions.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This material is based upon work supported by the National Science Foundation under grant award No. 1122654. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

ORCID iD

Ning Fang

Author Biographies

Ning Fang is Professor and Head of the Department of Engineering Education at Utah State University, U.S.A. He has taught a variety of courses at both graduate and undergraduate levels, such as engineering dynamics, metal machining, and design for manufacturing. His research in engineering education is in broad areas of engineering learning and problem solving, technology-enhanced learning, and K-12 STEM education. His research in engineering focuses on the modeling and optimization of metal machining processes. He earned his PhD, M.S., and B.S. degrees in mechanical engineering. He is a member of the American Society of Mechanical Engineers (ASME) and the American Society for Engineering Education (ASEE).

Yongqing Guo graduated from the Ph.D. in Engineering Education program in the Department of Engineering Education at Utah State University, U.S.A. She earned her M.S. degree in Civil Engineering from the University of Idaho and B.S. degree in Civil Engineering from China University of Mining and Technology. Her research in engineering education involves computer simulation and animation and students’ problem-solving.

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