Effect of using multiple representations in teaching mechanics problem-solving on engineering students’ academic performance in Rwanda

In recent years, the use of multiple representations in physics teaching and learning has become more common. This study sought to determine if engineering students’ performance in Rwanda might be improved by the use of numerous representations when solving mechanics problems. Multiple representations improve students’ comprehension and recall of mechanics ideas, supporting efficient teaching methods and critical thinking. This study employed a quasi-experimental research design with pre-and post-test control and experimental groups. A total of 100 students were enrolled in the study, divided into two groups: the experimental group consisted of 52 students who received instruction using multiple representations, and the control group consisted of 48 students who received instruction using traditional methods. In the study, students’ performance was measured before and after intervention using a mechanics test. The mechanics problem-solving pre-test findings indicated a p-value greater than 0.05 between the control and experimental groups, indicating no statistically significant differences between the two groups. A post-test revealed a p-value < 0.001 between the groups, indicating that the experimental group outperformed the control group significantly. According to the findings, engineering student’s academic performance in physics can be improved through the use of multiple representations in teaching and learning mechanics problem-solving. This study will support the development of Rwandan education policies, instructional approaches, and global pedagogy are all supported by this study.


Background to the problem
Problem-solving is a crucial skill for learning physics in prior 21st-century classrooms and in day-to-day life, as well as mastering it is a critical component of the science curriculum (Ince 2018, Wicaksono andKorom 2022).By learning physics, students become better at solving problems or developing abilities that enable them to apply their knowledge in engineering courses and in their everyday life.This helps those students to be able to implement their problem-solving skills and knowledge in the workplace after graduation as a result of their coursework (Yolenta et al 2019).Consequently, it is crucial to understand and study different ways in which physics concepts can be represented to solve problems effectively (Nurrahmawati et al 2019).In higher education students had great difficulties solving problems because of the lack of development of problem-solving skills during their previous levels of education (Yolenta et al 2019).As a solution, using multiple representations is essential because it helped them understand the concepts and solve problems in physics, particularly in mechanics.
A concept of multiple representations (mathematical, verbal, graphic, visual, etc) refers to a number of ways in which a process or concept can be expressed (Munfaridah et al 2021).Being able to develop multiple representations is a skill that involves learning how to encode appropriate information according to the domain of a given representation, identifying the relationship between representations, and producing appropriate representations according to the given problem (Nurrahmawati et al 2019).In mechanics, the problems must be solved by observing and figuring out patterns or rules.The research done by Saputra et al (2019) found that a student who is capable of representing many different kinds of information in the problem is likely to have a multiple representation ability.Basically, abstract mathematical problems must be developed on the basis of concrete application problems for students to gain a better understanding of their subjects.It is essential that students learn how to express the same idea in different ways and from different perspectives in order to formulate a problem effectively.Multiple representations are beneficial in many ways, including supporting different ideas and processes, restricting interpretation, and making the physical concept easier to understand.The use of different combination representations always helps to teach and learn by taking advantage of their different properties.Using a diagram, for instance, can exploit perceptual processes; by using a S, we can emphasise empty cells, highlight patterns, and highlight regularities in information.The combination of the representations reduces their shortcomings and limitations (Ainsworth et al 1997).Students can solve one problem using different representations.They can help them to select the best representations that could help them in learning and solving their problems.Here is an example of a mechanics problem that is expressed in different form of representations: The figure 1 above depicts a mechanics problem in five different representations (verbal, pictorial, diagram, graphical and mathematical).It is obvious that when a problem is presented in different ways, it can be better comprehended than when it is provided in a single form.
In solving mechanics problems, there are several common problems as stated by Mumthas and Abdulla (2019) such as identifying or demonstrating formulas, extracting information from diagrams, drawing schematic diagrams, and using mathematics to figure out mechanics problems.In most cases, students memorise formulas and plug numbers into formulas without even understanding how to prove or demonstrate their accuracy.Consequently, students face difficulties such as learning how to adapt their problemsolving methods to different contexts, not knowing the principle to apply or misusing it for solving problems.They have the misinterpretation of the formula, confusion between quantities used to describe the situation, inability to calculate on the basis of information provided, inability to calculate based on graph information (Nguyen and Rebello 2011).These difficulties in physics frustrate engineering students who do not consider it a career path, and they become discouraged and believe they are failing the course.These students must acquire the problem-solving approach needed to become proficient in mechanics problem-solving techniques, and practice them.Their ability to resolve challenges without getting frustrated could be enhanced by using multiple representations, especially in mechanics problems solving.Therefore, this study aimed at determining whether using multiple representations during mechanics problem-solving improves physics performance among the engineering students.

Theoretical framework
The theoretical framework of cognitive load theory serves as the foundation for this study (Sweller 1988, Cook 2006).According to the cognitive load theory (CLT), if the cognitive load (CL) is too high, learning may be impeded because student's working memory capacity is constrained.The theory suggests that learning is more effective when cognitive load is managed by designing instructional materials that match the cognitive architecture of the learners.According to cognitive load theory, using multiple representations can reduce cognitive load and enhance learning.
The figure 2 consists of Causal factors that include features of the subject (e.g.cognitive capacities), the task at hand (e.g.task difficulty), the surroundings (e.g.noise), and their interactions.Cognitive load, cognitive work, and performance are the three measured aspects of CL. 'Mental load' refers to the load imposed only by tasks and the external environment.Cognitive effort is the effort put into completing a task.Mental load, effort, and the characteristics previously mentioned all contribute to the subject's performance.The focus of CLT is the constraints of working memory and strategies for fostering learning by enforcing appropriate CL standards.The mental load is the proportion of cognitive load (CL) that is imposed by the task and the external demands, whereas mental effort is the cognitive capacity set aside for the activity.Working memory load is influenced by the material's inherent characteristics as well as how it is delivered.For the creation and long-term storage of schemata, germane CL is necessary.In accordance with CLT, intrinsic CL refers to the burden imposed by inherent characteristics of the task, whereas external CL corresponds to the effort needed to process poorly prepared instruction (Kirschner 2002).This theory states that increasing working memory capacity or reducing its cognitive load can reduce the burden placed on it.Working memory capacity can be increased by utilising more than one presentation mode.It is thought that either expanding working memory capacity or decreasing cognitive workload could alleviate the pressure on it.The use of multiple presentations is observed to enhance working memory capacity in mechanics problemsolving (Cook 2006).In some cases, however, teaching with multiple representations can strain a student's working memory.This is dependent upon the material being taught and how it is taught (Nyachwaya and Gillaspie 2016).

Research problem
The study of mechanics is crucial to engineering education because it lays the groundwork for comprehending many other disciplines, including physics and applied mathematics (Kraige and Meriam 2012).It is essential for engineering students to have a fundamental understanding of mechanics and the ability to apply them to their engineering courses.It is common for engineering students to have difficulty comprehending the complex and intricate concepts and principles of mechanics (Tiberghien et al 1998).The approach to assist those students in solving this problem is to use multiple representations, which refer to utilising different forms of representation to convey the same concept or problem, such as graphs, diagrams, equations, and verbal descriptions (Munfaridah et al 2021).The research have been found that multi-representations can be effective in enhancing students' understanding of complex concepts and improving their problemsolving abilities (Schnotz and Bannert 2003).The research studies also found that the engineering students often struggle with mechanics problemsolving due to the complex nature of the subject (Papadopoulos et al 2006).But, the better thing is that a recent study have found that the use of multiple representations in teaching mechanics can enhance students' understanding and improve their problem-solving skills (Wayan et al 2021).
As of yet, it is unknown whether this approach has any effect on the performance of engineering students at a selected public Rwandan university.Therefore, the problem addressed in this study is to investigate the effect of using multiple representations in mechanics problem-solving on engineering students' performance in Rwanda.

Research aim and research questions
This study investigated how using multiple representations in mechanics problem-solving affected engineering students' performance in physics at a selected public Rwandan university.This research sought to respond to the question below: Does the performance of engineering students taught mechanics using multiple representations differ statistically from that of students taught using traditional methods in emerging engineering education system of Rwanda?

Significance of research study
The study has significant potential to enhance engineering education by contributing to the improvement of teaching and learning approaches.Firstly, the study will provide light on the importance of employing a variety of representations, including graphs, diagrams, and mathematical equations in helping engineering students to solve problems involving mechanics.The research will aid instructors and curriculum designers in making judgments based on the best available data when creating instructional materials and programs that use a variety of representations, thereby improving students' comprehension and performance.Secondly, this research will also point out the difficulties engineering students encounter while employing different representations to solve mechanics problems.This knowledge may be used to guide the creation of successful solutions to overcome these obstacles, such as giving students who have difficulty understanding particular representations specialised training and support.Thirdly, the research will add to the corpus of information regarding Rwanda's emerging engineering education system.This information may be utilised to guide policy choices and raise the standard of engineering education across the country.Finally, the results of this study may have an impact beyond Rwanda.The findings may be transferred to various situations and help build successful teaching and learning practices in engineering education throughout the world as it continues to become more globalised.

Research methodology
This study used a quantitative research approach that involving first semester engineering students in Electronics and Telecommunication Engineering, and Electrical Power engineering undergraduate program.

Research design
A quasi-experimental design was used in this study to collect data from engineering students through pre-test and post-test phases.Through this approach, the existing situations can be better improved.These studies are called quasiexperiment study since they analyse the interconnection between a dependent and independent variable in detail, allowing the researcher to analyse causality and the interrelationships between variables to provide the most extensive analysis possible (Çepni and Çil 2009).In the current study, an assessment was conducted before and after the intervention on the participants, therefore it can be referred to as an empirical interventional study.

Sample selection
The sample size of 100 engineering students (see table 1) was selected purposefully in a public university in Rwanda based on the fact that they had just passed ordinary and senior high school level and they had a similar background in mechanics problem-solving.They also had been given approximately the same material related to the mechanics problems solving in high school.
They also did the similar combinations in secondary school.
The study adhered to ethical guidelines, and prior to their participation in the study, all participants provided informed consent.The participants' privacy and confidentiality were protected, and the data collected were used solely for research purposes.

Instruments and data collection procedures 2.3.1. Instruments.
The study used pre-and post-tests to assess the effectiveness of using different representations in solving mechanics problems.The pre-test consisted of eight problemsolving questions that assess the students' basic knowledge of mechanics.The post-test also had eight questions but was designed to examine the student's ability to solve mechanics problems based on their knowledge using multiple representations.Questions for pre-and post-tests were adapted from physics textbook (Giancoli 2005).To ensure validity of research questions, we submitted the achievement test to university teaching staff members who included science teaching methods in their bachelors and master's degree curricula to confirm its validity.Following their recommendations and suggestions, we removed some questions and added new questions, and the test was deemed most relevant.Based on the experts' ratings, the content validity index (CVI) was (0.84) which suggests that the instrument has adequate content validity.
Below there are some of the problems used in data collection: 1.A horizontal beam of mass 140 kg is supported at both ends.A quarter of the way from one end, a 320 kg piano is resting.How much vertical force is there on each support?2.3.2.Procedure.The study took place over a four-week period.The first week of class introduced the students to the idea of multiple representations and highlighted their importance in mechanics problem-solving.The students were also taught how to utilise different sorts of representations, such as diagrams, graphs, and equations, to solve mechanics problems throughout the second and third weeks.The lesson was given through lectures, in-class exercises, and homework assignments.The engineering students took the post-test in the fourth week to gauge how well the intervention had worked.For a period of four weeks following intervention, the data were gathered through tests (pre-test and post-test) on mechanics problem-solving.Prior to giving the pre-test problems to the two groups under study, the lecturer discussed and introduced the concept of mechanics problem-solving to them.During the intervention, all homework assignments were provided to both experimental and control groups with a copy of the list of problem-solving tasks.
There was a clear understanding among students that the test was not graded by the lecturer and was only used for research purposes.

Intervention.
An organised intervention consists of instructions on interpreting and creating representations (MRs) in order to solve mechanics problems and understand complex concepts.In the classroom, the instructor taught engineering students how to use MRs effectively, emphasising active learning and skill development.Through scaffolding practices, students gradually become more autonomous in using MRs in mechanics problem-solving.Thinking and problem-solving abilities are encouraged and improved by exposing those students to different exercises requiring multiple representations.As you revisit and enhance your usage over time, you can develop mastery and fluency.To ensure that differences in results may be linked to the intervention being tested, it is essential to provide both groups with similar amounts of support or training.Here, the control group received instructions, materials, or directions specific to the traditional technique of solving mechanics problems (plugging numbers into a formula).In this study, the researcher tried relatively to help both groups minimise confounding factors while attributing observed differences to the intervention that is being tested.Pre-testing to ascertain baseline ability must be part of this.

Data analysis
A descriptive analysis of the pre-and post-test data was conducted using descriptive statistics.An independent sample t-test as well as paired t-tests were used to compare the mean scores of the pre-and post-tests.We also performed a descriptive statistics analysis in order to determine whether the student's performance on the post-test was associated with their prior mechanics knowledge.All the analysis was done using SPSS statistical software.

Research results
The study utilised achievement tests, including a pre-test for engineering students before the  2 show that the data were normally distributed, p = 0.703 for pre-test and p = 0.34 for post-test.Therefore, parametric tests were conducted.

Pre-test results
Before introducing the multiple representations into the experimental group, the researchers employed descriptive statistics and an independent samples t-test to compare the outcomes of the pre-test on mechanics problem solving, as shown in table 3.This was done to determine whether the achievement of the two groups of engineering college students was comparable.
Table 3 shows that the obtained p (0.274) exceeds 0.05, which implies the test does not show statistical significance at the 0.05 level, demonstrating that there were no significant differences between the two groups, and the null hypothesis was accepted for the pre-test.With regards to the performance, there was no discernible difference between the experimental group (M = 3.584, SD = 1.9748) and the control group (M = 3.146, SD = 2.0031) before the intervention.

Post-test results
We used descriptive statistics and an independent sample t-test to determine the differences between the mean scores of students in the experimental and control groups on a post-test of accomplishment in order to verify the hypothesis.
The following tables display the findings.Table 4 shows that engineering students who solved mechanics problems using multiple representations had higher achievement test scores (M = 9.923, SD = 2.3668) compared to those who solved them using traditional methods of plugging numbers into formulas (M = 5.042, SD = 2.4317).Since the obtained p-value (<0.001) is less than 0.05, there is a significant difference between the groups at 0.05 level, indicating that the experimental group has a significant advantage over the control group.Therefore, the null hypothesis cannot be accepted.As a result of this test, it is concluded that using different representations in solving mechanics problems in Physics courses for Engineering College students positively affects how well they do in physics.
From the table 5 the results show that the mean test scores before and after the intervention differ significantly for both groups, for the control group (t-value = −4.555,p < 0.001) and for the experimental group (t-value = −7.409and p < 0.001).However, due to the intervention, the significance was quite high for the experimental group.The difference between the pre-test and post-test was significant for both groups because both groups acquired knowledge on mechanics during the intervention even though there were not using the same methodology.Therefore, Null hypothesis was rejected because there was significant differences in all groups for pre-and posttest results.

Discussions
The current study examined the effect of adopting multiple representations in teaching and learning of mechanics problem-solving on engineering students' academic achievement.The findings The results of this study can be clearly explained by taking an example of the first problem given in the instruments where one student solve it using traditional method and other solved it using multiple representations.For the student who used traditional approach, he/she followed the following steps: Step For the student who used multiple representations approach, he/she followed the following steps: Step From those approaches, it is clear that the students using a traditional method in figure 4 failed problem one while the students who used multiple representations in figure 5 performed well.This revealed clearly that traditional approach only focuses on formulaic solutions and is frequently passive and less applicable to real-world scenarios while multiple representations approach enriches learning by providing information in diverse formats, catering to a diverse range of learning styles, and developing a more thorough understanding of the problem at hand (Distrik et al 2021).The use of different representations aided in addressing student individual differences, which is another crucial discovery (Cook 2006).The introduction of numerous representations catered to the variety of learning preferences and styles among engineering students (Sankey et al 2011).Diagrams and graphs were helpful for visual learning, whereas mathematical equations and formulae were more useful for analytical thinking (Bego et al 2018).Instructors were able to engage students with various learning styles by offering a variety of representations, which enhanced academic achievement within the first-year engineering students.Furthermore, the current study showed that using different representations helped engineering students to develop problem-solving abilities and improving their performance in physics course in general.Diagrams and graphs' real, visual nature helped make abstract ideas more concrete, grabbing students' attention and encouraging active engagement.Students' academic performance and overall learning outcomes were positively impacted by their active participation in the learning process (Kohl and Finkelstein 2007).It is important to note that the beneficial effects of numerous representations on academic achievement were seen across the entire cohort, not only high achievers.This finding implies that students with different degrees of prior knowledge and cognitive ability can benefit from the inclusion of diverse representations in mechanics education.Multiple representations foster an inclusive learning environment that serves the various demands of engineering students by responding to various learning styles and preferences.This research was done in Rwanda engineering education context and have found that representations improve students' understanding and retention of mechanics concepts, thus leading to more effective teaching strategies.Using this method, students will develop the critical thinking and active learning skills they are going to need to solve complex mechanics problems in the future.Ultimately, the findings of this study can lead to an improved understanding of global pedagogy, support the development of instructional strategies, priorities, and continuous improvements in education, as well as support Rwanda's attempts to create curricula and education policies.

Limitations
Regardless of the promising results, it is critical to recognise the study's limitations.Firstly, the outcomes' generalisability was inhibited by the size of the study sample, which was somewhat small because it was limited to mechanics topics in Physics course that were taught to the engineering students in the academic year 2021/2022, and on the students in Electrical university Power Engineering and Electrical, and Electronics Engineering options at a selected public in Rwanda.For improvement of the validity and reliability of the findings, future study should take into account bigger and more varied sample sizes.Second, the study did not examine other variables that might have an impact on students' learning experiences, such as self-efficacy or motivation, and instead concentrated only on students' academic achievement.Future studies could better understand the effects of different representations on student learning by taking these factors into account.

Conclusion and recommendations
In conclusion, engineering students' performance has been found to be favourably impacted by the usage of multiple representations in mechanics problem-solving.According to the study, employing different representations in solving mechanics problems enables engineering students to grasp fundamental ideas more deeply and use them to tackle challenging problems.The results of this study point to the need for educators to think about adding multiple representations into their lesson plans, such as graphs, diagrams, and mathematical equations in order to improve their students' problem-solving abilities and overall performance in engineering courses because the findings imply that the employment of numerous representations considerably enhances engineering students' performance on tasks involving mechanics problem-solving.In order to widen the scope of this study, future research may also examine the efficiency of employing numerous representations in other Science, Technology, Engineering, and Mathematics (STEM) domains or at other academic levels.In order to enhance STEM education, this study emphasises the significance of implementing multiple representation techniques in mechanics problem-solving.The researcher recommended that engineering instructors could receive training on the effective use of multiple representations in teaching and learning of mechanics concepts and principles in problemsolving.The instructors should also be encouraged to develop and incorporate various types of multiple representations, such as diagrams, graphs, and mathematical equations, in their teaching and learning materials.Additionally, it is also recommended that long-term implications of employing different representations while teaching mechanics be investigated in future studies.The effects of employing numerous representations on other facets of engineering education, such as students' conceptual comprehension and problem-solving abilities in other engineering disciplines, can also be investigated further.Overall, the results of this study show that using multiple representations is an effective teaching method that may improve students' performance on tasks involving mechanical problem-solving, and its use in engineering education should be promoted.

Implications
In this work, we look at how multiple representations (MRs) in mechanics problem-solving affect the performance of engineering students in Rwanda, and we provide empirical evidence to back up our findings.The research proposes new techniques to incorporate MRs into mechanics instruction for engineering students, focusing on specific academic targets such as increased problem-solving skills and conceptual understanding.The study sheds light on the relative usefulness of MRs and other standard instructional approaches in mechanics education.The ideas for developing physics for engineers educational cur-riculum, instructor training, and reform initiatives have the potential to have an impact on Rwandan education policy and practice.In general, this research contributes to a better understanding of the role of MRs in engineering education in Rwanda.

Figure 1 .
Figure 1.Representation of a problem in different forms (Ainsworth et al 1997).

Figure 3 .
Figure 3.The graph of force vs extension.
1: Deducing given data in the verbal problem: Mass of beam (m b ), Mass of Piano (m p ), x (distance of piano from one end) = L/4 and g = 10 m s −2 .Step 2: Recall conditions of equilibrium ∑ F = 0 and ∑ τ = 0. Step 3: Plug numbers into formula and do calculations to find unknown.
1: Deduce the given data from the verbal represented problem.Step 2: Drawing free-body diagram showing all forces and their direction.Step 3: Statement of the conditions of equilibrium ∑ F = 0 and ∑ τ = 0. Step 4: Formulate the formula from those conditions based on the free-body diagram.Step 5: Plunging numbers into formula and perform calculations to find unknown forces.

Figure 4 .
Figure 4.A student solution to problem one solved using the traditional method.

Figure 5 .
Figure 5.A student solution to problem one solved using multiple representations.

Table 1 .
Distribution of participants by gender.

Table 2 .
Results of the Shapiro-Wilk of normality test.
. Their application, however, is not limited to small samples, they are also applicable to larger samples.In this test described above, the null hypothesis states that the data are collected from populations with normal distributions.As a result, when p > 0.05, the null hypothesis is accepted, and the data are said to be normally distributed(Mishra et al 2019).The results in table

Table 3 .
The outcomes of the pre-test independent t-test comparing the experimental and control groups.

Table 4 .
Results of the post-test independent t-test comparing the experimental and control groups.

Table 5 .
Results of a paired-sample t-test.
and Anderson-Darling tests J. Stat.Model.Anal. 2 21-33 Sankey M D, Birch D and Gardiner M W 2011 The impact of multiple representations of content using multimedia on learning outcomes across learning styles and modal preferences Int.J. Educ.Dev.Inf.Commun.Technol.7 18-35 Saputra A T, Jumadi J, Paramitha D W and Sarah S 2019 Problem-solving approach in multiple representations of qualitative and quantitative problems in kinematics motion Jurnal Ilmiah Pendidikan Fisika Al-Biruni 8 89-98 Schnotz W and Bannert M 2003 Construction and interference in learning from multiple representation Learn.Instr.13 141-56 Sweller J 1988 Cognitive load during problem solving: effects on learning Cogn.Sci. 12 257-85 Tiberghien A, Jossem E L and Barojas J 1998 Connecting Research in Physics Education with Teacher Education (The International Commission on Physics Education) Wayan Distrik I, Imam Supardi Z A and Jatmiko B 2021 The effects of multiple representations-based learning in improving concept understanding and problem-solving ability J. Phys.: Conf.Ser 1796 012044 Wicaksono A G C and Korom E 2022 Review of problem-solving measurement: an assessment developed in the Indonesian context Particip.Educ.Res. 9 116-36 Wong D, Poo S P, Hock N E and Kang W L 2011 Learning with multiple representations: an example of a revision lesson in mechanics Phys.Educ.46 178-86 Yolenta D, Jatmiko B and Prastowo T 2019 The effectiveness of the learning devices using investigation-based multiple representation to improve students' problem-solving ability on reflection and refraction materials Mathematics, Informatics, Science, and Education Int.Conf.(MISEIC 2019) vol 95 pp 156-60