How Multiple Representations Using Cyber–Physical System to Teach Rectilinear Motion Improves Learning and Creativity

Abstract

Learning physics can be seen by many as a problem, as the standard method of learning tends to focus on remembering and using concepts that fail to construct meaning. To overcome this problem in teaching rectilinear motion, we implemented multiple representations using a cyber–physical system that enables interaction between a physical model and the real world. We did so by using a microcomputer system housed inside a ball, including motion and force sensors. This system communicated with the teacher’s laptop in order to display the corresponding data via a projector. The study was conducted with 49 tenth-grade students across five sessions on rectilinear motion. Using a pre- and post-test, we observed that the experimental group performed significantly better than the control group, both in terms of learning as well as in the development of creativity (fluency and flexibility). With guidance from the teacher, the multiple representations allowed the students to improve their learning and creativity by connecting various forms of representation. In other words, the students were able to connect both abstract and concrete views through a real-world, physical experience. Our study reveals the potential of cyber–physical systems within the teaching–learning process for physics, specifically rectilinear motion, and how such a system supports multiple representations.

1. Introduction

Learning physics can be seen by many as a problem, as the standard method of learning tends to focus on remembering and using concepts that fail to construct meaning [1]. There is a need for learning experiences that facilitate the students’ transfer of concepts across multiple representations [2]. Multiple representations refer to an instructional approach based on cognitive engagement. Here, students make connections between different representations, addressing the gap between mathematical and conceptual reasoning [3]. It is supported by the constructivist learning theory, where learners construct knowledge through active engagement with the material, creating their own understanding [4], and the cognitive load theory, which emphasizes the importance of managing the amount of information processed at one time to maximize learning [5]. For example, a quantitative analysis facilitates problem solving, while a qualitative examination facilitates task understanding [6]. In this way, different cognitive representations can provide complementary information, where the elements of one cognitive representation can activate the employment of another. With this, learners can acquire an understanding of the phenomena under study that would not be possible from a single viewpoint [7]. While learning from multiple representations can be easy for experts, it can be more complex for students, given the complexity of connecting elements across representations [2]. Multiple representations should help students connect their own practical and symbolic understanding of a concept [8].

In physics, multiple representations can be achieved using the data provided by a cyber–physical system [9]. Multiple representations have great potential in students’ learning of physics concepts. Students learn more easily when problems include multiple representations, which can improve the outcomes of students’ learning processes [10]. There are multiple representations in physics, for example, analogies, diagrams, graphs, formulas, texts, and simulation, among others [11]. A cyber–physical system enables the simultaneous representation of the aforementioned aspects by providing corresponding data [9]. In a cyber–physical system, physical and computational components interact to manage complex, dynamic interactions between networked systems and physical systems [12], leveraging technologies such as the Internet of Things and big data [13]. This involves a series of problems, including the abstraction of real-time data, system robustness, component service quality, and knowledge engineering [14]. Cyber–physical systems have mostly been developed for industrial purposes, such as in medical devices [15] and manufacturing [16]. They have also been used as an active training tool for workers in a factory, where real-time feedback on how workers assemble pieces can lead to a highly interactive and active experience [17]. Similarly, they have also been used as virtual reality tools to improve the communication and interactivity between manufacturing and assembly teams in factories [18]. However, cyber–physical systems have not been widely used as a teaching tool, much less for teaching physics. Therefore, our first research question asks, “How can a cyber–physical system be used to teach physics through multiple representations?”.

Creativity has been shown to be an important skill for interpreting multiple representations [19]. When students use multiple representations, they not only acquire a better understanding of the underlying meaning but also see their creative thinking encouraged [20]. By learning to use different modes of representation, students enhance their ability to transition among these modes, which is essential for solving complex physics problems [21]. Multiple representations also allow a problem to be visualized from different perspectives while supporting creativity and self-discovery [22]. There are a number of definitions when it comes to understanding creativity, which vary based on the context. As such, how we understand creativity within business is not the same as how we understand it in education or psychology. Nevertheless, key elements of creativity include uniqueness/novelty, divergent thinking, and usefulness/appropriateness [23]. A creative experience involves engaging with novel person–world encounters grounded in meaningful actions and interactions by approaching the familiar in an unfamiliar way [24]. Since, during this process, creative people may violate certain social norms [25], the teacher’s support is key [26]. In this sense, they must look to strike a balance between a creative and a guided environment based on the situation [27]. This leads us to our second research question: “What effects can multiple representations have on creativity and learning when teaching physics using a cyber–physical system?”.

2. Materials and Methods

2.1. Domain

To answer our first research question, which asks how a cyber–physical system can be used to teach physics through multiple representations, we must first settle on a learning domain in which to apply the cyber–physical system. The idea is to create activities where students can experience concepts from physics by interacting with elements from their daily lives. Given the relative ease with which students can interact with objects and study their behavior, we decided on rectilinear motion as the domain for this study.

In the 10th grade curriculum in Chile, rectilinear motion is the study of movement itself and focuses on explaining the concepts of position (1), velocity (2), and acceleration (3), as well as how they influence one another [28]. While the concepts are inter-connected, they can be approached using different types of activities. Lesson planning can therefore be broken down into 3 sets of independent modules, with one module for each concept. By doing so, there is flexibility to add extra sessions between modules (e.g., to reinforce the use of mathematical tools) and therefore align better with the pedagogical needs of the students.

The learning objectives for this topic [28] emphasize the importance of practical experience and include the following: (A) understand the difference between absolute and relative positioning based on different reference frames; (B) differentiate between displacement and trajectory and understand how they are calculated; (C) understand how acceleration influences motion; (D) discern rectilinear motion from other types of motion, based on graphical data. These objectives therefore create a pedagogical need for teachers to effectively provide their students with a practical experience.

2.2. Sample

This study was conducted with tenth grade students at a high school in Chile, characterized by an average performance on national standardized tests [29] and high levels of vulnerability, with 92% of students living in vulnerable conditions [30]. A total of 49 students participated in the study (20 boys and 29 girls). The participants were split into two groups: a control group with 23 students (11 boys and 12 girls) and an experimental group with 26 students (9 boys and 17 girls).

The design of this study was quasi-experimental, as both groups were formed prior to the intervention. However, the decision as to which group would be the experimental group and which would be the control was made at random. The age of the participants ranged between 15 and 16, with the students from both groups showing low levels of motivation for the physics subject. This could be seen from their attitude in the classroom, where they would stand up without permission from the teacher, talk among themselves, and move around during class.

2.3. Experimental Design

The subject teacher planned 5 sessions to cover the unit on rectilinear motion. The students had 3 lessons of physics each week, with each lesson lasting 90 min. Both the control group and the experimental group were in similar conditions. For both groups, the same school physics teacher led the sessions and was accompanied by at least one member of the research team for all of the activities.

In both groups, the classes started with a brief review of the concepts studied in the previous class and an introduction to the new topics. The topic was then covered using a series of videos, where the concepts were shown in at least three different contexts taken from the students’ everyday lives. Following this, the teacher then led the students through a series of exercises before assessing the students’ knowledge at the end of the class with a brief quiz.

In the case of the experimental group, once they watched the videos, the students experienced the specific concept through a cyber–physical system. In this case, the students spent less time on the numerical exercises than the control group (Figure 1). A summary of the content from each class, as well as the learning objectives and planned activities, can be found in Appendix A,

Table A1. Lesson topics, objectives, and activities.

Lesson Topics	Learning Objectives	Activities
Lesson 1: Reference frames—trajectory and displacement	(1) Using simple experiments, show why it is important to use reference frames and coordinates when describing the motion of an object. (2) Explain kinematic concepts, such as position, displacement, and distance travelled.	(1) Analyze how the ball changes position within the classroom depending on the reference frame that is used. (2) Observe the displacement and trajectory of the ball in the classroom and identify the difference.
Lesson 2: Speed and velocity	(1) Explain kinematic concepts, such as time elapsed, average, instantaneous velocity, and speed.	(1) Determine the difference between speed and velocity based on the movement of the ball in the classroom.
Lesson 3: Addition of velocities	(1) Use Galilean velocity addition formulas in simple, everyday situations.	(1) Analyze what happens when there is more than one velocity involved in the motion of the ball. (2) Identify the differences when velocities are in the same direction or opposite directions.
Lesson 4: Uniform rectilinear motion	(1) Identify the kinematic characteristics of rectilinear motion in natural phenomena and everyday situations. (2) Draw conclusions about kinematic concepts based on experiments on objects moving with rectilinear motion and constant acceleration (null).	(1) Identify when the ball has uniform rectilinear motion and the conditions that must be met in order for this to occur.
Lesson 5: Uniformly accelerated rectilinear motion	(1) Identify the kinematic characteristics of rectilinear motion in natural phenomena and everyday situations. (2) Explain the concept of gravitational acceleration and consider its use with objects in freefall and in a vertical launch. (3) Draw conclusions about kinematic concepts based on experiments on objects moving with rectilinear motion and constant acceleration (non-null).	(1) Identify when the ball has uniformly accelerated rectilinear motion and the conditions that must be met in order for this to occur. (2) Observe how acceleration remains constant during freefall and in a vertical launch.

. Supplementary Material File S1 includes details on each of the 5 activities.

On the other hand, the control group focused on solving numerical exercises based on physics problems involving the concepts covered by the videos. The mathematical difficulty of these exercises was relatively low. The aim of this was to ensure that the students could focus on analyzing the situations and applying the necessary physics concepts, instead of focusing on the underlying mathematics.

For ethical reasons, both groups were exposed to multiple representations of the phenomena through the videos. However, only the experimental group had access to the cyber–physical system. This study received approval from the university’s ethics board.

2.4. Cyber–Physical Systems for Teaching Rectilinear Motion

The hypothesis behind this study is that a cyber–physical system allows students to relate the physical view of the rectilinear motion phenomenon to the abstract view provided by the underlying physical models. The focus is, therefore, on how to design a system that enhances the pedagogical role of the teacher and helps the students play a leading role in the development of certain skills [31].

Microcomputer-based laboratories (MBLs) use electronic tools such as motion and force sensors to help students learn about rectilinear motion, as well as using data logs to allow them to study experimental data [32]. These mechanisms are generally visible to the students and can be interacted with [33,34], therefore allowing for a practical experience. Although the measurement tools can help the students play a leading role in the activity, they can also become the main focus of attention, distracting from the concepts that are being taught [35].

The cyber–physical systems implemented by Tao et al. [17] and Cecil et al. [18], both for manufacturing, managed to motivate the users to focus on the task at hand rather than on the tools themselves. By doing so, their systems became an enabler for the activity. To achieve this, both systems were designed so that users could interact with them as they would normally do. The design of the systems also focused on using objects from the users’ environment so that the entry barriers were lowered, and the users could relate the tasks to their daily lives.

In Chile, football is the most popular sport among young people [36]. Its influence also extends beyond sport [37] and dates many years back [38]. This makes football an ever-present element in Chilean society and school life. A ball is therefore an ideal sporting object from the students’ daily lives that can be used to design activities that focus on concepts such as trajectories and rectilinear motion. As it can be easily handled, the ball allows the students to take control of the activity and plays a leading role in their learning when they are holding it. Using a ball also lets the students compare the measurements from the system with their own perceptions.

The aim was to create a “cyber ball” that looked like a real one on the outside, so as not to come across as being a laboratory tool. It contained a microcomputer core with sensors that could process information on its rectilinear motion (see photos of Appendix B). This information could then be displayed on the teacher’s laptop in order to provide a symbolic visualization of the ball’s behavior (Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7).

A foam ball with a diameter of 15 cm was used for the external structure. This type of ball was used, as it can easily be found in a volleyball class. The students could therefore easily recognize it as an element taken from their daily lives. Furthermore, this type of ball can also resist impact and therefore protect internal electronics, as well as be easy to cut. An incision was made in the surface of the ball, with the cut-out section kept as a lid. The foam core was then removed in order to make space for the electronics (Appendix B).

2.5. Teacher Software

The software used by the teacher consisted of a visual interface with a different view for each type of activity. The program received real-time data from the hardware in the ball and updated the graphic elements on the interface. These graphics were then displayed to the students using a projector. The software was made using Processing 3.X, with UDP communication with the cyber–physical ball provided through the laptop’s virtual ports.

To support the teacher’s needs, a user-centered design was implemented based on user stories [39] for defining the requirements of each activity. First, the essential elements were designed based on what the teacher would have to do or show in each lesson. Then, the layouts were designed based on interfaces from sports analytics in professional sports [40] and real-time data dashboards [41]. These designs aim to incorporate recreations of elements present in a real-world activity, such as diagrams of a classroom or drawings of the objects with measurement values next to them. Following this, the design was then adapted based on the teacher’s feedback and practical testing of the system.

The graphic user interface (GUI) was divided into 3 main views: Spatial, Ramp, and Data. These corresponded to the sets of activities involving iBeacon positioning (Supplementary Material File S1 Lesson N°1 and N°2), addition of velocities using a conveyor ramp (Supplementary Material File S1 Lesson N°3 and Lesson N°4), and acceleration analysis (Supplementary Material File S1 Lesson N°5), respectively. Each view had the following properties:

2.5.1. Spatial View

The Spatial View corresponded to the sets of activities involving iBeacon positioning (Figure 2, Figure 3 and Figure 4). Its aim was to allow students to see the location of the ball in the classroom at all times (Activities of Supplementary Material File S1 Lesson N°1 and Lesson N°2). It allowed the teacher to perform the following tasks:

• Show a vertical representation of the classroom space;
• Show the ball’s position inside the classroom in real time;
• Show an XY axis representing the current reference frame;
• Display lines to represent the projection of the ball’s current position on the actual reference frame;
• Set the origin for each of the axes from the XY reference frame;
• Freeze the screen so that no new positions would be updated;
• Plot the trajectory of the ball around the classroom;
• Erase the previous positions from the trajectory;
• Plot the displacement made by the ball and toggle its visibility when necessary;
• Display numerical values of the total trajectory and total displacement after the interface had been paused.

This view consisted of a map of the classroom from above, in which the teacher’s desk worked as a reference point (Figure 2). By using this view, students could identify where they would be on the map and associate physical positions in the classroom with the representation provided by the software.

In Figure 2, a movable X–Y axis was drawn to represent the presence of an arbitrary reference frame that could be placed anywhere inside the classroom. Furthermore, a drawing of the ball was always present so that students could reflect on how different reference frames changed the relative coordinates of the ball, depending on the origin of the axes. Previous positions of the ball could be stored in order to plot its path around the classroom and allow students to compare trajectory vs. displacement (Figure 3). Additionally, numerical values for distances could be shown or hidden depending on the activity (Figure 4).

2.5.2. Ramp View

The aim of the Ramp View was to show the addition of velocities (Figure 5). For this, graphs were displayed with the measurements that were taken when using the ball with a conveyor ramp (Figure 8) (Activities of Supplementary Material File S1 Lesson N°3 and Lesson N°4). The Ramp View allowed for the following actions:

• Plot the data for velocity vs. time for each experiment;
• Plot the data for distance vs. time for each experiment;
• Plot the three experiments on the same graph so as to easily compare them;
• Show an animation of each plot being drawn, with the time taken to draw the line proportional to the time the action took in real life;
• Simultaneously show the animations for all three experiments;
• Change which plots are being shown;
• Reset the saved data and draw the plots from scratch;
• Show referential values on the Y axis of the graph.

The Ramp View showed the velocity–time plot and the distance–time plot for the scenarios recreated using the conveyor ramp (Figure 5). The plot lines for each experiment were given a label (A and B) in order to differentiate them more easily and analyze their characteristics.

2.5.3. Data View

The aim of the Data View was to facilitate acceleration analysis of the data obtained by using the conveyor ramp (Figure 8). Graphs showed real-time data for the accelerometer readings from the ball (Figure 6 and Figure 7). This was used for the final set of activities (Activities of Supplementary Material File S1 Lesson N°5) and allowed for the following actions:

• Show plots of the accelerations measured by the ball;
• Show a plot of the magnitude of the ball’s acceleration vs. time;
• Select between viewing the plot of the magnitude or the detail for each direction (X,Y,Z);
• Pause and resume the program to control when it receives new data;
• Show a timeline to use as a reference for the graphs;
• Display average values for each interval when needed.

The interface had two different modes: one where the screen showed a graph of the magnitude of the ball’s acceleration over time (Figure 6) and another where it was divided into 3 graphs (Figure 7), one for each direction (XYZ).

2.6. Hardware/Software Architecture

The internal structure of the ball (Appendix B, Figure A1) consisted of a 3D-printed block of PLA with slots for each of the system’s electronic components. The block was designed to hold these components and protect them from collisions while the ball was being thrown or hit during the activities.

Most of the activities used in the lesson plans involved actions that lasted a couple of seconds, such as throwing the ball from one student to another. Variables such as velocity and acceleration can change significantly during this short period of time. To obtain enough data points for a reliable, real-time graph of these variables, a sampling rate of over 10 Hz was needed. The core of the cyber–physical system was therefore built around Adafruit’s Feather Huzzah development board, which is based on an ESP8266 microprocessor. It has an 80 MHz core and integrated Wi-Fi, offering enough processing power to meet the requirements. Live experiments showed that communication times were the bottleneck for the sampling rates, with delays in the ranges of 10–50 ms. To reduce this impact, a low latency communication protocol was used, the User Datagram Protocol (UDP). This protocol achieved a stable data rate close to 10 ms. With this, actions such as a 2 s throw of the ball could gather close to 200 data points. This was enough to provide a reasonably clear graph.

The Spatial View activities required position tracking across the classroom so as to analyze reference frames and the differences between trajectory and displacement. In order to be used in different school environments, the system had to work regardless of factors such as the availability of power outlets or a lack of suitable camera angles for image processing. For this reason, iBeacon technology was used to provide information on spatial positioning. iBeacons provide information on their proximity to a device using received signal strength indicators (RSSIs). They were therefore used to provide checkpoints inside the classroom so that the students could pass through these designated points and create different trajectories for their analysis.

The Ramp View activities involved calculating speed and velocity, as well as adding velocities. Velocity and speed values were analyzed by measuring the times and distances traveled using the checkpoints from the first set of activities. To provide a practical experience of adding velocities, a 2 m long conveyor ramp (Figure 8) with a constant spinning ratio was built so that the ball could undergo 3 different scenarios: free fall, constant speed (going up the ramp), and both effects at the same time.

The Data View activities required analysis of real-time acceleration, how it influences changes in the trajectory, and its direct effects on rectilinear motion. A LSM9DS0 accelerometer was therefore used to provide a 3-DOF measurement of acceleration from within the ball. The sensor has a ±16 g measurement range for acceleration values, covering all of the types of movement planned for the class. Although heavy impacts could still saturate the sensor, for pedagogical purposes, they could be shown as a peak in the graphs with no repercussions.

Finally, so as not to need a power outlet during the class, a 3700 mAh Li-ion battery was used to power the system. With the 3.3 V level logic of the board, the system could work for 8 h with no need for recharging and, if necessary, could easily be charged using the board’s integrated Li-ion battery charger.

The diagram of the components of the cyber–physical ball is shown in Figure 9, with a total cost per ball of USD 75 (detail of costs in Appendix C).

The software consists of an interface that processes and saves data from the Wi-Fi receiver to then be used in the graphic user interface (GUI) (Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7). The behavior of the GUI is controlled by the interface based on user input and the decoded message from the cyber–physical ball.

Wi-Fi Receiver: The ball sends its data as a character sequence with a specific format that is then processed according to the diagram in Figure 10.

Core Software (Figure 11): The data processed by the Wi-Fi receiver are used based on the teacher’s input commands from the core software’s interface to determine how each view from the GUI needs to be updated. Global variables are stored with data on measurements of rectilinear motion variables and the system’s current state. The ball’s behavior in the GUI is calculated and drawn by a ball handler module, which receives input from the software’s interface in order to proceed.

The interface is in charge of controlling the main flow of the program and performs the following tasks:

• STORE system’s images used in the different views of the GUI;
• ADD graphic elements to each view of the GUI;
• SET the parameters at the start of the system and when a soft restart is issued;
• DRAW the plot data on the corresponding graphs from the Data and Ramp Views;
• HANDLE mouse triggers when the teacher interacts with the GUI;
• CONTROL the current state of the system and which view is active;
• ENABLE the operation of the ball handler and the display of the active view.

The global variables are defined by the following parameters:

• Plot data generated from the outputs from the Wi-Fi receiver;
• Static parameters for the classroom dimensions, size of the ball, and sampling frequency;
• Parameters for the GUI design dimensions;
• Auxiliary variables for the program control flow.

The ball is a graphic element object that is updated with the current coordinates of the ball and changes its visual properties according to the situation. It also has the ability to draw its own projection on the current reference frame (Figure 2, Figure 3 and Figure 4).

The ball handler updates and draws the ball’s current trajectory inside the classroom. It is called by the interface to perform its tasks and has the following capabilities:

• STORE an array of ball objects with the current and previous coordinates of the ball’s position inside the classroom since the last reset;
• UPDATE the visibility of each ball within the array based on the state of the current program;
• DRAW a line with the trajectory travelled by the ball based on the array of coordinates saved previously;
• DRAW a line with the displacement based on the ball’s initial position after reset and its current position;
• DISPLAY numerical data on the total distance traveled and displacement, in meters.

The graphic user interface (GUI) comprises the 3 main views: Spatial, Ramp and Data. The defined objects represent all of the dynamic elements present in the GUI, such as buttons and graphs indictors. These have the following abilities:

• UPDATE its visual properties depending on the behavior of each subclass;
• DETECT whether the mouse is currently above it;
• TRIGGER a mouse-pressed event for the core software’s interface, if clicked;
• DISPLAY or HIDE itself on the GUI if required by the core software’s interface.

For a detailed description, please see Supplementary Material File S2.

2.7. Measurement Instruments

2.7.1. Physics Grades

The students’ pre- and post-intervention physics grades were used to determine whether the intervention had an effect on academic performance. The pre-intervention grades were the students’ grades on the unit before rectilinear motion (i.e., the unit that studies the universe). The grades could range between 1 (the lowest possible grade in Chile) and 7 (the highest possible grade). The post-intervention grades were taken from the students’ scores on the in-class quizzes. This information was gathered for all students at the end of each of the first four classes. Each quiz comprised 5 true or false questions, the aim of which was to measure the students’ knowledge of the topics covered during class.

2.7.2. Creativity Test

The students’ scores on a creativity test were used to determine whether the intervention had an effect on student creativity. This test was taken by the students on two occasions: before and after the intervention. The creativity test was based on the Guilford model [42], which suggests that creativity is directly related to divergent thinking, i.e., the ability to generate ideas. This can be assessed using the Alternative Uses Test [43], where students must list as many uses they can think of for certain household items. The item used for the pre-intervention test was a towel, whereas for the post-intervention test, it was a bottle. The students were given a sheet with the instructions, which were also read out loud. The test was collected after three minutes.

Divergent thinking is measured based on four dimensions [44], and the score is calculated as follows:

• Fluency: the ability to generate many ideas. The student is awarded 1 point for every idea they produce;
• Flexibility: the ability to move between domains. The student is awarded 1 point for each (different) category or domain they produce;
• Originality: the ability to produce novel and unusual ideas. The student is awarded 2 points for every idea that was generated by less than 2% of the class and 1 point for every idea generated by less than 5% of the class.

To ensure impartiality, three reviewers graded each of the tests and had to agree before a score could be assigned. The reliability of the two creativity tests (i.e., pre- and post-intervention) was calculated using Cronbach’s alpha. Cronbach’s alpha for the pre-intervention test was 0.9, which suggests a good level of reliability. For the post-intervention test, Cronbach’s alpha was 0.63. Although this is lower than the level required, given the size of sample (n = 49), it is still acceptable [45].

2.8. Quantitative Analysis

To answer our second research question, which asks what effects multiple representations can have on creativity and learning when teaching physics using a cyber–physical system, a quantitative analysis was performed. The quantitative analysis was carried out following the recommendations made by [46]. The baseline academic performance was determined using an ANOVA test of the grades from the unit prior to the intervention (

Table 1. Mean and standard deviation of pre-intervention grades.

Pre-Intervention Grades
Control Group (n = 23)
M	5.34
SD	1.23
Experimental Group (n = 27)
M	5.23
SD	1.25

). Similarly, baseline creativity scores were measured for both the control and experimental group using the creativity test, which was applied during the first week of the intervention before the first activity was completed (

Table 2. Mean and standard deviation of fluency, flexibility, and originality.

	Fluency Pre	Fluency Post	Flex. Pre	Flex. Post	Original. Pre	Original. Post
Control Group (n = 12)
M	4.92	4.33	4.33	3.83	0.17	1.33
SD	2.75	2.42	2.39	1.64	0.58	1.30
	Experimental Group (n = 16)
M	5.00	5.63	4.19	4.31	0.80	0.67
SD	2.22	3.73	1.52	2.09	1.47	0.90

). An ANOVA test was used to determine whether there were any significant differences between the groups for the three dimensions of creativity: fluency, flexibility, and originality. Likewise, the assumptions of univariate normality and homogeneity of variance were tested for academic performance and the three dimensions of creativity.

To study the effects of the intervention on academic performance, an ANOVA test was used to determine whether there were any significant differences between the experimental group and the control group in terms of the scores they achieved throughout the intervention. The variable used for this analysis was the mean score from the four quizzes (

Table 3. Mean and standard deviation of post-intervention grades.

Exit Tickets (Post)
Control Group (n = 23)
M	5.02
SD	0.85
Experimental Group (n = 25)
M	5.56
SD	0.60

). The assumptions of univariate normality and homogeneity of variance were also tested.

To study the effects of the intervention on student creativity, an ANCOVA model was used to determine whether there were any significant differences between the experimental group and the control group for the three dimensions of creativity: fluency, flexibility, and originality (Table 2). For the ANCOVA model, the scores on the pre-intervention creativity test were used as the covariate in order to control for the students’ pre-existing, baseline creativity levels. Furthermore, a series of assumptions were also tested for the three dimensions, prior to the analysis. This included homogeneity of variance, normal distribution of errors, homogeneity of regression, linearity between the covariate and dependent variable, and independence of the independent variable from the covariate.

2.9. Quantitative Analysis

To interpret our quantitative results, a mixed method approach was used [47]. Six students from the experimental group (1 boy and 5 girls) took part in the qualitative analysis. All six students were chosen at random.

Content analysis [48] was used to understand the students’ perception of the classroom activities. The information for this analysis was obtained by conducting a focus group. The session lasted for approximately 15 min and was conducted during class time. A member of the research team interviewed the students outside of the classroom, away from their teacher and classmates. The session was recorded and transcribed word for word.

The following questions were used to guide the conversation:

(1)

In terms of motivation: Were you happy to go to class, knowing that you were going to watch videos? Or play with the ball? During class, were you keen to comment on the videos/activities with the ball?

(2)

In terms of the content: In what way were the videos useful to you? And the activities with the ball? Did the way in which the teacher linked the content with the videos make sense to you? And what about the activities with the ball? If it were up to you, would you add more videos, more ball activities, or more examples on the board?

(3)

In terms of the context used to frame the videos and activities: Can you remember any of the videos or activities you did with the ball in class? Which ones? What was the topic, and what could you take away from the videos/activities with the ball? Did the content of the videos or ball activities make sense to you?

(4)

In terms of knowledge transfer: Was the content you studied in class in any way use-ful? What for?

(5)

Finally, in terms of the activities with the ball in particular: Would you have liked to have done more activities with the ball? What would you have done differently?

The transcript was read line by line, and the students’ comments were grouped into pre-defined categories, based on the initial aim of the focus group. Having read the transcript, new categories emerged that complemented the initial findings from the first reading. The results can be found in Section 3.1.

3. Results

3.1. Quantitative Results

An ANOVA test was used to analyze baseline academic performance for the experimental group and the control group. The results of the Shapiro–Wilk test (W = 0.94; p < 0.05) suggested that the residuals were not normally distributed. The more robust Levene’s test was therefore used, with the results (p = 0.93) suggesting that the variances between the groups were homogeneous. In this case, the assumption of homogeneity of variance was therefore met. The ANOVA test also suggested that there were no significant differences between the students from the two groups (F(1,48) = 0.074; p = 0.78, Table 1) in terms of their physics grades. This implies that both groups started the intervention with the same level of academic performance.

In terms of their baseline scores for creativity, there were no statistically significant differences between the two groups when it came to fluency (F(1,43) = 0.002; p = 0.96), flexibility (F(1,43) = 0.47; p = 0.49), and originality (F(1,43) = 1.05; p = 0.31). This suggests that the two groups were comparable for the three dimensions of creativity that were evaluated. Furthermore, the assumptions of normality and homogeneity of variance were met for each of the three dimensions. In the case of fluency, this was demonstrated by the results of the Shapiro–Wilk test (W = 0.94; p = 0.08) and Bartlett’s test (K = 0.33; gl = 1; p = 0.56). For flexibility, it was also demonstrated by the results of the Shapiro–Wilk test (W = 0.97; p = 0.37) and Bartlett’s test (K = 0.15; gl = 1; p = 0.69). Finally, in the case of originality, it was shown by the results of the Shapiro–Wilk test (W = 0.94; p < 0.001) and Levene’s test (p = 0.53).

When analyzing the data on academic performance following the intervention, the ANOVA test revealed significant differences between the experimental group and the control group (F(1,46) = 3.76; p = 0.05), in favor of the experimental group (Table 3). This suggests that students in the experimental group achieved significantly better grades than the students in the control group. Furthermore, the assumptions of normality (Shapiro–Wilk test W = 0.94; p = 0.65) and homogeneity of variance (Bartlett’s test K = 2.46; gl = 1; p = 0.11) were both met.

When analyzing the data on creativity following the intervention (Table 2), the ANCOVA model revealed significant differences between the two groups in terms of fluency (F(2,25) = 14.46; p < 0.001), in favor of the experimental group. There were also significant differences (F(2,25) = 8.11; p < 0.001) in favor of the experimental group when it came to flexibility. However, there were no significant differences between the two groups in terms of originality (F(2,25) = 0.30; p = 0.58). This suggests that the experimental group performed significantly better in terms of fluency and flexibility but not in terms of originality.

The Shapiro–Wilk test confirmed that the residuals were normally distributed (W = 0.93; p = 0.1) for fluency. Similarly, Bartlett’s test showed that the assumption of homogeneity of variance was also met for this dimension (K = 2.13; gl = 1; p = 0.14). The interaction between the dependent variable and the control variable was not significant (p = 0.29), meaning that the homogeneity of regression assumption was met. When it comes to the linearity between the covariate and dependent variable, the correlation was significant (p < 0.001), and the assumption was therefore met. Finally, the independence of the independent variable from the covariate was not significant (p = 0.93), and all of the assumptions were therefore met for the dimension fluency. In the case of flexibility, the results of the Shapiro–Wilk test (W = 0.94; p = 0.94) and Bartlett’s test (K = 0.68; gl = 1; p = 0.40) showed that both of these assumptions were met. The interaction between the dependent variable and the control variable was not significant (p = 0.06), whereas the correlation between the covariant and the dependent variable was (p < 0.05). Finally, the independence of the independent variable from the covariate was not significant (p = 0.84), and all of the assumptions were therefore met for the dimension flexibility.

In the case of originality, the results of the Shapiro–Wilk test (W = 0.91; p < 0.05) suggested that the residuals were not normally distributed. Levene’s test (p = 0.33) was therefore used to show that the assumption of univariate normality was met. For the homogeneity of regression assumption, the interaction between the dependent variable and the control variable was not significant (p = 0.89), whereas the correlation between the covariate and the dependent variable was (p < 0.05). Finally, the independence of the independent variable from the covariate was not significant (p = 0.17), and all of the necessary assumptions were therefore met for the dimension originality.

3.2. Qualitative Results

The following pre-defined categories were used for the qualitative analysis: (1) Assessment of the class, (2) assessment of the use of the ball in class, (3) relationship between the activities and the content with the emerging categories, (4) role of the students, (5) importance of innovation and technology, and (6) perception of how the ball can relate to real life. The results of the qualitative analysis can be found in Appendix D.

4. Discussion

The experimental group performed significantly better than the control group (Table 3). This shows that the cyber–physical system was a valuable bridge between multiple representations, connecting the physical view of the rectilinear motion phenomenon with the abstract view provided by the underlying physical models projected on the screen [49]. Qualitatively, this was expressed by one of the students who suggested that:

S3:

“(the classes) switched things up.”

We see that the learning environment can be key in providing suitable representations that will allow for metacognition [50]. After interacting with the cyber–physical system, the students showed signs of higher levels of metacognition when referring to their own understanding of the concepts:

S6:

“The ball allowed us to look at things from another angle, not just the theory.”

S5:

“The experiments had an impact on our learning, I mean we learned quicker.”

These results are in line with the findings by [51], where talks and activities to promote the development of metacognition are shown to have a positive effect on conceptual growth. This leads us to think of the cyber–physical ball as an effective tool for supporting metacognitive development, which is a component of critical thinking [52].

This metacognitive development also coincides with improvements in creativity, in terms of fluency and flexibility (Table 2). Hargrove et al. [53] suggest that working on creativity also fosters the development of certain cognitive processes, such as metacognition. Creativity is also fostered by engaging in practical activities in class [54]. However, practical activities on their own are not enough. It is important for teachers to explicitly plan for how to link theory with practice [55]. Here is where the multiple representations, guided by the teacher, allowed the students to think creatively by connecting various forms of representation. In other words, the students were able to connect both abstract and concrete views through a real-world, physical experience [49]. Furthermore, practical activities not only foster creativity; they are also appreciated by the students, who expressed their enjoyment at participating in such activities:

S3:

“I like it because it’s more practical”.

S4:

“The ball was more practical than theoretical”.

Even though originality did not show significant differences, some students showed more original answers in the post-test. For instance:

S1:

“use a towel as a medical supply to stop bleeding, reduce fever or as a sling”.

S2:

“using a towel as a filter”.

One common trend in the students’ comments reveals that the cyber–physical system allowed them to see things more clearly. In this sense, they were able to understand what the system was communicating and were open to incorporating it into their own view of the physical world. This highlights the importance of cyber–physical systems being self-explainable in order to build a level of trust between the end-user and the system [56]. This self-explanation is facilitated by the different representations of the phenomena [57]. In other words, the system should provide feedback that is easy to understand and consistent with what students perceive through the different views. This is reinforced by the students’ comments, where they refer to the ball as a living object that could be interacted with:

S1:

“it had a pulse”.

S2:

“you could revive it, or make it die…”

On the other hand, students appreciated that the classes were fun and dynamic. This was not only reflected in their opinion of the classes but also in their motivation towards learning and their discipline in the classroom. This is consistent with the literature indicating that motivation plays an important role in maintaining students’ discipline and perseverance in the face of academic challenges [58].

S1:

“What I liked most was that the teacher made the classes dynamic”.

S2:

“The classes were fun”.

The use of technology and how it allows students to play an active role is something that they value. This is highlighted by their comments, where they suggest that there is a lack of opportunity to play a leading role in their learning.

S1:

“I find that it’s better when the teacher makes us part of the class, when it’s not just them talking, when we also get to say what we think, what we understand and what we’re struggling with”.

S2:

“I think that maybe all of the teachers could, like, maybe learn from their colleagues, because there are teachers who, like… talk all class and the class is more boring, but if they could maybe look elsewhere and say: OK, I like how she teaches her classes… Like, more dynamic, where the students participate, I think that would be better”.

Technology alone is not enough to lead to significant improvements in learning [59]. Although the technology played a fundamental role, the actual pedagogy and lesson plans were important for allowing the students to develop their knowledge and play a leading role in their learning [60]. This can be seen when the students talk about their impressions of the classes:

S1:

“What I liked most was that the teacher made the classes dynamic”.

S2:

“Everything made sense”.

One example of this is the lesson on adding velocities (Supplementary Material File S1 Lesson N°3). Before the experiment with the cyber–physical ball and the ramp, the students were shown a video of a moving conveyor ramp. Therefore, during the activity, the students were able to make comparisons between the video and the experiment. This was valued by the students, who suggested that the classes were coherent.

S1:

“With the ball, you could draw on everything you’d seen before, like you could confirm what you knew”.

From the previous, which is a quote from category (3) relationship between the activities and content, and category (6) perception of how the ball can be related to real life, we can include a capacity for “analysis” from Bloom’s taxonomy since concepts are broken into parts in order to find out their relation [58].

5. Conclusions, Limitations, and Future Work

Our first research question asked, “How can a cyber–physical system be used to teach physics through multiple representations?”. A “cyber ball” allowed for multiple views of the same rectilinear motion experience, through a symbolic and a tangible representation. Our second research question asked, “What effects can multiple representations have on creativity and learning when teaching physics using a cyber–physical system?” The multiple representations provided by the “cyber ball” allowed for an improvement in learning, creativity (i.e., fluency and flexibility), and discipline. Our study reveals the potential of cyber–physical systems within the teaching–learning process for physics, specifically rectilinear motion, and how such a system supports multiple representations. The main difference it has in comparison with conventional laboratory experiences is the simultaneous multiple representations allowed for by the cyber–physical system, which allows for an interactive experience with multidisciplinary immediate feedback.

Sports analytics is a field that provides more insights into the real-time data of physical activities than simple visualization techniques [61]. It provides athletes with decision-making tools in order to improve their performance based on their activity [62]. Such insights can be used to support the teacher’s role and improve how activities are carried out, based on student behavior during class. For example, in Spatial View activities, the students have to study the differences between trajectory and displacement. In this case, the system can record the data for all completed trajectories and pose suggestions to the teacher as to which one to create next, in order to improve understanding. This might be done by recreating a specific trajectory that has not yet been attempted and is important to demonstrate.

Physics is not the only learning domain in which cyber–physical systems can be used. Oddball [63], originally designed to be used as an alternative musical instrument that creates different sounds depending on the strength of impact, could be adapted in the teaching of physical activities or in teaching music with automatic partiture creation. Another example is [64], which could be enhanced with the use of wearable biometric sensors to create a cyber–physical system to teach students about the nervous system.

The main limitation of this study is its sample size. The experimental design can be improved by not only expanding the sample size but also including a variety of classrooms from schools with different socio-economic backgrounds. Doing so would help measure the relevance of different students’ lifestyles and analyze patterns in the data. Even though the system was only used as a research experience, its costs (Appendix C) make it a viable product.