Effects of a thermal inversion experiment on STEM students learning and application of damped harmonic motion
O. I. González-Peña, G. Morán-Soto, R. Rodríguez-Masegosa, B. M. Rodríguez-Lara
EEffects of a thermal inversion experiment on STEM studentslearning and application of damped harmonic motion
O. I. Gonz´alez-Pe˜na, ∗ G. Mor´an-Soto, † R.Rodr´ıguez-Masegosa, ‡ and B. M. Rodr´ıguez-Lara § Tecnologico de Monterrey, Escuela de Ingenier´ıa y Ciencias,Avenida Eugenio Garza Sada 2501, Monterrey, N.L., Mexico, 64849 Department of Basic Sciences, Instituto Tecnol´ogico de Durango,Blvd. Felipe Pescador 1830, Nueva Vizcaya, Durango, Dgo, Mexico, 34080. (Dated: December 14, 2020)
Abstract
There are diverse teaching methodologies to promote both collaborative and individual work inundergraduate physics courses. However, few educational studies seek to understand how studentslearn and apply new knowledge through open-ended activities that require mathematical modelingand experimentation focused on environmental problems. In this work, we propose a novel homeexperiment to simulate the dynamics of a particulate under temperature inversion and model itas damped harmonic motion. Twenty six first year students enrolled in STEM majors answeredsix qualitative questions after designing and developing the experiment. These questions helpedanalyze the students epistemological beliefs about their learning process of physics topics andits applications. Results showed that this type of open-ended experiments could facilitate thestudents understanding of physics phenomena. In addition, this experiment showed that it couldhelp physics professors to promote students epistemological development by giving their studentsthe opportunity to search for different sources of knowledge and becoming self-learners insteadof looking at the professor as the epistemological authority. At the end, students described thisactivity as a positive experience that helped them realize alternative ways to apply physics topicsin different contexts of their environment. ∗ e-mail: [email protected]; [email protected] † e-mail: [email protected] ‡ e-mail: [email protected] § e-mail: [email protected] a r X i v : . [ phy s i c s . e d - ph ] D ec . INTRODUCTION Finding strategies to promote student engagement in introductory physics courses is achallenge of our times. For instance, something as simple as identifying students prefer-ences for learning physics by demonstrative problem solving on a blackboard or supervisedindependent collaborative work may improve the learning process [1].In a traditional learning environment, introductory physics curricula is usually designedwith the laboratory at the core of the learning process. It becomes a place to work onlearning theoretical concepts as well as carrying on experimentation [2, 17]. This methodol-ogy increases student engagement in physics courses and improves conceptual understand-ing through manipulation of instruments and materials [3, 17] to generate and processexperimental data [4]. A well designed experiment could help STEM students developself-regulated learning strategies [3], giving them the opportunity to build their own con-clusions and boost their knowledge about physical phenomena and its interpretation [5].Self-regulation and motivation is usually driven by epistemic beliefs [6, 7] that describe theway students think about the nature of knowledge and knowing [8].On the other hand, as engagement and cooperation play an essential role of the learningprocess in physics [9], it is important to develop Modeling Instruction (MI) plans to engagestudents beyond the four walls of an instruction laboratory. This is why developing plans toimprove the academic success of students by boosting their interest and involvement imple-menting active learning [10] using passive content [11] or interactive content [12] as well associal media platforms [13] to promote students interaction with their whole learning envi-ronment has become quintessential, and a dire necessity as education evolves and distancelearning methodologies are more important for students’ development.Developing better teaching strategies for physics courses, in general, could facilitateSTEM students understanding of physics phenomena. A better understanding of physicstopics could motivate STEM students and professionals to design and develop open-endedchallenges aiming to provide solutions to urgent global issues. Here, we focus on the issueof air quality control and pollution to build upon the concept of simple and damped har-monic motion applied to the dynamics of particulate dynamics in the atmosphere. Thisissue is specially relevant for us as five Mexican cities (Mexico City, Monterrey, Guadala-jara, Toluca and Leon) rank among the 13 cities with worst air quality according to a recent2eport from the Organization for Economic Co-operation and Development (OECD) [19],and it is common to observe pollutants trapped by temperature inversion in our daily life.Studying simple and damped harmonic motion applied to the dynamics of a particulate inthe atmosphere could provide a fertile ground to boost students cognitive process and tocreate awareness within the frame of the 2030 Agenda of Sustainable Development Goals. InSec. II, we state this purpose in detail and follow it with a literature review on approachesto teaching the damped harmonic oscillator in Sec. III. We present the details of the the-oretical model and experimental setup in Sec. IV and those of our qualitative research isanalyzed on the students epistemological beliefs about their learning process in Sec. V andSec. VI. Finally, we close with our conclusion in Sec. VIII.
II. PURPOSE
Students learning new topics usually undergo an epistemological process where they rea-son about specific information obtained from different sources, then they claim knowledge ofthese new topics [20]. Kitchener’s work suggest that open-ended problems or activities aremore likely to engage students on an epistemological process than solving problems in class[21]. Our research aims to help physics educators by analyzing the effect of constructingand experimenting with a simulator of thermal inversion on students’ understanding of thedamped harmonic oscillator.In this research, we present a methodology to construct an isobaric troposphere simulatorusing air confined by a glass vessel where it is possible to introduce a foreign gas and makeit oscillate by controlling the temperatures at the bottom and top ends of the container tosimulate temperature inversion. We present this activity to STEM students enrolled in firstyear introductory physics courses and ask them to collect experimental data of the dynamicsto compare it with a numerical simulation of the damped harmonic oscillator. Students’ goalis to find values for the various parameters of the system that provide a good fit betweenexperiment and theory. This is a collaborative activity for teams of four that submit asingle project report. Individuals undergo an argumentative test that serves as evidenceto evaluate and accredit the understanding and mastering of a technical competence. Inaddition to this academic evaluation process, a cohort of students answered a questionnairelooking for their point of view on the effect of this experiment in their understanding of the3hermal inversion phenomenon and its relation to damped harmonic oscillation.
III. LITERATURE REVIEW
The harmonic oscillator is at the core of our modeling of real-world devices involving in-tegrated circuits, fluid mechanics, optical systems, and quantum technologies among others.Thus, engaging STEM students in an cognitive process that allows them to claim knowl-edge of this concept and extend its use beyond particular examples becomes a fundamentalobjective of physics education.Pendulum and spring-mass systems are the standard textbook example of harmonic mo-tion in introductory physics lectures. A spring-mass experiment is simple enough to intro-duce the idea of damped oscillations by measuring the position of the mass [22–26]. Con-ducting experiments with pendulum may improve student satisfaction under self-evaluationof their learning experience and knowledge of the subject [27]. Of course, real world devicesare not completely harmonic; both spring-mass systems [28] and pendulum [29] beyondthe small displacement or oscillation angle limit, in that order, serve as examples of basicnon-linear models that undergraduate students may build using simple materials.In addition to physical concepts, the oscillation of complex systems, like membranes orstrings, allows the introduction of differential equations [30] and Fourier methods to physicsproblems [31]. In this direction, coupling a pair of simple harmonic oscillators may easeintroducing the idea of coupled differential equations to students with some experience inclassical mechanics [32]. From the simple to the complex, the harmonic oscillator offers anopportunity to understand the significance of mathematical modeling and visualize the effectof variable manipulation to engage STEM student into learning by physical interpretation[33].Furthermore, analogies to the physical concept of harmonic oscillators may help under-standing the workings of real-world devices and phenomena. For example, the infraredspectrophotometer [34] may be modeled as a spring-mass oscillator and the membrane vi-bration happening inside a microphone [35] is an analogy to a driven harmonic oscillator[36, 37]. For more advanced courses, the idea of a classical harmonic oscillator may beextended to the quantum realm, for example, using basic calculus and algebra [38] or study-ing fluorescence in diatomic sulfide [39]. The motion of an electron in the presence of a4wo-dimensional potential is another simple example of harmonic motion [40] and analogiesusing spring-systems with coupled masses may help introducing the formation of quantumbands to STEM students [41].On the education side, the idea of interactive conceptual instruction using collaborativeproblem solving [42], computational simulations [43] and virtual laboratories [44], or alterna-tive learning methods [45] show improvement clarifying misconceptions related to harmonicmotion. Furthermore, flipped learning using software simulation of electrical circuits showsimprovement in the students knowledge of the damped harmonic oscillator [46].Our experimental proposal focus on the importance of exploring systems beyond thespring-mass and pendulum in order to boost the epistemic cognitive process. In this di-rection, electronics present an opportunity to introduce highly controllable damping andnon-linearities to harmonic oscillators beyond mechanical systems [47, 48] and, for advancecourses, the ability to produce, for example, time-dependent control to introduce continu-ous symmetries and its invariants following Noether theorem [49]. We may look into thespace and introduce the damped harmonic oscillator using the dynamics of particular celes-tial bodies [50] or to more complex setups, for example, lasers and optical resonators [51],classical gases confined by harmonic potentials [52], or the oscillation of a superconductorring levitated by a magnetic field [53]. In particular, we are interested in fluids as they areexceptionally helpful to elucidate the effect of non-constant friction forces [54, 55].In the following, we describe a simple experimental setup that simulates the conditionsof temperature inversion and allows STEM students to explore the oscillation of a gas in acontrollable analogy of the troposphere.Together with the experiment, a theoretical modelwas generated. The bibliographic search revealed that modeling the effect of temperatureinversion by means of the damped harmonic motion has not been reported; the followingexperiment also incorporate
IV. EXPERIMENTAL METHODS
The core of our proposal is a toy model of the troposphere to visualize how a gas cloudunder temperature inversion behaves like a damped harmonic oscillator. Our experimentalset-up, Fig. 1, builds upon the idea that a transparent container whose ends are covered by agood thermal conductor may serve as a simulation of an isobaric troposphere at atmospheric5ressure p with control of bottom and top temperatures, T b and T t . An inlet in the bottomallows us to introduce an external gas that we model as a collection of non-interactingmicroscopic spheres with constant density ρ g in order to follow its dynamics. FIG. 1. Sketch of the experimental setup used to simulate an isobaric troposphere. A clearcontainer with two temperature sensors and an inlet to inject smoke.
Let us start with the model. Temperature control at the bottom and top ends of oursimulation allows us to assume an air density that depends on the height. For the sake ofsimplicity, we suppose constant pressure and linear temperature gradient that allows us toapproximate the air density, ρ air ( y ) = ρ b (1 − c y ) , with c = 1 h (cid:18) − T b T t (cid:19) , (1)up to first order on the height y , that we take as zero at the container bottom and h at thetop such that y ∈ [0 , h ]. We define the air density at the bottom and top ends, ρ b ≡ ρ air (0) = pMRT b and ρ t ≡ ρ air ( h ) = pMRT t , (2)in that order, where our local atmospheric pressure at 540 m above the sea level is p =101388 Pa [56], the molar mass of air is M = 28965 . × − kg mol − [57, 58], the ideal gasconstant is R = 8 . − K − , and the temperatures are given in Kelvin.Assuming the foreign gas as a collection of non-interacting microscopic spherical particles,allows us to model the dynamics of each particle using Newton second law, m d ydt = − w + F B − b dydt , (3)6here the forces in the right-hand-side of the equation are the weight w = mg pointingdownwards, the buoyant force F B = ρ air V gas g pointing upwards, and the Stokes drag for asphere moving through a viscous fluid proportional to the drag coefficient, b = 6 πr gas η air interms of the radius of the spherical particle r gas and the viscosity of the air η air , and thevelocity of the particle dy/dt .The mass of each gas particle is given by its density and volume, m = ρ gas V gas , such thatits weight becomes w = ρ gas V gas g and the dynamics reduce to the following second orderdifferential equation, d ydt = (cid:20) ρ air ( y ) ρ gas − (cid:21) g − bρ gas V gas dydt , (4)where we assumed that the gas density change induced by the temperature gradient isnegligible at the time scale of the experiment and that the height of the container is smallenough to produce no significative changes in the value of the gravity. For the sake ofsimplicity, we assume that the viscosity of air has a negligible change with the temperaturegradient. We use our linear approximation to the air density inside the container to unfoldthe model, d ydt = − cgρ gas y + (cid:18) ρ b ρ gas − (cid:19) g − η air ρ gas r dydt , (5)into that of a damped oscillator, d ydt = − ω y + a − γ dydt , (6)where the temperature difference controls the sign of the frequency, ω = ghρ gas (cid:18) − T b T t (cid:19) . (7)Without considering the rest of the terms in the right-hand-side of the oscillator equation,if the temperature at the top is lower than that at the bottom, T t < T b , we have a positivesquared frequency ω > T t > T b , we have a negative squared frequency ω > T t = T b the squared frequency is null, ω = 0 andonly the external effective acceleration, a = (cid:18) ρ b ρ gas − (cid:19) g (8)7as an effect on the dynamics. Without considering the rest of the terms in the right-hand-side of the equation, if the gas density is larger than that of the air at the bottom of oursimulator, ρ gas > ρ b , the effective external acceleration is negative, a <
0, and the gas sinksto the bottom of the container and stay there. If it is smaller, ρ gas < ρ b , the effective externalacceleration is positive, a <
0, and the gas rises to the top of the container and stay there.If they are equal, ρ gas = ρ b , the effective external acceleration is null and the gas does notmove upwards nor downwards. Finally, the approximate drag frequency for the sphericalparticles of gas, γ = 9 η air ρ gas r , (9)where we assume a constant air viscosity as it changes from η air ( T = 213 . . × − Pa s to η air ( T = 313 . . × − Pa s for a temperature gradient of 100 K[59]. We take the average of these values as our constant viscosity, η air = 0 . × − Pa s[59].Our toy isobaric troposphere model allows the simulation of diverse dynamical phenom-ena. Temperature control at the ends of the simulator, for example, allows to switch thedriven and damped oscillator between inverted or harmonic behaviour. Changing the atmo-spheric or external gases gives even more options to control and explore the parameters ofthe model. In the following, we focus our observations on temperature inversion.Under standard conditions, the temperature gradually falls with the increase of altitude,Γ = − dTdy . (10)This is known as the thermal lapse rate; for example, the dry adiabatic lapse rate is aroundΓ ≈ . × − K m − . Temperature inversion is the phenomenon that occurs when thethermal lapse rate Γ changes sign from positive to negative; that is, a hot layer of air withlow density hovers above a colder one with high density. In these situations, it is possibleto observe smoke, or other pollutant gases, form a ceiling as the top low density layer of airstops their ascend.In order to have a reference for the behavior, we present a numerical experiment ina container that is 0 .
15 m tall, take the standard value of gravity g = 9 .
81 m s − , thebottom of the container at room temperature T b = 298 K leading to the density of air ρ b = 1 .
225 kg m − [60], the top of the container heated to T t = 373 .
15 K and a constant8iscosity of air η air = 1 . × − Pa s. We assign the gas a density of ρ g = 1 .
140 kg m − with a particulate radius of r g = 6 × − m. These assumptions provide constants for thedifferential equation, ω = 3 .
400 rad s − , (11) a = 0 .
731 m s − , (12) γ = 1 .
567 rad s − , (13)leading to the damped behaviour shown in Fig. 2(a). Figure 2(b) shows the effect ofrandom variations on the temperatures, densities, effective particulate radius, air viscosityand initial velocity, { T b , T t , ρ b , ρ gas , r gas , η air , v } , following a normal distribution with meanvalue provided by the parameters above and standard deviation equal to one percent of themean. We want to stress how such a small change in parameters produces a strong changein the dynamics. (b)0 51 2 3 4(s) t (a)01 . . . . . t ( m ) y FIG. 2. Damped oscillation for (a) a single particle of gas in the experiment with effective param-eters provided by Eq. (11) to Eq. (13) and (b) mean value and region delimited by one standarddeviation above and below the mean for a thousand random realizations with parameters followingindependent normal distributions.
We ask our students to reproduce the experimental setup, Fig. 1, at home using atransparent tempered glass container to avoid fractures from temperature gradients; forinstance, we use a coffee jar. In order to record the temperature at the bottom and top,we use two Vernier Stainless Steel Temperature Probes placed inside the glass containerand a Vernier LabQuest Mini controller. These may be substituted by simple atmosphericthermometers in contact with the external facet of the container at home. The sensors and9 pewter straw to let smoke in are secured in place on the container lid using modelingclay to guarantee a good seal. We recommend securing a disposable plate to the containerin order to hold ice cubes and secure access to the inlet straw that connects to a smokecontainer using plastic tubes; for instance, we used a candy jar to contain smoke from papercombustion but a party balloon or plastic bag may play the role. A light bulb lamp oran iron covered in aluminium foil may be used to change the temperature at the top ofthe container. Finally, we follow smoke dynamics using a logitech HD Pro Webcam C920and Vernier Logger Pro but any given video capturing device and open source software likeTracker Video Analysis and Modeling Tool should do.
FIG. 3. Experimental setup used to simulate temperature inversion in an isobaric troposphere.
Figure 3 shows our experimental setup at home. As the container is not hermeticallysealed, the pressure inside should be constant and equal to the atmospheric one. Ourexperiment allows controlling the input speed of the smoke as well as the bottom and toptemperatures. We ask the students to experiment with these three parameters to explorethe different dynamical regimes available. In particular, we ask for a detailed analysis of acase whose dynamics are an analogy to the damped harmonic oscillator. Their experimentaldata should allow them to fit for the dampening frequency γ and the smoke density after10guring out the input velocity of the smoke without any temperature gradient. Figure 4shows a sequence tracking of the approximated smoke cloud center of mass in an experimentwith bottom and top temperatures in the order of 292 .
35 K and 306 .
35 K, in that order.
FIG. 4. Example from an experimental measurement sequence. The yellow dot indicates theapproximated center of mass of the smoke cloud. t (a)0 0 51 2 3 4(s) t ( m ) y . . . . . (b) FIG. 5. Example from an experimental measurement sequence (data points) and its correspondingfit (solid line) from (a) theoretical parameters and (b) a numerical fit using these parameters asstarting point.
Figure 5(a) shows experimental data points compared to the analytic model using anatmospheric pressure of p = 102300 Pa and temperatures of T b = 292 .
75 K and T t = 303 .
95 Kat the top and bottom of the container, in that order, leading to approximate air densitiesof ρ b = 1 .
218 kg m − and ρ t = 1 .
173 kg m − accounting to a height difference of h = 0 .
08 mbetween the temperature sensors. We assume the smoke density about ρ gas = 1 .
210 kg m − with radius r gas = 5 . × − m and initial velocity of the order of v = 0 .
145 m s − leading to an effective acceleration, a = 0 .
066 m s − , as well as effective oscillator anddamping frequencies ω = 1 .
93 rad s − and γ = 2 .
027 rad s − , in that order. The differencebetween experimental data and the dynamics under our educated guess may arise fromvariations in any of the assumptions, as we discussed before, and provides an opportunity11or discussion. Our ansatz provides a good starting point for a better fitting using, forexample, Newton least squares method or Levenberg-Marquardt method for nonlinear leastsquares yield an effective acceleration, a = 0 .
053 m s − , effective oscillator and dampingfrequencies ω = 2 .
025 rad s − and γ = 2 .
137 rad s − , in that order, and initial velocity v = 0 . − that provides a better fit shown in Fig. 5(b). V. QUALITATIVE RESEARCH METHODS
In the following, we address the qualitative methods used to analyze our students pointof view regarding the effect of this learning activity on their understanding of the dampedharmonic oscillation.
A. Participants
We selected a cohort of 26 students were selected from a total of 185 students that realizedthe experiment in different physics modules during the fall 2020 semester. These studentswere taking the introductory physics module with a professor that voluntarily acceptedto distribute a questionnaire with six open-ended questions at the end of the experiment.Students were offered extra credit if they decided to answer the questionnaire, and the100% of these 26 students answered the six questions. All students were in first semester ofdifferent STEM majors in the Tecnologico de Monterrey. Students in this Mexican universityare required to participate in multiple challenges related to real-world issues as part of theirprofessional competencies development [14, 17 ? ? ]. These 26 students were taking a 5weeks-long project for their introductory physics course at the moment of the data collection.
B. Data collection
Although physics students are used to conduct experiments to prove their knowledge,this thermal inversion experiment aims to explore the damped movement phenomena in aunique way that may help students to understand this topic. To be able to analyze theeffect of this open-ended experiment on students understanding of the damped harmonicoscillation, we distributed a questionnaire with the students after finalizing the experiment.12he six questions from the questionnaire were adapted from the Engineering Related BeliefsQuestionnaire (ERBQ) [61]. We selected the ERBQ a starting point to adapt the questionsdue to its aim for measuring students’ beliefs about the nature of STEM-related knowledgeand knowing, and also because this instrument has successfully helped to analyze STEMstudents’ epistemic process after solving open-ended problems in prior studies [62]. These sixquestions were selected due to their relationship with open-ended problem solving aspectsof the cognitive process of STEM students. The six questions were translated to Spanishlanguage and then adapted to the physics thermal inversion experiment context to askstudents about the certainty and sources of physics knowledge. The questionnaire was backtranslated to English language by an English professor for this paper (see Appendix A).
C. Data Analysis
The four researchers involved in this study conducted the qualitative analysis. We an-alyzed the data collected with the questionnaire using open coding to let emerging codesto stay as close as possible to students’ own words and ideas [63]. The final codes for eachstudent were compared side by side with codes from other students aiming to find similar-ities that could be coded together into meaning units [64]. This coding philosophy helpedus to draw conclusions of how the thermal inversion experiment influenced students’ knowl-edge and understanding of the damped movement, and also helped us to ensure that thesemeaning units appropriately reflected students’ responses and feelings about the experiment.Students’ comments were translated from Spanish to English language by the same professorthat translated the questionnaire to be included in the following section.
VI. QUALITATIVE RESULTS
Half of students (13) reported using a single methodology or theory for designing anddeveloping their thermal inversion experiment, while the other half (13) used a combinationof two or more different methodologies or theories for their design. Regardless of whetherthey used only one methodology or different methodologies, students reported that the mostlikely starting point for their thermal inversion experiment design was the methodologypreviously explained by their physics professor. Student A4 noted : “I thought of some less13rthodox methods but I mostly focused on the one taught in the lessons.”Most students (20) reported that they asked for their professor’s help during the designingand development of their thermal inversion experiment. While almost every student askedfor their professor’s help, seventeen students reported that they look for more than onesource of information asking other professors, classmates, or family members to confirm andcomplement the information they know about the damped harmonic oscillation. StudentA19 noted: “We asked the challenge’s instructor for help. However, we needed further helpand requested it from friends in a senior class.” Only one student reported completing theinversion experiment without asking for help.When students were asked if they searched for additional sources of information to com-plement what they know about the damped harmonic oscillation, almost all of them (25)decided to look for additional information in different sources outside of what they learn intheir course. Most of these students (17) looked for more than one source of external infor-mation. The most recurrent sources of external information were videos (15) and websites(13), and another less common sources were textbooks (5) and scientific papers (3). Eightstudents reported looking for only one external source of information, and only one studentsdecided not to look for external sources of information.Almost all the students (24) reported that the thermal inversion experiment helped themto better understand the damped harmonic oscillation. These students stated that thisexperiment helped them to clarify some doubts about damped harmonic oscillations, whilethey learned different ways to apply this topic in real life problems. Student A23 noted:“It was really helpful. Before, I thought that harmonic movement only applied to springs,but now I understand that it also applies to more complex systems such as fluids.” On theother hand, only two students mentioned that this experiment was confusing and it did nothelp them to understand the damped harmonic oscillation. Most of the students (23) statedthat the thermal inversion experiment could have different final results that could be validdepending of the methodology used during the design, or some differences in the obtainedmeasurements; and seven of these students argued that their responses need to be supportedby theory to be considered as a valid response.Half of students (13) stated that the thermal inversion experiment might have betterresults in students’ understanding of the damped harmonic oscillation if the professor couldspend extra time explaining the theory, and giving them more details about how to apply14his topic to solve different problems in different contexts. This issue was more evidentfor seven students that mentioned having struggles to answer the argumentative test dueto difficulties adapting their knowledge and experiences from the thermal experiment tothe test context. Student A11 noted: “I felt prepared to answer questions related to thechallenge, but the argumentative exam had nothing to do with thermal inversion.”
VII. DISCUSSION
Students in this research showed that they normally expect instructions from their pro-fessor to design the experiment following what they have previously learned and practicedin their physic course. These students were open to follow different methodologies to designand develop their thermal inversion experiment, but they stated that having guidance fromany expert in the damped harmonic oscillation phenomena is the key to be able to success inthis type of open-ended problems or experiments. This could be related with a low level ofepisteological maturity for college level students [65], where they need to learn new knowl-edge and ways to apply this knowledge from an epistemological authority that is consideredthe only source of reliable information [8]. Most of students asked for help during the exper-iment design and development, showing that they are likely to search for an epistemologicalauthority that could help them to develop their knowledge during the experiment processas well. Students that asked for help reported going directly with their physics professorwith specific doubts and questions about their thermal inversion experiment. This behaviorpinpoints the importance of physics professors and the information they provide to theirstudents before and during the development of the experiment.Students reported to be likely to search additional information sources to analyze whatthey know and solve some doubts, with the videos and websites being the most commonplaces where students look for more information. Very few students consulted science publi-cations and textbooks to expand their knowledge and solve doubts. This lack of interest onscientific publications could be considered an area of opportunity to improve students’ re-search abilities, and may be considered by physics professors when they advise their studentsabout the advantages of looking for information supported by scientific evidence.At the end of the thermal inversion experiment and the argumentative test almost all stu-dents described this activity as a positive experience that helped them to better understand15he damped harmonic oscillation and how this physic phenomena could be applied in differ-ent contexts. This type of open-ended experiments or activities could help students developtheir knowledge and make them think in different sources where they can search for infor-mation to solve their doubts. Giving students the opportunity to experience these type ofexperiments could help physics professors facilitate students’ epistemological development.Reaching higher levels of epistemological maturity could benefit students development ascritical thinkers, making them more likely to think that their knowledge development istheir responsibility and they need to search and confirm their own knowledge and believes[65]. This is relevant for physics professors because some students stated that they felt thatthe knowledge about the thermal inversion that they learned and practiced was not trans-ferable to different applications of the damped harmonic oscillation. This lack of abilitiesto apply the same physics principles to solve different problems is common in the low levelsof epistemological maturity [65], and this position about how to learn and apply new topicscould hinder students’ possibilities to understand complex physics phenomena.
VIII. CONCLUSION
It is important that physics professors provide enough information to their students togive them confidence to successfully complete open-ended activities like our thermal inver-sion experiment. The process of preparing students with the basic knowledge to performexperiments like the one presented in this research needs to be conducted with certain pre-cautions. Physics professors should provide enough information to their students withoutleading the entire experiment and giving students the opportunity of solving possible issuesby their own. Physics professors should try to conduct these open-ended activities as facil-itators, making their students responsible of solving their own doubts by searching sourcesof reliable information that might help them to develop their knowledge and solve theirstruggles. Our thermal inversion experiment could be used by physic professors to rein-force the students knowledge about damped harmonic oscillations, and also motivate themto evolve from low epistemological maturity levels to a more mature epistemological levelwhere they are more likely to search and develop their own knowledge. Additionally, ourproposal to implement the activity of modelling the phenomenon of temperature inversiontogether with the development of experiments, may help students develop research interests16nd skills leading to a deeper understanding of science topics at next semesters. Therefore, itopens a window of possibilities for faculty to propose more challenging activities that mightfacilitate facing the great issues that society have related to the 2030 Agenda of SustainableDevelopment Goals.
ACKNOWLEDGMENTS
O.I.G.P. acknowledges to Arath Mar´ın-Ram´ırez for the literature collecting process onthe previous studies in harmonic oscillator in the education context. R.R.M. is grateful to hisstudents for agreeing to share their evaluations anonymously for the academic analysis of thiswork. B.M.R.L acknowledges fruitful discussion and support from Benjamin Raziel Jaramillo´Avila. O.I.G.P., R.R.M. and B.M.R.L acknowledge financial support from Tecnologico deMonterrey through the project grant NOVUS-2020-308. The authors declare no competingfinancial interest and thank Tecnologico de Monterrey Writing Lab and TecLabs for financialsupport on the open access article. [1] J. Lavonen, C. Angell, R. Bymen, E. K. Henriksen, and I. T. Koponen, “Social interac-tion in upper secondary physics classrooms in Finland and norway: A survey of students’expectations,” Scand J. Educ. Res. , 81–101 (2007).[2] C. A. Bailey, K. Kingsbury, K. Kulinowski, J. Paradis, and R. R. Schoonove, “An IntegratedLecture- Laboratory Environment for General Chemistry,” J. Chem. Educ. , 15–199 (2000).[3] R. Thumper, “What do we expect from students’ physics laboratory experiments?” Journalof Science Education and Technology , 221–228 (2002).[4] V. Thomsen, “Precision and the terminology of measurement,” Phys. Teach. , 15–17(1997).[5] D. Roberts, “Errors, discrepancies, and the nature of physics,” Phys. Teach. , 155–160(1983).[6] S. Pieschl J. A. Greene, K. R. Muis, “The role of epistemic beliefs in students’ self-regulatedlearning with computer-based learning environments: Conceptual and methodological issues,”Educ. Psychol. , 245–257 (2010).
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