Smartphone-based undergraduate research projects in an introductory mechanics course

At the University of Göttingen, we implemented undergraduate research projects into a first-year mechanics course for physics majors and teacher-training students. Our primary goal was to foster students’ affective factors and higher-order thinking skills in a self-directed, crosslinking, inquiry-based learning setting. A total of 160 students were organized into 40 small groups which worked on one of six open-ended experimental tasks, utilizing smartphone sensors for flexible first-hand data collection outside laboratories. The tasks originate from the Erasmus+ project DigiPhysLab and were significantly modified and opened to be used for undergraduate research projects. In this manuscript, we present the underlying rationales behind this program, outline the core concepts behind the developed experimental tasks, and explain the actual implementation. Additionally, we offer insights into the assessment process for the project work, including the evaluation of scientific posters and responses to eight reflection questions. To facilitate this, we have employed two rubrics to ensure a comprehensive evaluation process.


Motivation and theoretical foundation of the program
The physics study entry phase challenges many first-year students.A compelling indicator of this issue is the current dropout rate of 60% at German universities, a figure that has experienced a concerning upward trend in recent years [1].Challenges can occur on three affordance levels students need to cope with [2]: The first level pertains to the subject matter that the students are required to learn.Challenges might be caused by the high difficulty or quantity of new subject matter within one semester.The second level is linked to the students' metacognition as they are not only expected to develop their learning habits, which are typically more self-directed compared to their previous school experiences but, e.g., they should also cultivate their own intrinsic curiosity and interest in physics.The third level is related to the students' socialization as they are expected to become part of the university, members of a peer group, and the scientific community.Students need to succeed in the process of identity formation on these three levels to perform a successful transition from school to university.
In various teaching and learning settings, university educators can support this transition process.One such setting is the physics lab course since labwork encompasses a wide spectrum of learning objectives [3,4].For example, Ref. [4] conducted a Delphi study among science educators in schools and universities in six different European countries to identify and rank the goals of labwork.The survey led to four different learning objectives of labwork that can be linked to the three mentioned affordance

Program overview: undergraduate research projects in an introductory mechanics course
In the teaching program, we implemented URPs in a first-semester mechanics course at the University of Göttingen in the winter term of 2022/23 in which small groups of students self-directed worked on a smartphone-based experimental task over a longer duration.Ultimately, they presented their findings on a poster.As outlined above, the overall goal was to foster affective factors and higher-order thinking skills among the students, including curiosity, autonomy, creativity, interests, and a sense of belonging.
To facilitate this objective, a set of six experimental tasks was developed to serve the students as a guiding tool and structuring fundament for their own investigations in their URPs.However, the tasks still need to be open enough so that the students can follow their interests and sub-questions and selfdirected work on their projects.The number of six tasks was chosen to provide a manageable but still diverse number of different topics.All task ideas originate from the Erasmus+ project DigiPhysLab (Ref.[24], www.jyu.fi/digiphyslab) that produced smartphone-based experimental tasks suitable for on-campus and distance learning aligned with the structure of a typical laboratory session spanning several hours.The task concepts underwent substantial modifications to transform them into effective URPs.As described in Ref. [25], this design process followed our own framework (cf.Ref. [26]).
Each task document starts with a short motivation of the task topic and presents the overall goal.This is followed by the actual task instruction, which is rather open, short (only about three sentences), linked to the beforementioned task goal, and usually provides the students with a research question.Each task requests the students to answer the research question by conducting an experiment, collecting data with the built-in sensors of their smartphone, and considering measurement uncertainties.While the instructions do not explicitly lay out the exact design and methodologies of the experiment, they do incorporate three to seven guiding questions that structure the experimental processes and direct students' attention to task-specific relevant aspects.Additionally, each task is linked to an original scientific paper that can facilitate the project work and is highlighted as the recommended starting point in the instructions.The documents further contain task-specific learning objectives that are divided into physics-, math-, and method-related objectives to show that the project tasks connect the contents of the physics, calculus, and algebra lectures and the lab course and therefore provide an opportunity for crosslinking learning.The objectives not only explicate the expectations regarding project work but also contain hints for the actual conduction, e.g., which physical quantities are relevant for the experiment.Moreover, the documents contain two to three task-related aspects that the students should address on their final poster as the learning product of the group work followed by further tips and hints for the experiment conduction (e.g., organizational tips, safety hints, or recommended software).Then, three to four aspects are presented how they can independently deepen their project work.This provides students with the autonomy and creative freedom to pursue their own interests and establish personal focal points within their projects.The task documents further contain recommended literature references (related to the physical background, the experiment itself, and the data analysis), further supportive materials (mainly step-by-step instructions for the recommended applications phyphox, SciDaVis, and tracker), and a recommended time schedule to structure the experimental processes over the available time period.Finally, offers of guidance like open consultation hours or a contact e-mail address are advertised.

Insight into the six experimental tasks used in the program
Here, we outline the concepts of the six experimental tasks for the URPs.All task documents are available as Open Educational Resources in German and English at https://doi.org/10.57961/49zr-w490.

Task A: The frictional behavior of doors (Slamming Door)
In task A, students should investigate the frictional effects that occur when a door is slammed shut.They should use the sensors of their smartphone and experimentally answer the question of which frictional model describes the slamming door most precisely, i.e., best fits the measurement data while still providing realistic model parameters.The students should also consider measurement uncertainties.
The task idea is based on Ref. [27], which also builds the basis for the students' project work.Students can attach their smartphones to the door face and measure the time-dependent angular velocity while the door slams shut, either using the gyroscope or accelerometer sensor.They should then extract relevant data and fit different models combining Coulomb, Stokes, and Newtonian friction.As discussed in Ref. [27], the choice of initial guesses for the fit parameters and the evaluation of whether the fit parameters are of realistic order of magnitude is crucial for choosing the right model.The best model depends on the specific door but often a combination of Coulomb and Newtonian friction is suitable.
In this task, students cannot only deepen basic principles of rigid body rotational motions and occurring frictional effects in an everyday situation but can also exemplarily learn the process and difficulties of modeling physical phenomena.The accompanying guiding questions point the students to relevant questions like the choice of the smartphone sensor, its positioning on the door face, the mode of how the door is slammed shut, or how one can compare the suitability of different frictional models.For in-depth analysis, students can compare the frictional behavior of different doors and windows or find an alternative experimental design for investigating the same phenomenon (e.g., video analysis).

Task B: Air resistance during falling motions (Paper parachute)
In task B, students should use their smartphone camera and video analysis software to investigate the relationship between air resistance and an object's velocity during free fall.In the end, based on their collected data, they should have an estimate of the dependency of the velocity on air resistance.They should perform this experiment using different objects, especially ones whose shape and mass distribution are susceptible to air friction (e.g., muffin cups or coffee filters).
The task idea is based on Ref. [28].Like in task A, students can apply and compare different frictional models to an everyday phenomenon with known applications like parachuting.For this, they use video analysis to determine the air resistance of different objects over the object's instantaneous velocity and fit these data.A typical finding is that there is a clear dependency between air resistance and velocity which can be either linear or quadratic and discussed by the students.
With the guiding questions, students are prompted to digest how they can determine and subsequently derive the interested quantities by video analysis, to reflect the influence of the experiment conduction (e.g., choice and dropping mode of the objects) on the findings, and to decide which model best describes the frictional behavior.Opportunities for in-depth analysis here are analyzing the influence of the object's initial velocity, investigating whether changes occur if the object is also rotating during the free fall, or using video analysis to examine frictional effects in completely different motion processes.

Task C: Analysis of smartphone sensors (Sensor analysis)
In task C, the students should examine the precision and accuracy of different smartphone sensors.First, they should compare the accelerometers of all group members' smartphones and estimate their precision (statistical measurement uncertainty) and accuracy (possible calibration offsets, i.e., systematic measurement uncertainties).Second, they should formulate a simple research question that can be answered by an acceleration measurement, then design and conduct an appropriate experiment using the different smartphones, and evaluate data again considering the specific measurement uncertainties.
The task idea is based on Ref. [29] and provides the students the opportunity to get a first impression of typical lab activities in designing and dimensioning experiments as well as analyzing measurement data.This task is the most open of all developed experimental tasks since the students should come up with their own research question and experimental design which should not be too complex but rather focus on the comparison of the smartphone sensors.As an inspiration for possible experiments, a collection like Ref. [20] is recommended in the task instructions.
The provided guiding questions stimulate the students to think about the criteria of a good/precise sensor, to what extent this precision/accuracy depends on the device, its spatial orientation, and intended use, and how different sensors can be quantified and compared in an experiment.For in-depth analysis, students could conduct further comparative experiments also considering different measuring ranges, analyze further smartphone sensors, or compare different methods of statistical data evaluation.

Task D: Mechanical oscillations of an elevator (Elevator oscillations)
In task D, the students should design an experiment in which they investigate the oscillations of an elevator car induced by cautiously jumping inside it when it is on a fixed(!) floor.They should use smartphone sensors to experimentally answer the question of how the oscillation period depends on the rope length of the elevator, i.e., the floor height.They should also consider measurement uncertainties.
The task idea is based on Ref. [30] and enables the students to investigate a large-scale version of a spring pendulum (if the cable-guided elevator car is modeled like this) and thus check the validity of a variation of Hooke's law by examining how the elevator's period of oscillation depends on the different floor heights (cf.pendulum lengths).Students cannot only deepen their knowledge about oscillations but also need to figure out how they would like to derive the desired period duration of the oscillations from the measurement data.Here, students can flexibly adapt their methods to their own ability level as the period duration can be determined with a built-in tool in phyphox that automatically applies a Fourier transform to the accelerometer data, by graphically estimating it from that data, or by applying Fourier transforms to the raw data on their own, guided by further supportive materials including a Python script (cf.Ref. [31]).A typical finding is a linear relationship between the estimated rope length of the elevator for different floors and the according squared period duration.
The accompanying guiding questions point the students to aspects like the determination of the elevator rope length for each floor, the mode of jumping, or the determination of the period duration.For in-depth analysis, students can compare the behavior of different elevators, vary the mass of the elevator (e.g., with more people inside), examine the oscillation behavior in the other two spatial directions, or learn more about the discrete Fourier transforms with the optional supportive materials.

Task E: Rolling motion with a smartphone (Rolling smartphone)
In task E, the students should use their smartphones placed inside a roll (e.g., a tin) to examine the timedependent rolling behavior (e.g., angular velocity and translation velocity) of the roll on an inclined plane.In their analysis, they should also consider the influence of the angle of the plane on the rolling motion and check the validity of the conservation of energy for individual angles.In addition, they should determine the critical angle from which slipping occurs and estimate how much the slipping affects the parameters of the rolling movement above this angle.
The task idea is based on the paper by Ref. [32] and provides the students with opportunities to experimentally deepen their understanding of rolling motions and related central parameters like angular and translation velocity, energy conservation, or moment of inertia in dependency of the angle of the inclined plane.When students plot the angular acceleration versus the angle of the inclined plane in a diagram, they can identify a specific angle (typically at around 30° with some variation depending on the used equipment) where the angular acceleration is lower than expected due to slipping effects.Notably, one can derive the frictional coefficient from this specific angle.
In the guiding questions, students are stimulated to think about the determination of setup parameters (like length and inclination of their plane or moment of inertia of the roll), the occurrence of measurement uncertainties, and the data analysis and modeling.Possibilities for in-depth analysis are finding an alternative method to determine the frictional coefficient for comparison and the systematic variation of the moment of inertia of the roll or the frictional properties between the roll and inclined plane to analyze the influence of these modifications on the motion parameters.

Task F: Rotating smartphone
In task F, the students should examine and describe the properties of the rotational motion when they manually initiate a rotation of their smartphone around its main axes and then let it fall freely.Experimentally they can investigate the temporal course of different physical quantities such as angular velocities, angular momentum, or rotational and total energies by using the gyroscope data.They can also find out which rotation axes are stable or unstable.The focus should be on the description of the rotational motion, not on the translational movement through free fall.
The task idea is based on Ref. [33] and uses the idea of Ref. [34] to determine the smartphone's moment of inertia.Like in task E, students can experimentally deepen their knowledge about the parameters of rotational motions and explore the (in-)stableness of different rotational axes.
The guiding questions point the students to relevant aspects of the experimental tasks like the determination of the smartphone's moments of inertia, their relationship to angular velocities, or characteristics of (un-)stable rotational motions.More in-depth analysis can be conducted by comparing different smartphone models, systematically varying the moment of inertia of the smartphone by attaching further objects to it to stabilize previously as unstable identified axes, or analyzing the influence of occurring frictional effects.This task is the only of a rather qualitative nature.

Course of the program and number of participants
The program was implemented at the University of Göttingen in winter term 22/23 in the introductory mechanics course "Experimentalphysik I" for physics majors and teacher training students.Figure 1 shows the chronological sequence of the program.It lasted for the first twelve out of 14 semester weeks (SW).In SW2, a kick-off event was held in which the students were informed about the project work and organizational issues were addressed.In SW3, students were divided into groups of three to five within the regular tutorial courses and could choose between two out of the six experimental tasks.This limited choice of group members and tasks was done for organizational purposes to ensure that each student finds a project group, that all tasks are similarly often chosen, and that in case of any difficulties with the project groups or with a specific experimental task, the weekly tutorial time slot could serve as a reliable contact possibility.Furthermore, this mode facilitates the networking of the students within their tutorial groups which might also lead to the formation of learning groups, e.g., for the weekly exercise sheets, which are very important for a successful study entry phase.
After receiving the task documents, students had time until the middle of SW10, i.e., in total about six semester weeks plus two further weeks during the Christmas break (X), to self-directed work on their project and prepare a scientific poster on which the project results are summarized.In small poster sessions, in which each five to six project groups with different experimental tasks participated, the students presented their project work in front of their fellow students and interested faculty staff.After that, the students had SW11 and SW12 to respond to eight reflection questions about their project work.All in all, the implementation of the URPs took place with only minor changes in the teaching in comparison to previous years.Neither the content of the lecture "Experimentalphysik I" nor the content of any other lecture, the tutorials, or the accompanying lab course for physics majors has been modified or influenced by the project work.Only two changes were made: First, the bi-weekly hall exercise was partly used for the project implementation, e.g., to have timeslots for the kick-off event, two workshops, and the poster session.Second, the weekly exercise sheets (problem sets, recitations) were shortened by about 25% (i.e., on average only three instead of four problem tasks) equivalent to approximately 25 hours of workload to counterbalance the additional workload caused by the URPs.
Throughout the program, we experienced a low dropout.In the beginning, we divided 160 students into 40 project groups.39 groups finally submitted a poster with 146 students (i.e., 91%) being listed as co-authors of one of these posters.110 students (i.e., 69%) submitted their responses to the reflection questions.This is noteworthy given the circumstances that the submission deadline needed to be set just two weeks before the conclusion of the lecture period and that some students had already accumulated enough points to meet the exam prerequisite without submitting their answers to the reflection questions.

Offers of guidance/support and their frequency of use
During the program, students were offered various offers of guidance and support (cf. Figure 1).In SW1 and SW2, the regular lecture addressed program-relevant topics of measuring physical quantities and dealing with measurement uncertainties.In SW4, immediately after students received instructions, a dedicated session for addressing central questions was organized as part of a hall exercise.In SW6 and SW8, students could participate in two workshops of 90 mins addressing the experimental process, the collaboration during this process, and the design of good scientific posters.Additionally, students could receive demand-based support via e-mail, in person after lectures, and during regular consultation hours.
The offers of guidance were used differently often.While students regularly asked questions via e-mail or in person, only five groups (13%) attended the flexible available consultation hours.For the on-site events, the actual number of participants has not been counted, however, the number of participants in different evaluation surveys conducted during these on-site events provides a conservative estimator.(This is because not all students responded to the surveys, which implies that the actual attendance at these events might have been higher than indicated by the survey responses.)Accordingly, at least 125 (78%) of the 160 initially assigned students participated in the kick-off event (SW2), and at least 65 (39%) students joined the hall exercise as the first question opportunity (SW4).The workshops were attended by at least 65 (41%) students in the first (SW6) and 112 (70%) in the second part (SW8).The level of participation in these events may have been influenced by several factors.One factor is the existence of parallel courses scheduled during the same time slot, which some students with specific subject combinations had to attend.Another factor is that all on-site events needed to be scheduled during lunchtime so that the events competed with a lunch break.

Students' assessment with scientific posters and reflection questions
With the implementation of the URPs in the introductory physics course and the desire that the project work is not only a voluntary offer but an integral part of the course, the students' project work needed to be assessed.At the University of Göttingen (as well as in many other German universities) students need to achieve a specific ungraded prerequisite to be allowed to participate in the final written exam.Only the grade for that exam is the overall course grade.The prerequisite typically consists of weekly exercise sheets (problem sets) that need to be solved and submitted after one week each.A tutor corrects the student's work and scores them.Over the whole semester, students need to collect a minimum of 50% of all possible points.In winter term 2022/23, we decided that the maximum number of possible points would be 360.Students could collect up to 240 points in the weekly exercise sheets (12 with 20 possible points each) and 120 points in the project work.By this, students could theoretically achieve the quota of 50% (i.e., 180 points) just with the weekly exercise sheets; however, in practice, they would need to participate in the project work as most students would likely not achieve an average of 75% (i.e., 15 points) in all exercise sheets.This ratio ensures that the project work is an integral component of the course and its assessment but prevents an overemphasis of the project work over the weekly exercises that are also crucial for the students' learning process and their exam preparation.
The 120 points for the project work were divided into two sub-assessments of 60 points each: the presentation of the project findings on a scientific poster and the responses to eight reflection questions afterward.This not only prevented a dependency of the students' success on a single assessment object but also increased fairness as not the whole assessment depended on other group members.Only the poster was assessed with the same number of points for all group members as this is collaborative work while the individual responses to the reflection questions were assessed separately.Both the posters and the responses to reflection questions were assessed with two rubrics provided to the students already in advance.The rubrics and the reflection questions are also published in German and English (https://doi.org/10.57961/49zr-w490)and will be described in more detail in the following.

Evaluation of the scientific posters as the product of the collaborative group work
The poster rubric, which is inspired by Refs.[35][36][37], consists of 14 criteria rated on a 5-point scale from 0 (does not apply) to 4 (applies).One criterion counts twice, the sum of all ratings provides the total number of points (maximum 60 points).The criteria follow the typical elements of a scientific poster and address both content and layout.The first nine criteria are linked to the typical process of science knowledge acquisition and require the students to provide a motivation for their project, the objective/question of their experiment, a short presentation of the central theoretical background, the design/measurement plan of the experiment as well as a sketch of the experimental setup, an appropriate presentation of the results and analysis of measurement uncertainties, a discussion of the results, and a conclusion/answer to the initial question.The students were informed that these criteria do not necessarily determine the structure of their poster, so students could combine aspects related to different criteria in the same poster element.Three further criteria address the design of the poster requesting a short summary or abstract, an appealing, clear, logically structured layout, and the fulfillment of typical poster conventions like a precise title or author information.To support the students in designing their probably first poster, an optional template was provided to them in advance.Another criterion assesses the depth of completion of the project work, so that not only the preparation of the poster but also the underlying experimental process and project work is reflected in the rubric.The last criterion assesses the oral presentation of the poster in front of fellow students in the poster session at the end of the project work because a scientific poster is a writing product intended to be used as a basis for oral communication and Thus, this criterion counts twice.
The described evaluation criteria reveal that the focus of the assessment was particularly on the design of the poster, i.e., on a product level, and not on the underlying experimental process or group work, i.e., not on a procedural level.This was intended to reduce the students' stress while conducting the open experimental group work which should be new to most students.It also acknowledges the circumstance that the students are engaged in self-directed work without a present instructor to assess the experimental process which aligns with the program's overarching objective that prioritizes the development of students' affective factors over the enhancement of their experimental skills.

Evaluation of the individual responses to the closing reflection questions
In the second assessment format, students were asked to respond to eight reflection questions that addressed the whole experience of the project work and the experimental process.In the first question, which has two sub-questions, students should first describe in their own words how they conducted their experiment and then evaluate their results, e.g., in terms of precision or informative value.In the second and third questions, they should reflect on their previous experience, learning growth, and development needs regarding experimentation and designing a scientific poster.Then, they should reflect on the skills they had acquired in the context of the project work in relation to their future relevance, e.g., for their studies or future jobs.After that, students should reflect on the collaboration within their project group.In the sixth question, again consisting of two sub-questions, students should first describe a challenging situation that occurred during the project work and subsequently explain the causes and their (possible) handling of this challenging situation.In the last two questions, the students should reflect on to what extent the project work enabled them to link the lecture contents with the project work and how they perceived the experimental task and the project work in general, i.e., what they liked, disliked, and how the program might be optimized.
The students' responses to the reflection questions were assessed with a similar rubric to the posters with different criteria again rated on a scale from 0 (does not apply) to 4 (applies).The first ten criteria refer to the eight reflection questions and assess whether each (sub-)question was adequately answered.Here, an adequate answer is operationalized as one that addresses all listed aspects in the reflection questions with a recognizable depth (of reflection), e.g., by not only giving statements but describing and analyzing experiences in more detail with examples, underlying reasons, and thoughts.For guidance, each reflection question had a specific operator (e.g., explain, describe) students already know from school and an approximate expected number of pages (0,5 to 1 page per question, 6 pages in total).
The rubric has two further criteria that are assessed only once for all reflection questions.The first, counting twice, assesses the coherence of the argumentation (e.g., comprehensibility and logical structure), and the second assesses the correctness and understandability of the (technical) language.
All in all, students can again reach up to 60 points for their responses to the reflection questions.The presented criteria show that like for the scientific poster, we did not actually evaluate the correctness of the students' responses but only if the questions were answered adequately.
The assessment of the 39 posters and 110 responses to the reflection questions with the two rubrics was done with the help of our tutors but outliers and extreme cases were double-checked by the instructors.This was done with the requirement not to evaluate too strictly because the project work was new both for students and tutors and students should ideally not fail in the prerequisite for the exam just due to the project work.The posters were assessed with M=46.7 (SD=8.1,Min=30, Max=59), the responses to the reflection question with M=49.8 (SD=8.4,Min=18.0,Max=60.0)out of 60 points each.

Summary and outlook
In this manuscript, we presented the rationales and thoughts behind a program implemented in an introductory physics course at the University of Göttingen in which students were engaged in selfdirected work on undergraduate research projects (URPs).Their group project work with an expected workload of 25 hours for each student was structured by one of six experimental tasks with a high degree of openness that utilized smartphone sensors to facilitate first-hand data collection even outside a laboratory setting.Throughout the program, students could use various offers guidance and support (workshops, consultation hours, etc.).The requested learning products, a scientific poster, and individual responses to eight reflection questions about the project work were assessed with two rubrics.
In the forthcoming phase, we will evaluate the program in two respects.First, as a sort of proof of concept, we want to assess the feasibility of integrating smartphone-based URPs into a first-year physics course.Second, we would like to gain insights into the students' perception of the tasks and the program itself allowing for enhancements and optimizations for potential future iterations.
For these purposes, not only the learning products can be analyzed but also the responses to six questionnaires that accompanied the whole program.In these questionnaires with up to 125 participants each, variables like students' curiosity and interest caused by the project work, their sense of belonging to the university and physics community, or the perceived quality and authenticity of the experimental tasks are addressed.An initial analysis of open text fields in these questionnaires revealed that the students liked the opportunities for autonomy and creativity as well as collaborative group work.The students expressed a sense of accomplishment and growth in their competencies through their participation in the program.They appreciated the opportunity to easily investigate everyday phenomena using readily available equipment, such as household items and smartphones.
In turn, some students disliked the perceived high time and effort requirements associated with the project work, even though, on average, they invested MW=24.6 h (SD=2.2h, based on survey findings) in their projects which is exactly within the range for the expected workload.Furthermore, the students had varying perceptions regarding the level of interest they found in the experimental tasks.They noted the high degree of openness and some students also reported certain difficulties within their project groups.Additional insights into the students' perceptions of the URPs will be gained through further analysis, shedding more light on their experiences and viewpoints.

Figure 1 .
Figure 1.Overview of the implementation of the undergraduate research projects (URPs) over the first twelve semester weeks (SW) and the Christmas break (X) including provided offers of guidance.