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Analysis of Brownian Motion by Elementary School Students

To stimulate the intellectual curiosity of elementary school students, we conducted a workshop in distance education aimed at exploring the microscopic world inside a cell. In this workshop, elementary school students motivated to learn more on the subject of science analyzed movies of the Brownian motion of micrometer-sized particles suspended in water, using an open-source software, Tracker. These students then performed two-dimensional(2D)-random walk experiments using a dice game sheet to examine the physical mechanism of Brownian motion. After the workshop, we conducted a questionnaire-based survey. Many participants answered that the contents were difficult but interesting, suggesting that our workshop was very efficient to stimulate the curiosity of motivated students.

the first and second workshops, respectively). Owing to the COVID-19 pandemic, we were forced to provide distance education. Therefore, we held remote workshops via the Internet using the Zoom application. YH, a physics teacher at a high school, organized the workshop, YY, a PhD student in the field of biophysics, developed the data aggregation and analysis tools, and MM, a principal investigator in the field of biophysics, gave a lecture.
In this workshop, we aimed not only to get the students interested in Brownian motion and the frontiers of scientific research, but also to provide an opportunity for the students to trace the fundamental research process: setting a question, doing quantitative analysis on observed phenomena, building a hypothesis, and verifying the hypothesis using a simple model, even though their knowledge of mathematics and physics was limited for understanding the mechanism of Brownian motion at the beginning of the workshop. We think that the aims of our workshop have much in common with that of introductory physics. Therefore, the contents presented in this article will be widely applicable to the education of both introductory physics for life science [9,10] and scientific research process for the students in the introductory-level physics course in high schools, colleges, and universities.

II. ANALYSIS OF BROWNIAN MOTION
Before the workshop, we administered a questionnaire to the participants. Therein, we asked the participants whether they like science, to which 85% of the participants (23/27) answered in the affirmative. Although this value was lower than the reported value in the TIMSS2019 (Japan: 92%), [8] participation in this workshop was voluntary, and the students appeared to be highly motivated. We also asked them whether and how much they knew about a cell and a molecule. The results of the two questionnaires are summarized in FIG. 1. According to the questionnaire results (FIG. 1a), only 22% of the students (6/27) knew about a cell well. Therefore, using microscopic images, we explained at the beginning of the workshop that all living systems, including humans, are made up of cells. We then conducted quizzes using the voting function of the Zoom application for the participants to recognize how small the cell is and what the cell is made of. This is because elementary school students do not learn the units of micrometers or the components of cells at school. Subsequently, we introduced the unit of micrometer and explained that typical cells are approximately about 10 µm in diameter, which is about 10 times smaller than the diameter of a single strand of hair. We also explained that a cell is mainly composed of proteins and water, and many kinds of tiny "protein robots" work "in the pool of water" inside the cell to maintain our life. Note that we used the term "protein robots" instead of "protein molecules" at this stage because elementary school students do not learn about molecules at school. According to the questionnaire results, less than 4% of the students (2/27) knew about molecules (FIG. 1b).
To help the participants imagine the working environment of the protein robots in a cell, we showed them a movie of plastic particles smaller than the size of typical cells suspended in water (FIG. 2 and Supplementary Movie 1). The particles exhibited random motion, which is generally known as Brownian motion.
[1] To learn the basic features of motion and infer the motile mechanism, we asked them to analyze the motion using their personal computers at home. We adopted the open-source software, Tracker, as the motion analysis tool. [4,5] Prior to conducting the workshop, we compiled the original movie file in a format compatible with the motion analysis software to simplify the analysis processes, and we sent it to the students' parents. Notably, we sent different movies to each family to avoid analysis of the same set of particles. We confirmed with the parents via e-mail that the installation of the analysis software on their personal computers was completed before the workshop.
During the practice, the students were divided into subgroups of two to six people, and each subgroup was supported by two teaching assistants via online chat. Using the motion analysis software, the students recorded the positions of the particle by clicking the center every 0.20 s (every 5 frames) for 20 s (100 time points in total) (FIG. 3, left). According to the Japanese math curriculum, elementary school students do not learn about the concept of negative numbers.
[7] Therefore, we set the origin at the lower left of the image so that negative numbers did not appear in the table of X-Y coordinates (FIG. 3, right bottom).
In addition, elementary school students had not yet learned the concept of coordinates. We explained that the X and Y positions shown in the table indicate how far the particle was displaced in the horizontal and vertical directions from the origin, respectively.
After the tracking stage was completed, we asked the students to share their analysis results (a time series of X and Y positions) using a Google spreadsheet with the help of their parents. We carefully checked the uploaded data, and if the tracking was incorrect, we requested the students to analyze it again, or excluded the data for further statistical analysis.
Through a comparison of the motion of motile objects in daily life, such as a car, we discussed specific features of the motion of the analyzed particles with the students. First, the particles moved randomly-that is, the direction of the motion changed in every video frame. This feature is completely different from the features of regular motile objects that such students are familiar with. Second, the particles took four times as long to move twice as far as read from the graph. Theoretically, it is predicted that the mean-square displacement of the analyzed particles is proportional to the time t[1]: where x(t) and y(t) are the X and Y positions of a particle at time t respectively, · represents the ensemble average, and D is the diffusion coefficient of the particles. This We confirmed that the analysis results ( During the experiments, the students were divided into subgroups and supported by the teaching assistants. The results shown in FIG. 8 show a similar trend to that of the plastic particles (FIG. 4).
In particular, the displacement does not seem proportional to the number of rolling dice N , but is rather proportional to N 1/2 (equivalent to t 1/2 in the case of plastic particles).
We explained to the students that our hypothesis was correct, and thus, the mechanism of Brownian motion was understood.

NAMICS IN A CELL
In the last section, we introduced the unit of nanometer and explained that any objects in nature are composed of nanoscale tiny particles, namely molecules. In a cell, protein molecules are exposed to the random collisions of water molecules and thus they exhibit Brownian motion. Based on the results of the video analysis and dice experiment, we dis-cussed that protein molecules will move a short distance quickly, but it will take a long time to travel a long distance solely by the Brownian motion. We then introduced the "special protin robot" called molecular motor exists in the cell. The molecule motor transports the other protins rapidly and unidirectionally along the tracks made of the other proteins, just like a car or train in the world of humans. We then showed some animations [11] and microscopic images of molecular motors such as kinesin and myosin [12] walking along the cytoskeletal networks. Growing evidence obtained from recent single-molecule experiments and advances in the theory of information statistical mechanics suggest that molecular motors utilize collision of water molecules as the major driving force for the unidirectional motion, and the energy supplied by ATP hydrolysis is used to bias the direction of the stepping motion. [13][14][15][16] Supported by these findings, we demonstrated using animations that molecular motors utilize collisions of water molecules as the driving force by converting the random force into unidirectional motion efficiently. State-of-the-art technologies, including the development of synthetic "molecular engines," as well as future visions of molecular sciences, were also discussed. [17][18][19] V. CONCLUSIONS AND DISCUSSION After the workshop, we conducted a questionnaire-based survey. FIG. 9a shows whether the video analysis was easy for the students to perform. More than half of the respondents replied that the video analysis was very easy or easy (17/26). We believe that difficulties in performing such video analyses are largely dependent on the complexity of computer operations, such as importing raw data files and setting the length scale and time intervals.
In this workshop, we prepared a compiled analysis file ready for particle tracking just by mouse clicking. We successfully demonstrated that even elementary school students can work on video analysis using personal computers without much stress, if the initial analysis file is prepared properly.
FIG. 9b shows whether the 2D-random walk experiment was easy for the students to perform. More than half of the respondents replied that the experiment was very easy or easy (18/26). As we set a goal to include a gamified environment, many students were excited for and enjoyed this experiment. However, we realized that the sample number n decreased as the number of trials N increased (see FIG. 8). This was because once a token reached the goal, the data for larger N values was lost. To improve the data accuracy, it would be better not to set a goal in this experiment.
We found that our workshop has a limit on its applications. Weak internet connection sometimes causes a delay on the time schedule both in the lecture and practice parts. In addition, video analysis requires that all the participants have a personal computer. It is important to study how we can arrange the workshop program for widely applicable package in various situations.
Although we were forced to conduct the workshop in the form of distance education because of the COVID-19 pandemic, we received positive responses from all the respondents.
[5] Douglas Brown and Anne J. Cox, "Innovative uses of video analysis," Phys.