Using computer simulation to aid the interactive learning of physics in secondary education

A survey of 1541 secondary school students has shown that they are more willing to take part in lab or interactive classes (e.g. using clickers) [1]. The popularity of such classes goes hand in hand with their effectiveness. The article presents the idea of combining experiments with the system of simultaneous answers. The tool that was created for this purpose is EduPython. The name comes from the educational platform that was created in the free and flexible programming language Python. The paper presents a way of using EduPython at school using the example of Coriolis Force. The charts attached show the answers received during the lesson.

Three elements of a lesson with the use of EduPython can be specified, based on problem-solving questions. The first one is storing students answers and presenting them in the form of a collective chart. The second one directly concerns teachers and the way they run their lessons. The teachers role is to indicate, give tips and ask provocative questions. A teacher should make sure all the students are involved in the lesson. The third element of a lesson is the possibility of free information exchange among students. It means that students can form their own hypothesis, convince others and argue their point. All the elements mentioned do not need to occur in a specific order. They can interweave as well as take place at the same time. Everything should be moderated by the teacher.

Form the observation of the lessons it can be concluded that teaching significantly gives way to self-reliant learning.

The application of running a lesson using the method presented in this paper can be downloaded from: http://northcoriolis.edupython.com.

There is a need to introduce the numeric methods at the secondary education level. Unlike many tools commonly used in teaching physics and maths such as analytical calculations, numeric methods can exceptionally develop the ability of symbolic thinking. Moreover, numeric methods have many other advantages, for example:

• performing very fast and precise calculations and their verification,
• creating very precise charts with possibility of their extrapolation,
• approximation of data,
• calculations with many variables,
• enriching scientific models with real factors like friction or other resistance forces, which are very often ignored in descriptions of phenomena,
• simulating experiments and phenomena very difficult to conduct in school environment and some of them even in laboratories.

Nowadays, more and more young people have smartphones. Of course, the wide range of functions the devices offer is becoming greater too. For example, they may have a fast Internet connection, high quality graphics and huge calculative potential. Since all students have smartphones and can use them proficiently our aim should be to encourage them to use these functions in the lesson. This is how the idea of replacing clickers with smartphones was born.

It is the example of rapidly developing m-learning. It is learning with the use of mobile devices. This term means all technological devices can be used in any place, at any time and can be easily carried. Among the many advantages of m-learning, it is worth mentioning that we see an increase in the students' motivation. The combination of mobile learning and interactive methods has also been applied [2].

In [1] the modus operandi, advantages and some examples of using the PRS system are presented. This is one of the most popular and effective interactive systems. It enables us to get answers in real time, simultaneously from all the students taking part in the lesson. All the students are equipped with a remote control with their own number that identifies them uniquely. Ones answers provided during a session of questions are sent to a computer and almost immediately presented, for example, as a chart. The results of the research we conducted for three years are also presented. The research proves the effectiveness of the tool. It is a very effective but a commercial tool. This means that a teacher has to buy one to use it. It would be better if teachers have access to free interactive tools. The first step was to replace clickers with smartphones. There is free software available to operate them. The software of the same company that produced clickers was used. The only cost to bear was the cost of software, without the necessity of buying clickers.

The next step was to create and implement our own software. The idea was that it had to meet three basic conditions. First, it should be absolutely free of charge. Secondly, it should let a user to collect answers to a broad range of questions. Finally, it should have high calculative potential. This was supposed to let us broaden the range of questions being asked and give students bigger opportunity to express themselves. In addition, a teacher can increase not only the spectrum of phenomena and experiments analysed during a lesson, but also the precision of the calculations performed. One more advantage of EduPython is the fact that a student does not need to install anything on his smartphone. It makes the lesson much smoother.

To create the application that meets the conditions above a widely used high-level programming language Python was chosen. It is an open source tool. It is characterised by the brevity and clarity of the source code. It has a well developed package of standard libraries.

What does the lesson with the use of the application look like? Just like in the case of clickers, questions are asked during a lesson. A question which is aimed to the whole class is displayed on a screen. It is an open question. Every students task is to give an answer in the form of a numeric value. The students connect to the Internet using their smartphones. After loading the page (e.g. northcoriolis.edupython.com) the students can enter their answers and send them to the server. Then, the application collects the answers from all the students and on the base of them generates the result. It can be presented in many different ways from a chart, animation, to a precise numeric value. The teacher can decide whether to present all the answers of all students at the same time (e.g. in the form of a string of numbers or superimposed charts) or in the form of consolidated answers (with the use of statistical value e.g. a mode). When the answers are given the application presents them. And the feedback is the crucial element of a lesson because according to the correctness of the students answers a teacher can decide about the further flow of the lesson. Besides the collective answer, ther application also saves students individual answers. The data can be later used for deeper anaysis (e.g. to create histograms or other useful statistics).

EduPython is an alternative to the clicker system. That is why there are so many similarities, but there are some differences too. Both applications aim to check students level of understanding during a lesson. They both give us the possibility to individualise the process of teaching. However, the differences can be easily noticed by the students as well as the teachers. From the students point of view there are two such differences. Firstly is the fact that they use smartphones instead of clickers. The second is that instead of a choice between answers a, b, etc. they have to input an exact numeric value. But for a teacher the difference is much bigger, especially from a substantive point of view. It gives teachers a chance to run a lesson in a way that gives students not only a qualitative but also a quantitative description of the issues and phenomena. A teacher can instigate students to do more independent work. Students are given an opportunity to draw their own conclusions from observation or simulations.

There are more and more examples of using numeric methods in the analysis of physical phenomena, especially the Python language [3]. Although the example presented in the article does not include very advanced calculations, it can be sufficient for teaching purposes.

One of the examples of experiments, which obviously cannot be conducted in a school building, and where an EduPython application can be very useful, is studying Coriolis force [4]. More specifically, a simulation of experiment that can be measured, so it would allow both teacher and student to carry out not only qualitative but also quantitative analysis. To be more precise, studying the variance in trajectory of a body caused by the force. In the particular case, for bodies moving parallel to the Earth surface. It is supposed to show the possibility to present students answers in the form of a chart instead of numeric values. The graphic way to present students answers lets us make quick and approximative statistical analysis. The charts superimposed on each other can show the accuracy and dispersion of answers as a group. In the example below there are answers of 23 students. They were supposed to answer:

Question 1: How fast (an approximate constant) should a hockey puck move if it was expended at latitude 50, so the trajectory deviation caused by Coriolis force was equal to 2 cm for 100 meters of a distance?

The quantity can be counted with the formula below:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle y(x)=\frac{\omega x^2 {\rm sin} \alpha}{v}, \nonumber \end{align} \tag{ 1 }$$

where

y—trajectory deviation,

x—distance traveled or length of trajectory,

ω—Earth's angular velocity,

α—latitude,

$v$—velocity of body.

It is easy to notice that the deviation is too big for most of the students (figure 1(a)). It is a teachers job to analyse and use discussion to help a student to find out if the value he gave was too big or too small. The first step is to give them a hint is by presenting a movie with an excerpt from an ice hockey game. Despite the fact that some students are unable to notice the direct effect of Coriolis force, it makes it easier for them to estimate the speed of the puck. The second step is to give an example based on precise measurements and calculations. A good source can be the work of Garry and Ian Robinsons which includes many exemplifications, mainly from the world of sport [5]. After the hints given by their teacher, students gave more analogous answers. However, most of them were still far from the correct one (figure 1(b)).

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As it is seen, there are far less wrong answers. Especially those giving very little deviation from the trajectory. Before the third session of answers, still on the Question 1, a teacher suggests a discussion of the problem in pairs. Their choice can be left to the students. Now, the answers are even closer to the right one (figure 1(c))

Then, a teacher suggests a discussion of the problem in larger groups. Next the students answer for the fourth time Question 1. On the base of the chart of the answers, a teacher can conclude their quality. It means that a teacher has to decide if they are good enough that there is no need to ask Question 1 again. In the present case all the answers were within the range of 1,5 to 2,5 cm (figure 1(d)).

The answers presented above were obtained during a lesson of group 1 (23 students). They are readable and easy to interpret. In this form they are seen by a teacher during a lesson.

More precise analysis can be done after class. It is a good idea to present results in the form of histograms. A teacher can choose any software he wants to create them. The histograms present the answers of 5 groups (117 students) (figure 2). There is a variety of answers given by the students. That is why while creating histograms numerical ranges were separated. The width of the range is 1/25 of the whole range of all the answers. The histograms present their amount. Using a normal distribution one can also give useful feedback (figure 3).

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Significant progress is clearly seen after each stage of the lesson. The stage which is a summary of the answers to the main question collected from all the students. It is also worth noticing some very important details. When students answered for the first time, many of them thought that to be able to observe Coriolis force, the body velocity needs to be really high. There were many answers above 100 m s⁻¹ (the highest of them even 200 m s⁻¹), which is a big divergence in comparison to the default value (around 29 m s⁻¹).

When they were given some tips and digression the students answers were much closer to the correct on in their second attempt. Analysing the histograms, we can notice that students very often give values which are a multiple of number 10. As an example, at the first attempt, 56 of 117 students gave a multiple of the number. The last conclusion which is worth emphasizing is the fact that the biggest surprise for the students was not the velocity value itself but the fact that the trajectory deviation was not directly proportional but inversely proportional.

In the example above a relation of Coriolis force to body velocity for a determined latitude was studied. The situation can be reversed and we can study an influence of latitude to determine the body velocity. Even if we distinguish between Northern and Southern Hemisphere (southcoriolis.edupython.com). The EduPython application can be used to teach many physical phenomena. It gives a teacher a wide scope of possibilities. It all depends on the algorithm and initial conditions we use.

In the first months since using EduPython we improved and made some amendments to it. Mostly, we have shown that EduPython is helpful in teachers, work. It is also positively accepted by students. It means that the tool can be found as effective and attractive for both parties. But what is special about EduPython is the fact that it combines the advantages of interactive systems and numeric methods including conducting and analysing computer simulations. Both tools are closely correlated. Values of physical quantities stated by the students determine the simulation procedure. The analysis of such simulation helps students to draw conclusions and understand the essence of issues being discussed better. EduPython is not a technical supplement of a clicker-type systems. It is a complete and independent application. The EduPython application can be used by everyone. To do it the way it is presented above you just need to visit the internet site (e.g. northcoriolis.edupython.com). There is no need to install any programs on your computer or a smartphone. All you need is a web browser. However, for those who want to use EduPython to a greater extent there is a source code on https://github.com/edupythonpzs/edupython. It needs basic knowledge of programming in Python language and using source code on your own server. The possibility to modify it gives even more opportunities. First of all, it includes the choice of initial values as well as other values that may influence the experiment simulation process. We also take into consideration the need to improve and develop EduPython, especially its thematic spectrum. Due to the fact that it is easy to use and access, the authors hope that EduPython will be used by a growing number of teachers. They also hope for constructive opinions and new ideas. This will make it possible to develop the application faster.

The authors would like to thank Professor Jerzy Zioło (Department of Physics, University of Silesia, Poland) for his valuable feedback.