Python-based simulations of the probabilistic behavior of random events for secondary school students

 
  EURASIA Journal of Mathematics, Science and Technology Education, 2022, 18(9), em2149 
    ISSN:1305-8223 (online) 
  OPEN ACCESS  Research Paper  https://doi.org/10.29333/ejmste/12309 
 
 
 
© 2022 by the authors; licensee Modestum. This article is an open access article distributed under the terms and conditions of 
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/). 
 [email protected] (*Correspondence)   patcharee.[email protected]   [email protected]   [email protected]
 [email protected]  
Python-based simulations of the probabilistic behavior of random events for 
secondary school students 
Supot Seebut
 
1*
  , Patcharee Wongsason
 
1
  , Dojin Kim
 
2
  , Thanin Putjuso
 
3
  , Chawalit Boonpok
 
4
   
1
 Department of Mathematics Statistics and Computers, Ubon Ratchathani University, Ubon Ratchathani, THAILAND 
2
 Department of Mathematics, Dongguk University, Seoul, SOUTH KOREA 
3
 School of General Science, Rajamangala University of Technology Rattanakosin, Prachaub Khiri Khan, THAILAND 
4
 Department of Mathematics, Mahasarakham University, Mahasarakham, THAILAND 
Received 22 June 2022 ▪ Accepted 1 August 2022 
 
Abstract 
Simulation modeling is an effective tool for solving problems that cannot be explained analytically 
or when data cannot be collected. This is done by simulating the observed behavior of a problem 
under  study  using  a  computer  program.  In  math  education,  this  can  develop  knowledge  and 
fundamental competencies of simulation modeling at a higher level and foster its applications in 
everyday life. This study created learning activities for secondary school students to simulate the 
probabilistic behavior of random events using Python. 28 grade 12 students took part in these 
activities using appropriate scaffolding strategies and a powerful mathematical tool, Python. After 
completing the activities, student competency in simulating the probabilistic behavior of random 
events with Python was evaluated using rubrics and the factors of student enjoyment, perceived 
value,  interest,  and  self-efficacy  were  determined  through  a  Likert-scale  questionnaire.  The 
assessment results showed that the activities had a positive effect on student competencies and 
emotions.  The  outcomes  of the  study  can  serve guidelines  for teachers  who  are  interested  in 
expanding the results for further student development. 
Keywords:  mathematical  modeling,  simulating  probabilistic  behavior,  simulation,  simulation 
modeling 
 
INTRODUCTION 
Mathematical  model  is  the  application  of 
mathematics  to  explain  observable  phenomena.  If  a 
mathematical  model accurately  describes or represents 
the phenomenon, it can be extraordinarily useful in any 
field.  Consequently,  research  is  being  conducted  to 
investigate  the  learning  management  process  in 
mathematical  modeling.  This  endeavor  began  with 
research  on  mathematical  modeling  in  elementary 
(English,  2012;  Kazak  et  al.,  2018;  Patel  &  Pfannkuch, 
2018;  Shahbari  &  Peled,  2017)  and  secondary  schools 
(Balakrishnan  et  al.,  2010;  Krutikhina  et  al.,  2018; 
Stillman, 2010). The objective is to develop the learners’ 
ability  to  create  mathematical  models  that  solve 
everyday problems (Blum & Leiß, 2006; Galbraith et al., 
2020;  Hartmann  et  al.,  2021;  Schukajlow  et  al.,  2015b; 
Wake, 2015), as well as developing student competency 
in creating mathematical models of various types. Such 
models could be deterministic (Farihah, 2019; Ortega & 
Puig,  2017;  Yanagimoto  &  Yoshimura,  2013), 
probabilistic (Frejd & Ärlebäck, 2017; Greefrath & Siller, 
2017;  Kazak,  2010;  Kotelawala,  2011),  or  dynamic 
(Blomhøj,  2020;  Kaiser  et  al.,  2011;  Leung,  2013; 
Rodríguez, 2015). This leads to proficiency in applying 
specific solutions that correspond to the type of model in 
question  and  provide  a  foundation  for  studying 
mathematical models at a higher level. 
Simulation modeling is another fascinating modeling 
technique. It is crucial in real-world situations where the 
behavior of the problem cannot be explained analytically 
or  where  data  cannot  be  collected  directly.  This  is 
because analyzing such real-world scenarios is difficult, 
expensive, and time-consuming. Using the appropriate 
computer  technique,  modelers  create  simulations  that 

Seebut et al. / Python-based simulations of the probabilistic behavior of random events

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mimic the behavior observed in actual problems. The

outcomes of the simulation study should then be used to

address the appropriate issues (Kin & Chan, 2011; Maria,

1997; Tobrawa et al., 2022; Volosencu & Ryoo, 2022;

Zárate Ceballos et al., 2021). Previously, simulations had

to be done manually, which was inefficient. However,

currently here are a variety of computer programs

available for simulation. This simplifies model

development. Therefore, computer simulation for

behavioral modeling is widely used (Albright & Fox,

2019; Fox, 2013; Gordon & Guilfoos, 2017).

It was discovered, however, that there were not many

school-level learning management systems that

prepared students with a foundational competency in

simulation modeling. Students may participate in

simulations of the probabilistic behavior of random

events, if deemed appropriate. It is highly likely that

such simulations will serve as a starting point for

developing fundamental competency in simulation

modeling (Giordano et al., 2013). This is because

simulating the probabilistic behavior of random events

is an important foundation for simulation modeling. It is

linked to the probability content that students have

already studied (Giordano et al., 2013).

Another factor to consider when deciding to simulate

the probability behavior of random events is the

computer program that will be used as a simulation tool.

Learning management research seeks to use a free

program to make it easier for those interested in research

findings to apply them in the classroom. Python is a

powerful mathematical tool that can be used in

simulations (Gordon & Guilfoos, 2017; Liu, 2020;

Tendeloo et al., 2019). This program is unique in that it is

free and has many useful features. It is convenient to use

without the need to install programs on the computer,

while the code and results are automatically saved in

cloud storage. Since Python can run online programs on

a variety of devices, including smartphones, tablets,

portable computers, and personal computers, its use in

learning activities based on simulating the probability

behavior of random events improves learning

management.

Moreover, the inclusion of Python in this learning

environment has alleviated some of the common

criticisms of using the program, which is that lesson

designers often create automated instructions for

learners to follow to get results, which affect the learning

efficacy of the learners relatively little. Although it is

convenient to use and has many functions to choose

from, the process of using it is not an automatic button

press, but users will have to start by analyzing problems

that require the use of Python in ways that help find

answers. It converts problems into mathematical and

logical forms. Use the mathematical and logical models

created to write an algorithm, such as pseudo-code, are

necessary before implementing the actual program code.

Running the output that will bring back the original

problem description. This, in addition to promoting on-

demand competence, is also an important motivation for

developing the initiative to adopt mathematics in a

STEM-oriented manner, enhancing mathematical and

digital literacy and fostering computational competence.

This study developed learning activities for

secondary school students that simulate the probabilistic

behavior of random events to provide them with the

knowledge and basic competency required for more

advanced studies in simulation modeling and

applications to real-world problems. Following

completion of an activity, student competency in

simulating the probabilistic behavior of random events

was evaluated using a rubric whose scores could be

analyzed and interpreted both quantitatively and

qualitatively. Furthermore, a Likert-scale questionnaire

was used to evaluate student enjoyment, values,

interests, and self-efficacy. The evaluation results will be

used to improve the activities, making them more

beneficial and applicable to those who want to apply

learner development in other contexts.

SIMULATING THE PROBABILISTIC

BEHAVIOR OF RANDOM EVENTS USING

PYTHON

Monte Carlo simulation is a popular and well-known

technique that generates results based on the probability

of an event. The probability of each event is proportional

to its likelihood. Simulations are run using a random

sampling method, but theoretical sampling based on

random numbers is used instead of sampling actual

data. In this randomization, the data distribution is

sampled to match or closely resemble that of the actual

data in the problem scenario. Random events that

Contribution to the literature

• A simulation model is an important specific mathematical model for dealing with contextual problems

when the problem cannot be explained analytically or data cannot be directly collected .

• The development of subject-specific competencies in simulating the probabilistic behavior of random

events with Python is one approach to introducing students to simulation modeling. This serves as basic

knowledge and competency to learn at a higher level and to apply these skills in everyday life.

• Student competency in simulating the probabilistic behavior of random events with Python was enhanced

through the development of specific learning activities.

EURASIA J Math Sci Tech Ed, 2022, 18(9), em2149

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students have already studied are highlighted for the

problem situations in this activity.

The activities listed in Table 1 were designed for

students based on a previously presented academic

concept of simulating the probabilistic behavior of

random events (Albright & Fox, 2019; Fox, 2013;

Giordano et al., 2013; Gordon & Guilfoos, 2017).

It is necessary to describe how to simulate the

probabilistic behavior of random events. A simulation of

simultaneously flipping two coins can be done according

to the steps listed below. The sample space for random

occurrences can be described as

.

A sample space is often required that has two possible

random outcomes with equal probability. This is

referred to as a “fair coin” random event that simulates

a coin toss. The function,  below, is similar.

However, it allows for four outcomes, each with a

probability of 0.25. Consider the set  to create a

simulated function as



















Then apply the simulation function to write the

simulation algorithm as follows in Figure 1.

Table 1. Activities for learning about simulation of probabilistic behavior of random events. Each activity yields a number

of occurrences and a probabilistic proportion of each outcome of the simulation

Simulation activity

Description

Type of activity

Tossing dice

Create a simulation of the probabilistic behavior of tossing a die

using Python.

Demonstration by a

teacher

Flipping two coins

Create a simulation of the probabilistic behavior of flipping two

coins with Python.

Demonstration by a

teacher

Tossing a coin & a die

Create a simulation of the probabilistic behavior of tossing a

coin and a die with Python.

Teachers led students to

practice.

Determining a random event

Create a simulation of the probabilistic behavior of random

events as determined by each group of students with Python.

Group activity

Picking a card

Create a simulation of the probabilistic behavior of randomly

picking a card numbered 0-9 with Python.

Individual activity

Flipping three coins

Create a simulation of the probabilistic behavior of flipping

three coins with Python.

Evaluation of

competency in

simulating probabilistic

behavior of random

events with Python

Figure 1. An algorithm for simulating a simultaneous flip

of two coins

Seebut et al. / Python-based simulations of the probabilistic behavior of random events

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During the simulation, Python commands can be

used for simulation as shown in Figure 2.

After executing the program, the following

simulation results in Figure 3 for a two-coin flip can be

obtained.

From this example, the sub-competencies in

simulating the probabilistic behavior of random events

with Python are analyzed and summarized in Figure 4.

SCAFFOLDING

Since students are unfamiliar with the learning

activities that involve simulating the probabilistic

behavior of random events, the instructor must

incorporate a support process into the learning

management activities to increase student abilities to

achieve the set goals. Scaffolding is an effective learning

management technique when students must learn

something new or difficult. We can help our students

help one another by demonstrating, acting out, or using

prompting questions to promote learning. A rescue goal

is set to help learners who are unable to work alone at

first, until they are able to finish a task independently.

When learners gradually improve their ability to

complete activities on their own, the complementary

learning process shifts and declines (Schukajlow et al.,

2015a; Stender & Kaiser, 2015; Tropper et al., 2015). A

scaffolding process for learning activities to simulate the

probabilistic behavior of random events can be thought

of as discussed below.

Classroom Scaffolding

Classroom scaffolding involves simultaneously

augmenting learning by everyone in the classroom. The

instructor explains the concepts and procedures for

simulating the probabilistic behavior of random events

with Python. Then, he demonstrates how to use Python

to simulate probabilistic behavior and walks learners

through the process. Learning is arranged utilizing a

Facebook group as a host of the M30225 Mmodeling

technology course while performing research on the

spread of COVID-19. After all students have joined the

Facebook page, they are able to get news and crucial

information regarding the courses here. Instructors post

instructional materials and a link to a Zoom classroom

on the Facebook group as part of the learning

management process. The teacher then administers the

course using Zoom, which makes emulating the Python

process simple using Google Collaboratory. While the

teacher instructs, shows, and guides the students in

practice, every phase of simulating the probabilistic

behavior of random events with Python is recorded from

Zoom. The teacher posts the recorded video on the

Facebook group for learners to review after the session.

Figure 2. Python code for a computer simulation of flipping

two coins

Figure 3. Simulation results of two coins being

simultaneously flipped

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Group Scaffolding

Group scaffolding involves augmenting learning

through group activities. Here, the teacher guides

groups of learners. The outcome of this cooperative

learning exercise will be shared so that students may

learn together. Instructors publish instructional

materials and post a Zoom classroom link on the

Facebook group, after which he runs the course using

Zoom. An instructor introduces students to objects that

behave in a probabilistic manner such as coins, dice, and

cards. The learners are place in groups in the Zoom break

out room, each with its own set of probabilistic situations

to simulate. Probabilistic media is supplied by the

instructor or other probabilistic media encountered by

the learner is used design a simulation. Students show

their work via video clips and submit it using Google

forms, which the instructor then posts to the Facebook

group. Then, he fixes the presentation footage and posts

it to the Facebook group for everyone to learn. Students

work in the Zoom break-out room to define a random

event, create a sample space, and create simulation

functions during this portion of the learning process.

Writing a simulation method, coding it in Python for

simulation, and generating video presentations are all

outside-of-class activities.

Individual Scaffolding

Individual scaffolding is intended to supplement the

learning of individuals in this setting. Since the students

have previously learned about simulating the

probabilistic behavior of random events with Python,

the instructor is prepared to examine each student

individually in this step to determine which students

require additional instruction. A small number of

students will require assistance at some point during the

simulation, so the teacher will personally assist them.

Instructional materials are posted as is a link to the Zoom

classroom in the Facebook group as part of the learning

management process. After that, instructors schedule

their lessons through Zoom. Probabilistic behavioral

occurrences are identified. Then, using Python, each

student should create a method for simulating the

probabilistic behavior of a given random event. When

they finish, they present video recordings of worksheets

based on the instructor’s assignments and submit them

via a Google form that includes a link to submit the

assignment to the Facebook group. After that, he goes

over the work one-on-one with students to provide

feedback and information. In this section, learners use

Zoom to complete the learning process, which includes

designing a random event, building a sample space, and

developing a simulation function. Throughout the

lesson, students request additional assistance via

Facebook Messenger.

Evaluation Criteria

Considering the previously presented academic

concept of assessing modeling competency (Ferri, 2017;

Hidayat et al., 2022; Lingefjärd & Holmquist, 2005), an

assessment framework demonstrating competency and

student thinking is proposed for simulating the

probabilistic behavior of random events with Python. At

each level of the procedure, there should be evidence of

competency and critical thinking. Evaluation is

separated into five sub-competency phases, as follows:

1. S1: Competency in analyzing sample space of

random events.

2. S2: Competency in generating simulation

functions from a sample space.

3. S3: Competency in writing algorithms to simulate

the probabilistic behavior of random events.

4. S4: Competency in coding Python to simulate the

probabilistic behavior of random events.

5. S5: Competency in presenting the results of

simulating the probabilistic behavior of random

events.

Since this is an evaluation of an activity, rubric

scoring is used, which reflects each student’s level of

competency based on their performance. A Likert-scale

questionnaire was employed as an instrument for

analyzing the enhancement of enjoyment, perception of

value, interest, and self-efficacy of each learner. Based on

the previously presented academic concepts (Krawitz &

Schukajlow, 2018), four questions were used to

summarize these factors as follows:

1. Q1: I enjoy solving the problem of simulating the

probabilistic behavior of random events with

Python.

2. Q2: I think it is important to be able to solve

problems by simulating the probabilistic behavior

of random events with Python.

3. Q3: It would be interesting to solve problems of

simulating the probabilistic behavior of random

events with Python.

4. Q4: I am confident that I can solve problems of

simulating the probabilistic behavior of random

events with Python.

Figure 4. The process of simulating probabilistic behavior

of a random event and the sub-competencies required

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RESEARCH METHODOLOGY

Participants in the Research

The participants in this investigation were secondary

school students who were enrolled in a science

classroom in a university-affiliated school project. There

was a total of 28 students in grade 12 who were between

the ages of 17 and 18 years old.

Research Instruments

The research tools used in the current study included

three instruments. The first was a learning activity plan

for simulating the probabilistic behavior of random

events with Python. A competency test with an

evaluation rubric criterion was used for simulating the

probabilistic behavior of random events with Python.

Finally, a Likert-scale questionnaire was employed to

assess the enjoyment, perceived value, interest, and self-

efficacy of the activities.

Methods of Data Analysis

Our approach to data analysis uses the results of a

rubric assessment of competency in simulating the

probabilistic behavior of random events with Python.

The frequency of students at each level of competency

for each sub-competency is presented. Students’ mean

scores are used to summarize the overall level of

competency in each sub-competency. The mean scores

and standard deviations from the Likert-scale

questionnaire are presented to determine the impact of

the activity on learner enjoyment, perceived value,

interest, and self-efficacy.

Procedure

The study started with developing and preparing

research tools. This was followed by preparing the target

audience, running the activity by simulating the

probabilistic behavior of random events with Python

with the target audience according to the scaffolding

strategy. Finally, the results were evaluated and

analyzed to draw conclusions.

RESULTS AND DISCUSSION

The following results of a competency test and

questionnaire evaluation are presented. This is to

establish that the developed activities can enhance

learner competency in simulating probabilistic

behaviors of random events with Python in a way that

students find enjoyable, valuable, interesting, and

supportive of their self-efficacy. Students were

evaluated in their ability to simulate probabilistic

behavior of random events with Python. They simulated

the probabilistic behavior of a three-coin toss to

determine the probability of all three tosses being heads.

The rubric evaluation results can distinguish the level of

competency for each sub-competency, as depicted in

Figure 5.

From Figure 5, it can be surmised that the

competency assessment of S1 showed that most students

had excellent competency, followed by good

competency, while the satisfactory and needs

improvement levels were almost nonexistent. As for S2,

most of the students had excellent competency, followed

by the good level, with a small number of students at the

satisfactory and needs improvement levels. For S3, many

students were at the needs improvement and

satisfactory level, while only a few were good or

excellent. In S4, almost all students were at the good

level. A few students were at excellent and satisfactory

levels. Finally, in S5, the majority of students were at the

good level, followed by excellent, with only a few

students scoring satisfactory and none scoring needs

improvement.

The scores generated by individual rubrics can be

used to provide an overview of the student competency

in each of the sub-competencies needed for simulating

the probabilistic behavior of random events with

Python, as shown in Figure 6.

Figure 5. Number of students at each competency level for

each sub-competency of simulating probabilistic behavior

of random events with Python

Figure 6. Mean score for each sub-competency of

simulating probability behavior of random events with

Python

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Figure 6 shows that the mean sub-competency scores

for S1 were 3.68. Those for S2, S4, and S5 were 3.11, 2.93,

and 3.25, respectively. For S3, the mean was 2.07. Based

on the mean scores, the overall level of learner

competency in each sub competency for simulating the

probabilistic behavior of random events with Python

could be described as follows. The competency in

analyzing sample spaces of random events was excellent

while that for generating simulation functions from a set

of sample spaces was good. Writing algorithms to

simulate the probabilistic behavior of random events

was satisfactory and competency in coding Python to

simulate the probabilistic behavior of random events

was good. Finally, the competency in presenting the

results of random events was good.

Figure 7 depicts an illustration of the outcomes of

analyzing a sample space from random events. The letter

H depicts an instance of a heads coin toss while T

represents tails. The student’s work in the figure is

completely accurate. In accordance with the criteria of

the rubric, the assessment results were given a score of

4, which corresponds to the level of excellent.

Figure 8 depicts an example of the output of

generating a simulation function from a set of sample

spaces. It is a satisfactory level for student work because

assigning 7/8≤x<1 values of the HHH simulation

function based on remark 1 may result in errors since the

simulation function cannot produce a result at x=1. So, it

should be revised to 7/8≤x≤1, and for the same reason,

x<1/8 should be revised to 0≤x≤1/8 in remark 2. As a

result, its score is 2 according to the rubric criteria.

However, the majority of the student assessments were

at a good level. This reflection is presented as a guideline

for making suggestions for improving student

performance.

Figure 9 depicts an example of the outcomes of

writing algorithms to simulate the probabilistic behavior

of a random event. Considering remark 3, the algorithm

is written in steps ordered to generate a random number

x_i but lacks a specified range for x_i. This should be

revised in step 3 to generate a random number, x_i,

where x_i  [0, 1] evaluates the result. Its score is 2 points

on according to the rubric, which is a satisfactory level.

This is due to a lack of explainability indicating that

additional practice and development is required. Aside

from that, students are unaware of the significance of

writing algorithms. They are unaware that a good

algorithm can be used to develop other programming

languages and improve programming skill. As a result,

there is a lack of attention to detail in writing good

quality algorithms. When teachers bring the importance

of writing good algorithms to the attention of students,

it should lead to development of improved algorithms.

Figure 7. A graphical representation of a sub-competency

in analyzing a sample space for random events

Figure 8. A schematic representation of sub-competency in

generating a simulation function from a set of sample

spaces

Figure 9. A schematic representation of the sub-competency

in writing algorithms to simulate the probabilistic behavior

of random events

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Figure 10 depicts an example of coding Python to

simulate the probabilistic behavior of a random event.

Given the position of remark 4, the code should be

changed from (0, n) to (1, n+1) so that the emulation

begins at 1 and ends at n due to Python’s unique

functionality that does not iterate a loop for the last

number of a specified range. The rank, (0, n), is evaluated

as 0, 1, 2, ..., n-1. So, index must be adjusted to (1, n+1) so

that the simulation sequence is 1, 2, 3, ..., n. The statement

“y=“THT” and “counterTHT=counterTHT+1” can be

left in the remark 5 condition. The other positions in the

if …, elif …, and else conditions can be modified in the

same way. Finally, the position of Remark 6 should be

changed from (1, n) to (1, n+1) because (1, n) will execute

loops 1, 2, 3, ..., n-1, failing to execute that last cycle.

However, this is a minor error. As before, when we

simulate large n values, better simulation results are

achieved. This is completely an aesthetic factor, so, the

assessment results in a score of 3 points according to the

rubric, which is at a good level.

Figure 11 depicts an example of presenting the results

of simulating the probabilistic behavior of a random

event. Remark 7 reveals that students used only 20

simulations to reach a conclusion. A greater number of

simulations with large n values will result in better

results. As a consequence, the assessment score is 3

points based on the rubric criteria, which is a good level.

The results reflect the success of activities to promote

learners’ competency in simulating the probabilistic

behavior of random events with Python. The factors that

led to this result include, first and foremost, the learners’

ability to perform activities. This is because only

academically gifted students are chosen to participate

the science classrooms in a university-affiliated school

project. Therefore, they are academically exceptional.

The second critical aspect is scaffolding strategic

planning, which involves pre-planning scaffoldings,

both at the micro- or macro-levels.

Figure 10. A schematic representation of the sub-competency of coding Python to simulate the probabilistic behavior of

random events

Figure 11. A schematic representation of sub-competency in

presenting results of simulating the probabilistic behavior

of random events

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Anticipating the challenges that students will face

when simulating the probabilistic behavior of random

events with Python is necessary. It has a significant

impact on increasing competence to achieve goals. As a

result, the success of promoting competency in

simulating the probabilistic behavior of random events

with Python is affected by the development of a good

scaffolding strategy. This is consistent with research on

the significance of scaffolding strategies in promoting

mathematical modeling competencies (Geiger et al.,

2022; Greefrath & Vorhölter, 2016; Schukajlow et al.,

2015a). The final, but very important element is Python,

a mathematical tool used to simulate the probabilistic

behavior of random events. Greefrath and Siller (2017)

emphasized the significance of embracing digital

technology. It is used in mathematical modeling

processes, particularly simulation modeling, which

takes advantage of Python’s ease simulating the

probabilistic behavior of random events. Furthermore,

Rodríguez Gallegos (2015) and Rodríguez Gallegos and

Quiroz Rivera (2015) concluded that selecting the

appropriate digital technology for mathematical

modeling activities can improve the modeling

performance of learners. The use of Python for

simulating the probabilistic behavior of random events

resulted in positive outcomes for learner competency, as

data analysis of the activities revealed. All of these

elements are essential to learning activities designed to

promote learner competency in simulating the

probabilistic behavior of random events with Python.

The mean and standard deviation of the analysis of

the developed activities on enjoyment, perceived value,

interest, and self-efficacy from the Likert scale

questionnaire were computed to determine the effect of

this activity on these four domains, as shown in Table 2.

Based on their responses to the questionnaire, the

students agreed that the activity was enjoyable. In terms

of value, the majority of students strongly agreed that

this activity was worthwhile. The majority of students

agreed that the practical activities piqued their interest.

When asked about their self-efficacy, they all agreed that

the activities gave them confidence in their ability to use

Python to simulate the probabilistic behavior of random

events. The results of the questionnaire indicate the

success of the activities in simulating the probabilistic

behavior of random events with Python. Additionally, it

positively affected student enjoyment, perceived value,

interest, and self-efficacy. Instructional management

that focuses on learners is very important. These

characteristics are consistent with organizing learning

activities through group processes, learning assistance,

and empowerment strategies (Davadas & Lay, 2018;

Schukajlow et al., 2012).

CONCLUSIONS

The goal of developing learners with fundamental

competency and knowledge for simulating the

probabilistic behavior of random events with Python

was achieved. This is a significant model with unique

characteristics that require effective application to real-

world problems. In these cases, there is uncertainty

regarding the probability of the observed behavior. To

drive the required baseline competency for students to

accomplish simulation modeling at a higher level,

learning activities about simulating the probabilistic

behavior of random events with Python were

developed. These activities encourage students to

practice the simulation process until it becomes a

competency so that they can continue in the study of

simulation modeling at a higher level and to apply

simulation modeling in real-life situations. The 28 grade

12 students in the science classrooms of a university-

affiliated school project served as the study’s target

group for examining the effects of activities on

competency development. Students completed a

subjective test using a rubric at the end of the activity to

assess how well the activity affected their competency in

simulating the probabilistic behavior of random events

with Python. Additionally, the students provided

information via a Likert-scale assessment that asked

them to reflect upon how the activity affected their

enjoyment, perceived value, interest, and self-efficacy.

The assessment results revealed that learning activities

involving simulating probabilistic behavior with Python

were positively evaluated in both the cognitive and

affective domains. Student competency in simulating the

probabilistic behavior of random events using Python

was more than satisfactory. They agreed that practicing

activities increases their enjoyment, perceived value,

interest, and self-efficacy. All of these are necessary for

continued development of learners in simulation

modeling. The activities of the current study are deemed

successful because they achieved the goal of developing

learners.

Table 2. The results of the questionnaire on learning activities for simulating the probabilistic behavior of random events

with Python on learner enjoyment, perceived value, interest, and self-efficacy

Item for evaluation

Average

Implication

I enjoy solving problems simulating the probabilistic behavior of random events with Python.

4.29

0.95

Agree

I think it is important to be able to solve problems by simulating the probabilistic behavior of

random events with Python.

4.50

0.72

Strongly

agree

It is interesting to solve problems simulating probabilistic behavior of random events with Python.

4.08

1.06

Agree

I am confident that I can solve problems simulating probabilistic behavior of random events with

Python.

3.63

1.31

Agree

Seebut et al. / Python-based simulations of the probabilistic behavior of random events 
 
10 / 12 
Author contributions: All authors have sufficiently contributed to 
the study and agreed with the results and conclusions. 
Funding: This study was supported by Faculty of Science, Ubon 
Ratchathani University. 
Declaration  of  interest:  No  conflict  of  interest  is  declared  by 
authors. 
Data  sharing  statement:  Data  supporting  the  findings  and 
conclusions  are  available  upon  request  from  the  corresponding 
author. 
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