



















































Journal of Green Learning


Journal of Green Learning, e-ISSN 2807-890X 

Vol. 3, No. 1, June 2023, pp. 46-53. 
DOI: 10.53889/jgl.v3i1.216 

-------------------------------------------------------- 

 

 

Development of the constructionist concept in conjunction with 

the Bar model for a mathematics course 
 

Chirarat Malai1 & Parichart Prasertsang1 

 
1 Faculty of Education, Roi Et Rajabhat University, Thailand  

  

Article Info  ABSTRACT 

Article history: 

Received May 17, 2023 

Revised   June 20, 2023 

Accepted June 26, 2023 

 

 This research aims to find out the effectiveness of the plan to 

organize the mathematics course in the first grade according to 

the constructivist concept in conjunction with the Bar model. 

The results of the study found that the effectiveness of the plan 

to organize the mathematics was most suitable level. The results 

of the first grade mathematics course based on the constructivist 

concept and the Bar model. It has an average assessment result 

of 4.65, the most appropriate level. Ability to solve math 

problems of students before the activity, the student passes the 

criteria. 70% of 2 students out of 4 students (50%) had an 

average of 66.25% and a standard deviation of 2.55%. 70% of 

people, or 100%, have an average of 78.33% and a standard 

deviation of 1.63%. 

 

Keywords: 

Bar model 

Constructivist theory 

Mathematics 

Problem-solving  

 

This is an open access article under the CC BY-SA license. 

 
Corresponding Author:  

Parichart Prasertsang 

Faculty of Education 

Roi-Et Rajabhat University  

Thailand 

Email: Parichart.p@reru.ac.th 

 

1. INTRODUCTION  

 Although mathematics is important, in reality, mathematics in Thai schools has 

experienced significant regression. When considering the scores of the Basic National 

Educational Test (O-NET), it was found that the average was low in all subject groups, and the 

scores from the PISA test were lower than in many other countries with similar development 

levels. These problems are caused by limitations in the curriculum and teaching system that 

emphasize content and memory rather than skill development and competency, resulting in a 

lack of creativity in solving problems, which is a challenge in the current Thai education system 

(Changthong et.al., 2020).  

In terms of learning management goals, mathematics subject groups Ban Thonglang 

Noi School Academic Year 2019. Students have learning achievement in the mathematics 

subject group by 31.25  percent in 2020 has 65 percent and 57.14 percent in 2021 can be seen 

as below the 70 percent threshold set by the school. The researchers analyzed the classroom 

and found that 50 percent of Grade 1 students. Understanding and using the properties of 

equality and properties of numbers to analyze and solve problems using single-variable linear 

equations, falling below the 70% threshold, which is the basis for solving other mathematical 

https://creativecommons.org/licenses/by-sa/4.0/


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problems. Most problems arise from students not being able to create sentences, symbols, or 

equations from the problem.  

Learning mathematics for students is becoming very problematic when a problem is 

found, it is not possible to analyze what it wants to do, and it cannot find the desired value. 

Because it requires knowledge, reading, and interpretation to find words and mathematical 

calculations (Verschaffel et.al., 2020). Students must have a background in mathematics and be 

able to analyze math problems very well. Transforming the learning process to develop Thai 

people into complete human beings in the 21st century focuses on the 3Rs and 8Cs skills 

(Prachagool & Nuangchalerm, 2021). Mathematical problem-solving skills are process skills at 

the heart of mathematics instruction, and students should be trained to develop problem-solving 

skills. In order to be able to apply knowledge, one must learn things that will bring knowledge 

and apply it in life (Hasibuan & Fauzi, 2019; Ergen, 2020; Nur et.al., 2020; Pambudi et.al., 

2020).  

In addition, classroom instruction often focuses solely on building numerical skills. 

Emphasis is placed on children practicing skills over and over again, even if they have quick 

numeracy skills. But it is not enough because students will lack the skills to interpret problems. 

The use of mathematics to solve problems increases as children learn mathematics in higher 

grades, which is more complicated to understand (Genc & Erbas, 2019; Yayuk & As' ari, 2020). 

It requires more logic to solve problems, children will begin to learn mathematics but will not 

understand it. This is in line with Piaget's theory of intellectual development, which emphasizes 

the importance of understanding nature and children's development rather than stimulating them 

to develop faster (Fuady & Rahardjo, 2019; Sugianto et.al., 2022). 

 Organizing learning activities based on the concept of constructivism, problems that 

generate intellectual conflicts, that is, prior knowledge and new perceptions that are 

inconsistent. To allow students to observe information, compare it with previous knowledge, 

and search for answers to reduce intellectual conflict through planning, action, and social 

constructivism. The opportunity to build their own knowledge based on the concept of 

knowledge creation is a concept that can be used in student-centered teaching and learning. By 

allowing students to think and build knowledge on their own using important processes. 1) 

Allowing students to revise their previous knowledge; 2) Allowing students to 

acquire/seek/collect/experiential information by themselves using process skills; 3) Allowing 

students to study, think critically, and create meaningful information or experiences by 

themselves using various process skills; 4) Allowing students to summarize and organize 

knowledge or information or structuring knowledge as well; and 5) Allowing students to 

express what they learn in a variety of ways. In the field of pedagogical evaluation (Jonassen, 

1992). 

Since learning according to this constructivist theory depends on the interests and the 

creation of different meanings of individuals. The resulting learning outcomes are therefore 

varied in nature. Therefore, evaluation requires a variety of approaches. Mathematics 

instruction has a specific characteristic in its content. There is only one answer to the problem. 

In order to achieve the accuracy of mathematical problem solving, problem-solving strategies 

are needed to support learning activities. The Bar model has been used to improve mathematics 

learning since 2007 (Osma et.al., 2018; Lowrie et.al., 2019; Rosé et.al., 2019). Teachers 

approve of it, and it originated in Singapore. Because it has been used to solve math problems 

for a long time. It is a learning management materials that are explained using diagrams to 

accompany problems. In the United States, bar models are used to solve counting problems by 

training students to draw rectangles or model bars representing quantities and the relationship 

between quantities in the problem (Morin et.al., 2017; Sevinc & Lizano, 2022).  

Drawing bar models improves mathematical problem-solving abilities and develops 

mathematical thinking abilities as they are concrete solutions to explain abstract data 



 

48 

 

relationships. It is presented through rectangular models to allow students to visualize and better 

understand the relationship between what the problem assigns. It is also a way to encourage 

students to develop their knowledge in solving advanced problems (Baysal, & Sevinc, 2022). 

This makes it possible to see the relationship between all the given information and can link to 

the answer to the question that the problem wants to know clearly. Students can analyze 

problems. It is linked to students' mathematical analysis and drawn into a bar model, which 

allows students to solve problems easily and accurately. For that reason, the importance of 

applying learning activities based on constructivist theory with bar models to adapt learning 

activities at all grade levels in accordance with 21st century learning management and to guide 

learning activities to help students develop their ability to solve math problems. 

  

2. METHOD  

This research employed an action research, the procedure can be drawn as following. 

Plan: The research plan consists of creating a plan for learning activities and preparing 

research tools. 

1.1 Survey students with math problem-solving abilities using the mathematical 

problem-solving ability assessment. The exponential numbe), which is the content that students 

have already learned in the first semester of the academic year 2022, only explored the first 

practical cycle. In the next practice cycle, the results of the analysis and problems from the end 

of the practice cycle will be used to plan the next learning activity. 

1.2 Study the core curriculum of basic education B.E. 2008 (Revised Version 

2017), curriculum of the Ban Thonglang Noi School, and study literature and research related 

to the organization of learning activities using the learning management model based on 

constructivist theory together with bar models that promote the ability to solve mathematical 

problems. Analyze learning standards, indicators, and study time using one-variable linear 

equations. Grade  1 Prepare 10 learning units and 10 learning activity plans. Course designed 1 

hour per plan, including 10  hours of class time Present the written learning activity plan to five 

experts. The acceptable assessment criteria must be from 3.51 to 5.00 or higher, with an average 

assessment result of 4.63. In addition, experts give advice on how to adapt the example scenario 

to real-life situations. To encourage meaningful learning 

1.3 Study literature and research related to the organization of learning activities 

using the learning management model based on constructivist theory together with bar models 

that promote the ability to solve mathematical problems. The criteria for evaluating learning 

activities from five experts that are acceptable must have an average of 3.51–5.00 or higher, 

which has an average assessment result of 4.65. Organizing learning activities based on 

constructivist theory together with bar models consists of 5 steps. as follows 

1. Preparing is an introductory step to the lesson. It is an interest-building step to 

encourage students to be ready to review their previous knowledge. The purpose 

of each lesson is to inform the students of their learning objectives in order to 

link them to new knowledge creation. 

2. Construct is the stage where students will face the problem situation and solve 

it on their own. The teacher presents the problem in the form of an activity sheet. 

Students use their knowledge, experience, and understanding. Plan a solution by 

drawing a model bar. Determine how to perform mathematical operations. Write 

one-variable linear equations. Systematically execute the plan. The answers 

obtained by searching for answers are summarized manually. 

3. Interaction: Divide students into small groups. Groups of 2 Discuss ways to 

solve each other's problems. Exchange ideas in small groups, help each other 



49 

 

 

investigate, and select appropriate solutions to problems. Facilitated by teachers 

Encourage the exchange of learning in groups. 

4. Guidelines: The representative of the subgroup will propose solutions to the 

whole class. Discuss, question, propose group guidelines, and verify accuracy 

and reasonableness. The teacher presents an approach that the student has not 

yet presented and compiles a reasonable, correct solution that the whole class 

accepts. Discussion the advantages and limitations of each option and then 

summarize the best approach. 

5. Predicate is the stage where students work together to summarize the concepts 

and principles and ideas for the subject learned. The teacher provides additional 

briefing so that students can examine their ideas and correct their principles. 

                1.4 Study the school curriculum and analyze the content. Mathematics Fundamental 

Mathematics Units C21102 Grade 1 Subject: One-variable linear equations analyze the 

relationships between material strands to serve as a framework for constructing subjective 

mathematical problem-solving capabilities. Establish a scoring measure of subjective 

mathematical problem-solving abilities (Institute for the Promotion of Teaching Science and 

Technology, 2012: 130). Conduct the creation of mathematical problem-solving ability 

assessments. subjective model in accordance with a total of 20 learning objectives. The 

assessment of the ability to solve the created mathematical problems was presented to five 

experts to determine the consistency of the content with the learning outcomes as a guideline 

for improvement to be more appropriate.Select items with an index value from 0.5 to 1.00 that 

fall within the criteria of consistency between the question and learning objectives. We selected 

10 questions that clearly meet the learning objectives and cover the most content for this 

research, divided into 5 questions per operating cycle. 

  Action: It is the process by which the researcher acted according to the plan of the 

learning activities created. Plans for learning activities based on constructivist theory in 

conjunction with Bar Model Re: One-variable linear equations of 1st graders that promote their 

ability to solve mathematical problems 10 plans Two operating circuits are defined according 

to the structure of the content of a single-variable linear equation. 

Observation: This is the observation that occurs in the teaching action, and the 

researchers also make the observation.Record all events by observing the operation, listening 

to the results of the operation, and using the following tools. The student behavior observation 

model to observe the target students during the activities in each learning plan. Test the ability 

to solve mathematical problems with the target students after the end of each activity cycle. 

Reflection: We evaluate the organization of learning activities based on constructivist 

theory in conjunction with the bar model. Promote the math problem-solving abilities of Math 

1 students by analyzing all students' math problem-solving abilities compared to the 70% 

threshold. This will use the information obtained to help design the next operating circuit to be 

more efficient. 

  

3. RESULT AND DISCUSSION  

The students in the target group improved their ability to solve math problems after class 

a lot more than before class, and they were very chaotic. Through appropriate allocation of time 

to solve problems and behavioral observation, it is found that students have the behavior to 

show the ability to solve problems. According to the mathematical search of items that need to 

be observed for behavior, there is a higher incidence of behavior in each learning activity plan 

(Figure 1). 

 



 

50 

 

 
 

Figure 1 Comparison of students’ mathematical problem solving ability 

 

Figure 1 shows that students have the ability to solve mathematical problems according 

to the items they want to observe, and the rate of behavior increases with every learning 

management plan. Identify what the problem is and what you want to know. Plan a solution by 

drawing a model bar. Display each variable with the appropriate symbols. Performing 

mathematical operations and write one-variable linear equations. It can proceed according to 

the laid-down guidelines by showing how to systematically perform mathematical operations, 

finding the result of a single-variable linear equation. It also summarize the results of the 

solution according to what you want to know (Willyarto et.al., 2015; Osman et.al., 2018; 

Ramasamy & Puteh, 2018). Bar models are drawn to see concretely, easier to look at solutions 

It was also a mutual aid for friends to practice presenting in front of the class. 

The ability to solve math problems of 1st graders was learned by organizing learning 

activities based on constructivist theory in conjunction with model bars. It was found that 70 

percent of all students had the ability to solve math problems. This is due to the plan of learning 

activities based on constructivist theory in conjunction with effective model bars. focusing on 

solving mathematical problems that aim for students to create new knowledge by applying 

experience, knowledge, understanding, and ideas to solve math problems. The key steps are:  

• A preliminary step to the lesson (Preparation) to generate interest To encourage 

students to be prepared. Review previous knowledge and inform students of the 

objectives of learning each hour so that they can relate to the creation of new 

knowledge.  

• Construct is the stage where students will face problems and solve them on their 

own. The teacher presents the problem in the form of an activity sheet. Students 

use their knowledge, experience, and understanding. Plan a solution by drawing 

a model bar. Determine how to perform mathematical operations. Write one-

variable linear equations. Systematically execute the plan. The answers obtained 

by searching for answers are summarized on their own.  

• Cognitive reflection in small groups (Interaction) divides students into small 

groups. Groups of 2 Discuss ways to solve each other's problems. Exchange 

ideas in small groups, help each other investigate, and select appropriate 



51 

 

 

solutions to problems. The teacher facilitates and encourages the exchange of 

learning in the group.  

• Guidelines the representative of the small group will present the solution to the 

problem to the whole class. Discuss, question, propose group guidelines, and 

verify accuracy and reasonableness. The teacher presents an approach that the 

student has not yet presented and compiles a reasonable, correct solution that the 

whole class accepts. Discuss the advantages and limitations of each choice and 

then summarize the best approach.  

The teacher provides additional conclusions so that students can examine their ideas and 

correct principles to measure their ability to solve mathematical problems, which can be 

measured by doing a mathematical problem-solving ability assessment created by the 

researcher that covers the students' abilities in four aspects: 1) Understanding the problem, i.e., 

the student analyzes the problem, 2) Problem-solving, planning students plan to solve problems 

by drawing bar model (Schoenfeld & Kilpatrick, 2008; Kho et.al., 2014; Olteanu, 2017). 

Display each variable with the appropriate symbols. Choose a mathematical operation method 
and write a one-variable linear equation, 3) Plan execution requires that students follow the 

guidelines laid down by showing how to systematically perform mathematical operations to 

find the result of a one-variable linear equation, and 4) Summary of answers: Students 

summarize the results obtained from solving problems in accordance with what they want to 

know.  

  

4. CONCLUSION  

The results of the first grade mathematics course based on the constructivist concept 

and the Bar model. It has an average assessment result of 4.65, the most appropriate level. 

Ability to solve math problems of students before the activity, the student passes the criteria. 

70% of 2 students out of 4 students (50%) had an average of 66.25% and a standard deviation 

of 2.55%. 70% of people, or 100%, have an average of 78.33% and a standard deviation of 

1.63%. 

 

5. ACKNOWLEDGEMENT  

 I would like to express my sincere thanks to Phubet Tieansri, Penpron Tipano, Prasit 

Krueadeang, Chatchapong Chueasa, and Yuthaphome Dontian who compassionately expertly 

reviews the tools as well as provides useful suggestions. We are really appriciated the students 

and teachers of Ban Thonglang Noi School, Buayai District, Nakhon Ratchasima Province, We 

would like to express our gratitude to all those involved in the study. 

 

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