



















































Journal of Green Learning


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

Vol. 1, No. 2, December 2021, pp. 41-48.  
DOI: 10.53889/jgl.v1i2.32 

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

 

 

The integration of multiple intelligences theory and TAI 

cooperative learning for teaching Calculus for  

Engineering 1 for bachelor’s degree students 
 

Chanokgan Sahatsathatsana1, Sattra Sahatsathatsana2, Wirawan Heman3  
1,3 Department of Science and Mathematics, Faculty of Science and Health Technology, Kalasin University,  

Kalasin, Thailand  
2 Department of Foreign Languages, Faculty of Liberal Arts, Kalasin University, Kalasin, Thailand 

 

Article Info  ABSTRACT 

Article history: 

Received September 16, 2021 

Revised   December 10, 2021 

Accepted December 15, 2021 

 

 The purposes of this study were (1) to compare the pre and post-tests scores of 

learning through the developed lesson plans based on the theory of multiple 

intelligences and TAI cooperative learning, and (2) to evaluate the students’ 

satisfaction on learning through the developed lesson plans based on the theory 

of multiple intelligences and TAI cooperative learning. The subjects were 41 

students of the Faculty of Engineering and Industrial Technology who enrolled 

in the Calculus for Engineering 1 subject in the first semester of the 2019 

academic year received from cluster random sampling. The research instruments 

were lesson plans, learning achievement test, and a questionnaire on students’ 

satisfaction. The results revealed that : the mean score of the post-test on the topic 

of differentiation of algebraic functions was significantly higher than mean score 

of the pre-test at the level of .05. The mean score of the students’ satisfaction on 

learning through the developed lesson plans was at the highest level. 

 

Keywords: 

Calculus for Engineering 

cooperative learning 

multiple intelligences 

TAI  

 

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

 

Corresponding Author: 

Chanokgan Sahatsathatsana 

Deaperment of Science and Mathematics 

Faculty of Science and Health Technology 

Kalasin University 

Thailand  

Email: Chanokgan.na@ksu.ac.th 

 

1. INTRODUCTION 

Research on teaching and learning of mathematics has become an area of research focusing on the teaching 

of mathematics in the past decade. Studies have indicated that teachers need to equip themselves with more flexible 

approaches (Galton & Eggleston, 1979) in the teaching of mathematics. The teaching and learning of mathematics 

is no longer regarded as only a simple and technical procedure involving teaching objectives and learning 

outcomes. Teachers are encouraged to adopt progressive teaching styles to accommodate the varied abilities of 

students, in order to enable these students to excel in their learning. Consequently, the teaching methods for 

teaching mathematics should be focused on serving the needs of learners by establishing a suitable learning 

environment for students.  

For mathematics teaching and learning, students are not only required to have knowledge of numerical 

facts, but also be adept in problem solving that are adjustable in accordance with their individual strength and 

weaknesses (Jones & Tanner, 2002). So, lessons in mathematics should be structured into three parts: a mental and 

oral introduction, the main teaching and activity and a conclusion. Effective teaching of mathematics does not 

depend on a fixed structure of instructional strategy but involves with a lively and interactive two-way process in 

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


 

42 

 

which students play an active part by answering questions and engaging in discussions, explaining and 

demonstrating their methods to others in the class where a rich set of teaching strategies is required from the 

teachers to ensure the effectiveness of the lesson (Sulaiman et.al., 2010). 

Calculus for Engineer 1 is the subject that helps to improve the thinking process and allows students to 

experience the creative thinking for self-problem solving. It is also the fundamental course for further learning in 

advanced calculus and engineering. However, there were many factors which negatively affected the teaching 

Calculus for Engineer 1 which resulted in the failure of being successful based on the goals of the subject such as 

the content of the subject itself which were overwhelming and difficult, the attitude of students towards learning 

mathematics, teaching time limitation due to the amount and difficulty, and the teachers lack of teaching techniques 

and materials.  

The researchers, therefore, were aware of the importance of the implementation of teaching techniques 

basing on the individual differences and the cooperative learning giving the students opportunities to develop 

knowledge, analyze and synthesize information, think creatively and critically, be able to search for information 

by themselves, to be continuously develop themselves, have working skills, and work with others (Parchagool 

et.al., 2016). It is utterly challenging for teachers to help students learn mathematics effectively. Teachers have to 

realize that a single teaching method is insufficient (Sulaiman, 2011). Effective teaching strategies are essential in 

ensuring a successful teaching and learning process. Individual qualities within each teacher have been recognized 

as a major influence on their capacity and ability in creating opportunities for their students to learn effectively 

(Ball & Perry, 2009).  

Discovering the effective teaching strategies that teachers are comfortable with in teaching and students 

learn with happiness and in a relaxed manner will be beneficial for learning mathematics. It is important to mention 

that all learning materials should include opportunities for students to develop their strengths and strengthen their 

weaknesses in each particular intelligence area (Lash, 2004). Therefore, it is necessary to assess the effectiveness 

of our current teaching style and consider innovative ways to improve our teaching to enhance the teaching and 

learning effect (Delaney & Shafer, 2007). Regarding the situation mentioned earlier, the researchers studied the 

theory of multiple intelligences (MI) of Howard Gardner (1983) basing on the belief of different capabilities and 

abilities of individuals resulting in the different functions of brain which affect the multiple intelligences in one 

person.  

This theory influenced on the principle of education aiming at developing the students to be complete 

persons, paying attention to individual differences, developing students based on their actual capabilities and 

aptitudes, integrating arts, self-awareness, communication, and promoting body language (Ezeh et.al., 2021). 

According to Gardner (1996), Multiple Intelligences included: Linguistic Intelligence, Logical-Mathematical 

Intelligence, Spatial Intelligence, Musical Intelligence, Bodily-kinesthetic Intelligence, Interpersonal Intelligence, 

Intrapersonal Intelligence, Naturalist Intelligence, and Existential Intelligence. The teaching that relates, connects, 

and integrates multiple intelligences can develop the intelligences of individuals regarding the potential of ones 

stimulating the learning, reducing the stress, and increasing happiness (Bullough, 2011; Keawchuer, 2014).  

The Team Assisted Individualization or TAI is the learning process which integrates the cooperative 

learning and individualized instruction. It focuses on group work. Each group consists of the multi learning ability 

including high, medium, and low abilities. The member of each group will be assigned a learning task that suites 

their learning ability. The members in the group will help each other to learn and work through sharing experiences 

for improving the learning ability, learning and working skills, and responsibilities (Adams & Slater, 2002; 

Peysner, 2021). In regards with the aforementioned, the researchers, as the lecturer in mathematics teaching 

Calculus for Engineering 1) are interested in studying the learning instruction based on the theory of multiple 

intelligences integrated with the TAI cooperative learning to improve the students’ critical and systematic thinking 

and mathematics process skills. The developed instruction was based on Limit Calculation included 3 steps which 

were : 1) Preparation 2) Teaching and 3) Formative and Summative Evaluations as illustrated in Figure 1. 

 



43 

 

 

 
Figure 1 Learning procedures 

 

2. RESEARCH OBJECTIVE 

 (1) To compare the pre and post–tests scores of learning developed lesson plans of Calculus for 

Engineering 1 subject on differentiation of algebraic functions calculation basing on the theory of multiple 

intelligences and TAI cooperative learning.  

 (2) To evaluate the students’ satisfaction on learning through the developed lesson plans of Calculus for 

Engineering 1 subject on differentiation of algebraic functions  basing on the theory of multiple intelligences and 

TAI cooperative learning. 

 

3.  METHOD  

3.1  Populations and Subjects 

The populations of this study were students of the Faculty of Engineering and Industrial Technology who 

were enrolled in the Calculus for Engineering 1 subject in the first semester of the 2019 academic year. 

The subjects were 41 students of the Faculty of Engineering and Industrial Technology who were enrolled in the 

Calculus for Engineering 1 subject in the first semester of the 2019 academic year obtained from cluster random 

sampling. 

3.2  Research Instruments 

There were 4 research instruments used in this study. The development of each instrument is as follows:

 1. The lesson plan for teaching Calculus for Engineering 1 subject on differentiation of algebraic functions  

function calculation which was developed according to the following procedure: 1) studied the course description 

of the Calculus for Engineering 1 subject and selected the topic for teaching including meaning of vector algebra 

function, examples of vector algebra function, meaning of integrals calculation, and examples of integrals vector 

algebra function calculation, 2) studied the theory of multiple intelligences and TAI cooperative learning, 3) 

developed the lesson plan, 4) tried out the lesson plan with different groups of students, and 5) revised the lesson 

plan according to problems and inconveniences found during the trials. 

2. Learning achievement test of Calculus for Engineering 1 subject on differentiation of algebraic 

functions consisted of 5 subjective items with 10 points and 30 items of 5 alternatives multiple choice questions 

with 30 points. The total was 40 points. It was tried out with another group of students to find out the item difficulty 

and the item discrimination. It was found that the item difficulty was 0.35 0 0.70 while the item discrimination 

was 0.86 respectively.  

3. The questionnaire on students’ satisfaction on learning through the learning activity developed by 

integrating the theory of multiple intelligences and TAI cooperative learning of Calculus for Engineering 1 subject. 

It was tried out with another group of students to find out the reliability. It was found the reliability was 0.74. 

3.3 Research Procedures 

The learning activity in this study were developed by integrating the theory of multiple intelligences and 

TAI cooperative learning of Calculus for Engineering 1 for Bachelor’ s degree students which could be divided 

Step 1

• Preparation
(1) Students Analysis
(2) TAI Grouping learners 

based on TAI principle
(3) Teaching through 
multiple intelligences 
principle
(4) Preparing teaching 
media and activities
(5) Develop teaching 
media and activities

Step 2

• Teaching
(1) Stimulating
(2) Teaching
(3) Summary

Step 3

• Formative and Summative 
Evaluations



 

44 

 

into 3 steps including: 1 ( preparation, 2 ( teaching, and 3 ( formative and summative evaluations which could be 

described as follow: 

Step 1 :Preparation 

(1) Students Analysis: The researchers analyzed the students through the observation, activity participation, 

interview, and taking the pre-test .The data were summarized for improving the students ’potential. 

(2) Choosing high learning ability students: The researchers selected the students who had high learning 

ability based on the results from the grade of the mathematics subjects learnt in the previous semester and the 

voluntary of students. 

(3) TAI Grouping learners based on TAI cooperative learning principle: The researchers arranged the pre-

test scores of students in descending order and used it for grouping students . Each group consisted of 4 students 

including 1 high learning ability student, 2 medium learning ability students, and 1 low learning ability student as 

illustrated in Figure 2. 

 

 

 
Figure 2 Grouping Process 

 

(4) Teaching through multiple intelligences theory: The researchers developed the lesson plans on of 

Calculus for Engineering 1 subject on differentiation of algebraic functions  calculation based on the theory of 

multiple intelligences and TAI cooperative learning according to the following steps :1 (studied the course 

description of the Calculus for Engineering 1 subject 2 (studied the theory of multiple intelligences and TAI 

cooperative learning 3 (developed the lesson plan 4 (tried out the lesson plan with a different group of students 

and 5 (revised the lesson plan according to problems and inconveniences found during the trials. 

 Step 2 :Teaching 

The researcher taught the students through the teaching steps of the developed lesson plans on of Calculus 

for Engineering 1 subject on differentiation of algebraic functions  calculation based on the theory of multiple 

intelligences and TAI cooperative learning including 1) using questions to stimulate the students’ interest in the 

warm up to relate to the new topic with their prior knowledge, experiences, and expectations, 2) teaching the 

content by explaining (Linguistic Intelligence), using gestures (Bodily-kinesthetic Intelligence), using numbers 

(Logical-Mathematical Intelligence), using pictures (Spatial Intelligence), and practicing calculation individually 

(Intrapersonal Intelligence), and 3) summarizing the learning by working in groups (Interpersonal Intelligence) to 

present the summary of what they have learned, the importance of what they have learned, how to apply what they 

have learned to real life situations, how to integrate what they have learned with other subjects, how what they 

have learned will help them live happily and work successfully (Existential Intelligence) in the future through the 

mind map of animals or trees (Naturalist Intelligence), and stimulating students to cover famous musical 

compositions with the content of what they have learned (Musical Intelligence). 

Step 3  :Formative and Summative Evaluation 

There were two kinds of evaluations of this study namely formative evaluation and summative 

evaluation .After the teaching of each unit was done, the quiz was administered to students to verify their 

understanding as a formative evaluation .The scores were analyzed and the results of the analysis were employed 

for improving the lesson plans in the nest unit .The post-test was used as a tool for summative evaluation .The 

scores of summative evaluation were used to analyze for checking the students ’learning achievement and 

High

1 student

Medium

2 students

Low

1 student



45 

 

 

satisfaction of leaning through the developed the lesson plans on of Calculus for Engineering 1 subject on 

differentiation of algebraic functions based on the theory of multiple intelligences and TAI cooperative learning 

respectively. 

3.4 Data Collection 

 After all lesson plans were completely taught, the data were collected from according to the following 

steps : 1) the researchers administered the learning achievement test (post–test) on differentiation of algebraic 

functions  calculation and the questionnaire about the subjects, and 2) the scores of the tests and questionnaire 

were statistically analyzed. 

3.5 Data Analysis 

 The results of both learning achievement test and questionnaire were gathered and analyzed through 

statistically software to find out the results of the learning achievement and satisfaction of learning through the 

developed the lesson plans of Calculus for Engineering 1 subject on differentiation of algebraic functions  

calculation based on the theory of multiple intelligences and TAI cooperative learning . 

 

4. RESULT 

The results of this study were as follows: 

 The results of the comparison of pre and post– tests scores of learning through the learning activity developed by 

integrating the theory of multiple intelligences and TAI cooperative learning is shown in the Table 1. 

 

Table 1 The comparison of pre- and post–tests scores  

Test n x̅ S.D. t Sig. 

Pre - Test 41 11.29 2.36 20.53 0.00 

Post - Test 41 31.29 5.53 

 

Table 1 presented the mean score of pre–test of learning through the learning activity developed by 

integrating the multiple intelligences theory and TAI cooperative learning which was 11.29 while the mean score 

of post–test was 31.29 respectively .This obviously shows that the mean score of post–test was significantly higher 

than pre–test at the level of .05. 

 The results of the evaluation of students ’satisfaction on learning through the developed lesson plans on 

of Calculus for Engineering 1 subject on differentiation of algebraic functions based on the theory of multiple 

intelligences and TAI cooperative learning are shown in table 2 below: 

 

Table 2 The students ’satisfaction on learnings 

No. Statements x̅ S.D. Interpretation 

Learning Atmosphere 

1 I like the learning atmosphere that students could 

be able to participate in learning process 

4.45 0.552 High 

2 I like the learning atmosphere that promoting 

students’ responsibility 

4.35 0.530 High 

3 I like the learning atmosphere that helped improve 

students’ enthusiasm  

4.76 0.585 Highest 

4 I like the learning atmosphere that allowed 

students to ask and answer questions, discuss, and 

ask for suggestions from teacher. 

4.82 0.448 Highest 

Mean score of learning atmosphere aspect 4.61 0.26 Highest 

Learning Activities 

1 I like the learning activity which is suitable with 

my ability 

4.53 0.508 High 

2 I like the learning activity which allows students 

to share their ideas in classroom 

4.62 0.595 High 



 

46 

 

3 I like the learning activity which promote thinking 

and decision making 

4.51 0.711 Highest 

4 I like the learning activity which promotes 

confidence 

4.51 0.597 Highest 

5 I like the learning activity which allows students 

to learn from multiple ways 

4.83 0.495 Highest 

6 I like the learning activity which allows to present 

knowledge in multiple ways 

4.61 0.542 Highest 

7 I like the learning activity which allows students 

to use their aptitude in learning 

4.61 0.494 Highest 

Mean score of learning activities aspect 4.60 0.28 High 

Utilizing of Knowledge 

1 I think that I can apply the knowledge that I 

learned in daily life 

4.78 0.475 Highest 

2 I think that the knowledge that I learned will help 

me work successfully  

4.55 0.708 High 

3 I think that the knowledge that I learned can be 

applied for learning in other subjects 

4.67 0.581 Highest 

4 I think that the knowledge that I learned will help 

me be able to work individually 

4.56 0.594 Highest 

5 I think that the knowledge that I learned will help 

me work as teamwork  

4.80 0.401 Highest 

                Mean score of utilizing of knowledge aspect 4.67 0.552 Highest 

Total 4.63 0.18 Highest 

 

Table 2 shows that the mean score of the students ’satisfaction on learning through the developed the lesson plans 

of Calculus for Engineering 1 subject on differentiation of algebraic functions based on the theory of multiple intelligences 

and TAI cooperative learning was 4.63 which was the highest level .When considering each aspect, it was found that the 

mean score of learning atmosphere aspect was 4.61, the mean score of learning activities aspect was 4.60 and the mean 

score of Utilizing of Knowledge aspect was 4.67 respectively.  

 

5. DISCUSSION 

The results of the study revealed that the mean score of pre-test of learning through the learning activity 

developed by integrating the multiple intelligences theory and TAI cooperative learning which was 11.29 while 

the mean score of post-test was 31.29 respectively. This obviously shows that the mean score of the post–test was 

significantly higher than pre-test at the level of .05. This might be due to the fact that learning through the 

integration of the theory of multiple intelligences and TAI cooperative learning helped students to improve their 

learning via multiple ways of teaching and learning (using all 9 intelligences). The students could learn in the way 

that they prefer as a main approach, while the other less preferable ways of teaching might be the beneficial support 

of their learning. Moreover, they could use multiple ways to present their knowledge such as song mind map, 

pictures instead of using only writing work in the traditional classroom.  

Moreover, working in group under both interpersonal intelligence and TAI cooperative learning also helped 

students to learn effectively since they can help explaining, sharing ideas, or discussing for finding the answer and 

solving problems in learning. When they feel satisfied or comfortable in learning, the results of learning are higher 

as well. This corresponds with the study of Sulaiman et.al. (2010) who stated that effective teaching of mathematics 

does not depend on a fixed structure of instructional strategy but involves lively and interactive two-way process 

in which students play an active part by answering questions and engage in discussions, explaining and 

demonstrating their methods to others in the class where a rich set of teaching strategies is required from the 

teachers to ensure the effectiveness of the lesson. Moreover, the success of the integration of theory of multiple 

intelligences with the TAI cooperative learning for teaching mathematics in this study was supported by the study 

of Serin et.al. (2009) who proposed that teachers should be aware that there is no single and absolute method in 



47 

 

 

any teaching and learning process. Regarding what has been discussed, these were the reasons why the developed 

lesson plans based on the integration of the theory of multiple intelligences with the TAI cooperative learning 

could help students get the higher learning achievement.  

 The mean score of the students’ satisfaction on learning through the developed the lesson plans on of 

Calculus for Engineering 1 subject on differentiation of algebraic functions basing on the theory of multiple 

intelligences and TAI cooperative learning was 4.61 which was the highest level. This might be the fact that the 

developed lesson plan and learning activities encouraged students to learn happily and effectively since there were 

multiple ways of both teaching, learning, and presenting knowledge are well-designed to serve the different needs 

and aptitudes of students. When they had a chance to learn in the manners that they like, they could learn happily 

and effectively. Due to the high satisfaction of students in learning, it encouraged to learn effectively and actively 

since they have multiple ways wo learn and to express their understanding. This was supported by the study of 

Haley (2004) who mentioned that students in the experimental classes were more enthusiastic about learning and 

behavior problems were minimized. Teachers felt that their classroom management skills were enhanced.  One 

surprising result of the MI study was the affective outcome that most students expressed positive feelings about 

teachers using a variety of instructional strategies as well as assessment practices that addressed the multiple 

intelligences. 

 

6. SUGGESTION  

Regarding the results of this study, the researchers would like to present the suggestion for both utilization 

and further study as follows: 

Suggestion for utilizing the results of study 

 1. Teaching through the integration of both the theory of multiple intelligences and TAI is quite different 

from traditional way that almost all students are familiar with, the teacher who would like to adopt this teaching 

activity should, therefore, use the first hour of teaching explain the process of teaching and learning to help students 

understand the learning process and reduce problems in learning.  

 2. Since the teachers try to integrate all 9 intelligences in both teaching and learning, this might cause 

some problems for some students in creating individual work. The teachers who would like to adopt this teaching 

activities should, consequently, adapt the activities basing on the individual differences of the target students.  

Suggestions for the further study 

 1. The study of implementing the theory of multiple intelligences and TAI cooperative learning should 

be done with the other mathematics subject not only calculus such as mathematics for business to see whether the 

results will be similar as in this study. 

2. Since most of the subjects in this study were male students, there should be the study on implementing 

the theory of multiple intelligences and TAI cooperative learning with the class that has a lot of female students to 

see whether the results will be similar as in this study. 

3. Since there are 9 different intelligences regarding the multiple intelligence theory, to use all of them 

for teaching one subject might be difficult. So, there should be the study that investigates the suitable intelligences 

that are suitable for mathematics learning.  

 

7. ACKNOWLEDGEMENT  

We would like to sincerely thanks all reviewers for the valuable and creative comments for improving 

the quality of the paper. Our appreciation also goes to Mr. Jonathan Wary for his assistance in editing the language 

usage in the paper. 

 

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