The Development of Integration Technique Teaching Materials based on

Problem Based Learning in Integral Calculus Course

Zetriuslita and Rezi Ariawan

Mathematics Education Study Program, Universitas Islam Riau, Pekanbaru, Indonesia

Keywords:

Integration Technique, Teaching Materials, Problem Based Learning.

Abstract:

This study aims to develop teaching materials of integration technique in Calculus course based on Problem

Based Learning approach that meet valid and practical criteria. The research method is development research

which consists of three stages: planning, development, and testing. The subjects of this study were the third

semester students of Mathematics Education involving 40 people. The data collection instrument consists

of validityand practicality sheets of teaching materials. The data collection technique was conducted with

non-test technique. The data analysis used descriptive quantitative technique. Based on the results of the

study, the teaching materials have met the valid criteria by 88.96% with Very Valid criteria. Furthermore, the

teaching materials also met practical criteria by 88.75%)with Very Practical criteria. Therefore, the ﬁndings

of this study indicate that the integration technique teaching materials based on Problem Based Learning in

Integral Calculus course meet very valid and very practical criteria.

1 INTRODUCTION

To improve the nation’s competitiveness in facing

the globalization era, higher education is needed to

develop science and technology. Higher education as

part of the National education system has a strategic

role in educating the nation’s life and advancing

science and technology. According to Law Number

12 of 2012 concerning Higher Education Article 4,

the functions of higher education are: (1) developing

capabilities and forming digniﬁed national character

and civilization in order to educate the nation’s life;

(2) developing academicians who are innovative,

responsive, creative, skilled, competitive, and

cooperative through the implementation of Tridharma

Perguruan Tinggi (the University’s three main

purposes); (3) developing science and technology by

paying attention to and implementing the values of

humanities.

As one of the formal education institutions,

Universitas Islam Riau (UIR) is one of the institutions

which take part in realizing the function of higher

education that has been described above. In the ﬁeld

of teacher training and education, FKIP (Fakultas

Keguruan dan Pendidikan—Faculty of Teaching

Training and Education) is a pioneer in producing

professional and reliable education personnel.

So far, the Mathematics Education, one of the

study programs in FKIP UIR, has tried to take

various actions in order to achieve the goals of higher

education, namely by trying to produce professional

and reliable education personnel. There are several

important elements, one of which is teaching staff or

lecturers. Law Number 12 of 2012 concerning Higher

Education Article 12 states that: (1) lecturers as

members of the academic community have the task of

transforming the knowledge and/or technology they

master to students by creating a learning atmosphere

so that active students develop their potential; (2)

lecturers as scientists have the task of developing

a branch of science and/or technology through

reasoning and scientiﬁc research and disseminating

it; (3) lecturers individually or in groups must

write academic textbooks, which are published by

universities and/or scientiﬁc publications as a source

of learning and for the development of academic

culture and civilization of writing activities.

The reality, however, contradicts the statement

above. Scientiﬁc writing in Indonesian universities

is unsatisfactory. The contribution of scientiﬁc

publications by Indonesian universities is only

0.0125% (Suroso, 2004; Mokhtar et al., 2010). He

supposes that Indonesia has 45 state universities and

1400 private universities with a total of 1,850,000

lecturers. If every lecturer in one year writes a book,

there will be 1,850,000 titles. But in reality, it is

Zetriuslita, . and Ariawan, R.

The Development of Integration Technique Teaching Materials based on Problem Based Learning in Integral Calculus Course.

DOI: 10.5220/0009094701230129

In Proceedings of the Second International Conference on Social, Economy, Education and Humanity (ICoSEEH 2019) - Sustainable Development in Developing Country for Facing Industrial

Revolution 4.0, pages 123-129

ISBN: 978-989-758-464-0

123

different. He added that the cause of lecturers’ weak

writing ability is the low activity of accessing the

internet. Lecturers do not have writing facilities such

as availability of collections, laziness in library visits

or downloading on the website. Furthermore, the

ability of lecturers to buy books, subscribe to journals,

and allocate a portion of their money to complete

their writing activities is also low, and include poor

translation skills. Besides, their weak writing ability

is also caused by people’s low interest in buying

books.

Meanwhile, according to Team Jago Nulis

Publisher Deepublish (2016), there are several

beneﬁts from writing activities, including: (1)

obtaining passive income; (2) as a medium

for promotion / position; (3) self-promotion and

institution of work; (4) obtaining invaluable pride; (5)

getting credit points; (6) giving valuable contribution

to the people; (7) avoiding senility and improving

self-quality; (8) passing on the knowledge of future

civilizations.

Due to the beneﬁts and the effort to carry out

the Law on Higher Education, the researchers are

interested in developing teaching materials. In

addition, the development of teaching materials

is based on several observations, experiences and

interviews that the researchers have done as the

permanent lecturers in the Mathematics Education

Study Program. The researchers found that: (1) most

teaching materials are not available for each subject,

so that this can raise doubts about the professionalism

of the lecturers who teach the subject; (2) learning

resources available to students are very limited,

especially textbooks that are prepared exclusively for

certain subjects by lecturers; (3) the interaction of

students in the class when lecturing takes place is very

low because some students do not bring the learning

resources and some bring the intended learning

resources but they have difﬁculties in learning and

understanding the material.

In addition, based on an unstructured interview

with several students during the lecture process in the

second semester in the academic year of 2017/2018,

it was found that; (1) students are easy to ﬁnd

book references related to the subjects, but ﬁnd

difﬁculties in determining which material should be

studied in accordance with the competencies that

must be possessed while participating in the course.

Then, there are several materials in many different

books. Consequently, students must have many

books as learning resources, while they have ﬁnancial

constraints to buy them. (2) students often ﬁnd

learning resources that are invalid (incomplete); (3)

the authors of the books (articles) they ﬁnd on the

internet are often ambiguous especially from blogs;

(4) if the lecturer assigns certain materials to the

students, then they only take what is relatively easy

to understand, while the relatively difﬁcult one is

disposed because it is not understandable, so the

urgency or point of learning is not achieved; (5)

students are most happy during the group’s paper

presentations, because their presentations are clariﬁed

by lecturers in the class.

The ﬁndings presented above also occur in the

subjects that the researchers have been able to teach so

far, namely Integral Calculus. Integral Calculus is one

of the compulsory courses in Mathematics Education

study program. With 3 credits, students are required

to pass this course, because this course is prerequisite

for advanced calculus courses, Differential Equations,

and Initial Value Problem and Boundary Condition

Problem. Therefore, it must be mastered by the

students.

It is considered important and urgent to do

a development research that can produce Integral

Calculus teaching material.In the teaching of science

and biology the didactic materials are fundamental

tools in the taeching-learning process, being an

important and variable alternative in schools of public

scholls system. Teh use of these materials can help

the student in the contextualization of knowledge,

ﬁlling many gaps felt during learning, facilitating the

students to build their own conceptions of scientiﬁc

knowledge in relation to common knowledge, and

the socialization to common knowladge and the use

the contruction of new designs more elaborate. The

availability of references for Integral Calculus is now

very large and accessible. However, the references

do not support the achievement of competency

standards. In addition, several references only teach

students to calculate. Even though the demands

of integral calculus courses do not only provide

skilled students in calculating integrals, but also

provide understanding about integrals and using them

in solving various problems associated with them.

Therefore, teaching materials must be created to

teach and encourage students to actively involve and

construct their own knowledge.

To be able to develop teaching materials, the

teaching materials can be arranged based on problem

based learning. Problem-based learning is an

alternative learning model that allows students to

develop thinking skills (reasoning, communication,

and connection) in solving mathematical problems

(Rusman, 2010). Ben Martz and Morgan Shepherd.

(2005: 1-2) states, ”PBL at its core is an interactive

tool that uses prolems as the context for students

to acquire knowledge. Problem Based Learning in

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124

centered on providing the student with a problem

environment which that students can create and store

memories and meanings”.

Furthermore, Wina Sanjaya (2011) suggests that

there are 3 main characteristics in a problem-based

learning strategy, namely: (a) a problem-based

learning strategy is a series of learning activities,

meaning that in implementing a problem-based

learning strategy there are a number of activities

that students must do. The problem-based learning

strategy does not expect students to simply record,

listen, then memorize the subject matter, but through

problem-based learning strategies students actively

think, communicate, search and process data, and

ﬁnally conclude; (b) learning activities are directed

at solving problems, meaning that problem-based

learning strategies place problems as keywords of

the learning process, without problems there is no

possible learning process; (c) problem solving is done

by using a scientiﬁc thinking approach. This is similar

to what was conveyed by Savin-Baden in Wendy

Barber, et al (2015):

”There are signiﬁcant characteristics of PBL that

include: (1) Complex real world situations that have

no one ‘right’ answer are the organizing focus for

learning; (2) Students work in teams to confornt the

problem, to identify gaps, and to develop variabel

solutions; (3) Students gain new information through

self-directed learning; (4) Staff act as facilitators;

(5) Problems lead to the development of clinical

problem-solving capabilites”.

Based on the problems above and due to

time constraints, the researchers are interested in

conducting this research entitled ”The Development

of Integration Technique Teaching Materials in

Integral Calculus Courses Based on Problem

Based Learning”. The textbook is systematically

organized as follows: Cover, chapter titles,

material concepts, competency standards, basic

competencies, indicators, sub-chapter headings,

material presentation that directs students to do

activities with the following steps entitled: (1) let’s

focus on the problem; (2) let’s collaborate with your

group members; (3) let’s start working; (4) let’s

innovate and understand the results; (5) let’s analyze

and evaluate, examples of exercises, summaries,

exercises.

2 RESEARCH METHODS

Research that produces a product is known as

development research. According to Sugiyono

(2010), research and development is a research

method used to produce certain products and test the

effectiveness of these products.

Nana Syaodi Sukmadinata (2008) (Sukmadinata,

2011) stated that the steps of research and

development broadly consist of: (1) a preliminary

study consisting of literature review. In the literature

review, ﬁnd and read articles in international journals

and national journals as well as source books related

to the textbook material that you want to develop;

(2) product development; activities carried out from

drafting instruments, validating instruments and

revising instruments, lastly (3) product testing. The

activity is to test the testing instruments that have

been valid and revised by the validators, and carry

out the analysis. Thus, in general the research design

consists of three stages including: development stage

(conducting observations and interviews, conducting

material analysis, analysis of competency standards

and learning indicators), planning stage (compiling

teaching materials according to material that has been

analyzed at the planning stage, compiling the validity

sheet and practicality sheet of teaching materials,

validating teaching materials to 3 experts, conducting

an analysis of the validity result, revising the teaching

materials that have been validatedby the experts,

and the testing stage (conducting trials and revise

teaching materials based on the result of the tests).

This research was conducted in the Mathematics

Education Program FKIP UIR in the odd semester

of 2018/2019. The subjects in this study were the

third semester students of the FKIP UIR Mathematics

Education study program who had taken part in

Integral Calculus course. The location, research time

and the subject of this study were selected on certain

considerations, namely:

• Ease of communication between researchers and

students because researchers are lecturers from

the students concerned.

• A research on the development of teaching

materials for integration techniques based on

Problem Based Learning in integral calculus

course has never been conducted in Mathematics

education study program.

The research instrument used to collect data in

this study is the validity sheet of teaching materials

compiled using several aspects: presentation, content,

compatibility with the principles of problem based

learning and mathematical critical thinking skills, and

language. Then, the practicality sheet of teaching

materials is compiled using the following indicators:

Interest in mathematics teaching materials based on

Problem Based Learning, Effect of Problem Based

Learning teaching materials on student learning

activities and motivation, Use of sentences in teaching

The Development of Integration Technique Teaching Materials based on Problem Based Learning in Integral Calculus Course

125

materials based on Problem Based Learning, Ease of

understanding material in teaching materials based

on Problem Based Learning, teaching materials

support mastery of material, teaching materials based

on Problem Based Learning in accordance with

students’ thinking background, Teaching materials

help construct understanding of a material, Delivery

of the material is associated with daily life, Teaching

materials help facilitate the students’ mathematical

critical thinkingability, Questions based on Problem

Based Learning are straightforward and challenging,

and It is good or not to be used in Mathematics

learning.

Data collection technique is carried out with

non-test technique. To get the data about the validity

of teaching materials, the researcher requested

validity from the experts by using the validity sheet

that had been designed. Lastly, to obtain the

data about the practicality of teaching materials, the

researchers used a practicality sheet given to students

during the testing process.The result of validity test

was analyzed in the following stages:

• Add the values of each indicator of the validity

sheet.

• Find the average value of each indicator given by

the validator with the following formula:

• Determine the combined validity with the

following formula:

• Determine the average value category based on

the Likert scale and determine the textbook

validity category. The following are the validity

categories of teaching materials.

Table 1: Interpretation Criteria for Teaching Material

Validity

Mean Score Category

85,01% ≤ V ≤ 100%

Very practical, or can be used

without revision

70,01% ≤ V < 85,01%

Quite practical, or can be used with

minor revisions

50,01% ≤ V < 70,01%

Less practical, it is recommended not

to use because it requires major revisions

V < 50,01% Not practical, or may not be used.

Source: Sa’dun Akbar, 2013

Next, the data from the practicality questionnaire

was analyzed by calculating the percentage of

practical teaching materials. According to Sudijono

(2008), the percentage of a value can be calculated

using the following formula:

P =

× 100% (1)

Description:

P: Percentage of assessment

f: Score obtained

N: Total Score

The category of mean score and textbook validity

is determined based on the Likert scale. The

following table describes the categories of teaching

material validity.

Table 2: Interpretation Criteria of Teaching Material

Practicality

Mean Score Category

85,01% ≤ ∨ ≤ 100% Very valid, or can be used without revision

70,01% ≤ ∨ < 85,01% Quite valid, or can be used with minor revisions

50,01% ≤ ∨ < 70,01%

Less valid, it is recommended not to use because it

requires major revisions

V¡ 50,01% Not valid, or may not be used.

Source: Modiﬁed from Sa’dun Akbar, 2013

Figure 1 describes the procedures of this research.

Figure 1: Procedures of the Research

3 FINDINGS AND DISCUSSIONS

3.1 Findings

Based on the development procedure in the planning

stage, the researcher conducted several things,

including:

3.1.1 Planning

The planning phase gins by analyzing the curriculum.

Curriculum analysis is carried out by conducting

reviews and discussions. The results of curriculum

analysis of the teaching material to be examined are

presented in Figure 2.

Moreover, in the planning stage, researchers

have also done observations and interviews with the

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126

Figure 2: Curriculum analysis of the teaching material.

lecturers who teach integral calculus courses. The

information was obtained that innovation is needed

in conducting integral calculus learning. One of the

innovations is the development of teaching materials

that can involve students actively. In addition,

most students want integral calculus material to be

straightforward especially the material of integration

technique. Then, the learning process can involve

students and improve their mathematical thinking

ability.

3.1.2 Development

After the planning stage is carried out, the next

step that the researchers do is to develop teaching

materials. Teaching materials include: (1) cover; (2)

introduction; (3) table of contents; (4) Explanation

of basic learning competencies; (5) Explanation of

learning indicators; (6) A description of the focus of

teaching materials; (7) Instructions for using teaching

materials; (8) Exposure to teaching material presented

with the following activities namely let’s focus on

the problem, let’s have a discussion with your group

members, let’s start working, let’s innovate and

understand the results, let’s analyze and evaluate ; (9)

Sample Questions; (10) Summary; (11) Exercise.

The draft of teaching materials will be validated

by 3 experts. Experts will provide validity of teaching

materials with aspects of presentation feasibility,

content feasibility, conformity with the principles of

Problem Based Learning and mathematical critical

thinking skills and language feasibility. The results

of the validity can be seen in Table 3 and Figure 3

below.

Table 3: Teaching Material Validity Result by Experts

Aspects Assessed Percentage (%) Criteria

Presentation

Feasibility

95.83 Very Valid

Content Feasibility 88.72 Very Valid

Conformity with the

principle of problem

based learning and

mathematical critical

thinking skills

82.29 Quite Valid

Language Feasibility 86.46 Very Valid

Overall Percentage

(%)

88.96 Very Valid

tSource: Processed Data

Figure 3: Curriculum analysis of the teaching material.

Based on the result of the validity from the

experts, it can be seen that overall the validator

assessed that the teaching material has been very

valid and feasible for testing with minor revisions.

At last, referring to the feedback from the experts,

the researchers revised the teaching material that had

been developed.

3.1.3 Testing

The product testing was conducted on 40 third

semester students of Mathematics Education who had

attended Calculus II course. The test was conducted

on October 18, 2018 in room 6.09 Building A,

2nd ﬂoor. The trial process started from 13.30

- 16.00 WIB. The test was carried out in several

stages, including: (1) Opening lessons by conveying

apperception, giving motivation, delivering learning

objectives, and explaining the steps of learning to be

carried out by students in the class; (2) instructing

students to study in groups that have been formed at

the beginning of the meeting; (3) Providing revised

teaching materials; (4) Instructing students to study

The Development of Integration Technique Teaching Materials based on Problem Based Learning in Integral Calculus Course

127

with other group members by following the learning

steps contained in the teaching material; (5) At

the end of the meeting, the researcher distributed

questionnaire to students which serves to provide

an assessment of the new instructional materials in

terms of practicality.Table 4 shows the result of

the practicality of teaching materials according to

students.

Table 4: Practicality Result of Teaching Materials

No. Indicators Percentage (%) Criteria

Interest in mathematics

teaching materials based

on Problem Based Learning

87.5 Very practical

Effect of Problem Based

Learning based learning

materials on student learning

activities and motivation

86.56 Very practical

Use of sentences in teaching

materials based on Problem

Based Learning

90 Very practical

Ease in understanding the

material in teaching materials

based on Problem Based

Learning

84.06 Quite practical

Teaching materials support

mastery of the material

86.88 Very practical

Teaching materials based on

Problem Based Learning are

in accordance with students’

thinking backgrounds

88.75 Very practical

Teaching materials help

construct understanding of the

subject

84.34 Quite practical

Submission of material is

associated with everyday life

88.13

Very

practical

Teaching materials

help facilitate students’

mathematical critical thinking

skills

79.69 Quite practical

The questions given in

teaching materials based

on Problem Based Learning are

straightforward and challenging

70 Quite practical

It is good or not to be used in

mathematics learning

88.75

Very

practical

Overall Percentage (%)

88.75

Very

practical

After testing and getting the students’ practicality

result of teaching materials with very practical

criteria, it can be stated that the ﬁnal product of

teaching materials has been produced.

3.2 Discussion

In developing both the development of mathematical

critical thinking ability test instruments and teaching

materials, researchers have followed the stages and

procedures. Testing and processing of test result have

also been done by researchers with the procedures and

steps stated in chapter 3. The results of the validity

test showed that the teaching material falls into a very

valid category, can be used with a slight revision.

But there is avalidator who considers that the sample

questions and exercises presented in the teaching

material have not been able to stimulate students’

HOT skill. It is mentioned that the sample questions

and exercises are too easy for students, even though

they are based on indicators of mathematical critical

thinking. Meanwhile the other validators consider the

sample questions and exercises to be appropriate but

the variations are lacking, so it must be added. The

feedback is actually good, but the researchers have

other considerations, related to the difﬁculty level of

the sample questions and exercises. The researchers

consider that the sample questions that the researcher

presents with steps , but students also still have to

ﬁnd it themselves, adjusted to the level of ability

and needs that researchers get based on research and

experience of researchers as the lecturer who teach

integral calculus course. It is assumed that such

teaching materials can help the students’ learning

process in integral calculus. We can compare this with

the results of the practicality questionnaire obtained

from the testing of the use of integral technique

teaching materials based on Problem Based Learning.

The result of the testing shows that that the

teaching materials are “very practical”. However,

there are Problem Based Learning indicators in

teaching materials that are straightforward and

challenging. Teaching materials that help facilitate

the students’ mathematical critical ability have

practical criteria and have the smallest percentage

score compared to other indicators. This was in

line with the statement that the sample questions

and exercises had not been able to stimulate HOT

students. But based on the interviews with the

students, the sample questions and exercises were

too difﬁcult for them to complete. Based on these

statements, the researcher assumed that the statement

by the validators and the students had different

meanings. The former stated that the questions and

exercises must be changed and the level of difﬁculty

increased so as to stimulate students’ higher order

thinking skills, while the latter stated that the sample

questions and exercises were too difﬁcult for them. In

conclusion, the teaching materials that the researchers

have developed are “very valid” and “very practical”.

4 CONCLUSIONS AND

SUGGESTIONS

In conclusion, teaching materials of integration

technique based on Problem Based Learning are

considered very valid and very practical. The

researchers have developed valid and practical

materials to be used in teaching integration technique

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in integral calculus course. The researchers suggest

that the practicality of students in using teaching

materials should not be used as a benchmark

in determining or seeing an increase in students’

abilities. The practicality does not describe their

abilities. Then, teaching materials must be presented

in steps with a variety of problems that are more

straightforward.

ACKNOWLEDGMENTS

The authors would like to thank the ﬁnancial support

provided by University of Indonesia University

through the PITTA 2019 funding scheme managed

by Directorate for Research and Public Services

(DRPM) University of Indonesia.

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