Journal of Education, Teaching and Learning 

Volume 2 Number 1 March 2017. Page 47-52 

p-ISSN: 2477-5924e-ISSN: 2477-4878 

 

47 

 

Developing Instructional Mathematical Physics Book Based on Inquiry 

Approach to Improve Students’ Mathematical  

Problem Solving Ability 

Syarifah Fadillah
1)

, Wahyudi
2)

, Dwi Fajar Saputri
3)

 
1)

IKIP PGRI, Pontianak,Indonesia 
E-mail:atick_fdl@yahoo.co.id 

 
2)

IKIP PGRI, Pontianak,Indonesia 

E-mail: wahyudi.kakap@gmail.com 

 

 

Abstract.The problem in this research is to know how the process of developing mathematics physics instructional book 

based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The 

purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting 

documents (semester learning activity plan, lesson plan and mathematical problem-solving test) to improve students' 

mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, 

design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook 

and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test 

questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed 

that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach 

book was better than the students who use the regular book. 

Keywords: Instructional Book;Mathematical Problem Solving Ability; Inquiry Approach 

 

 

I. INTRODUCTION 

The curriculum at IKIP PGRI Pontianak requires the 

students of Physics education program to master some basic 

physics courses, one of which is mathematical physics. In 

learning physics, the students are required to master 

mathematics, this is because in learning physics the students 

are not only required to learn the concept of physics but also 

required to formulate a mathematical concept formulated in 

the form of a mathematical law or formula. In addition, 

students also learn how to use math to discuss physics 

problems. Wanhar [1], states that mathematics plays a main 

role in physics, to solve physics problems from the simple to 

the most complex. In addition, mathematics is also very 

helpful in reasoning someone in tracing the complexity 

learning physics. 

Nevertheless, the students consider mathematical 

physics as one of the difficult subjects. This is shown from 

the results of the final examination of mathematical physics 

course given to students of IKIP-PGRI Pontianak in the 

academic year of 2010/2011 with an average score below 60, 

as well as in the academic year of 2011/2012 the average 

scores below 65. From these two sets of data it can be seen 

that the percentage of students who have difficulty working 

on mathematical physics problems is still quite large, 

especially on the question that requires a mathematical 

concept; for example, in kinematics material with vector 

analysis, in learning the concept the student experienced 

difficulties to solve the problems because they did not 

master integrals and derivatives. In fact, this course is a 

prerequisite course for students to take the next courses 

including modern physics courses, statistical physics, and 

quantum physics. 

Based on the results of interviews with physics 

lecturers and some students of Physics education study 

program, it is revealed that the students' difficulties in 

studying mathematical physics due to the low ability of 

problem-solving mathematics. The results of the researchers’ 

initial tests on students’ mathematical problem-solving skills 

showed that most of the students were still difficult in 

solving mathematical problems. The mistakes made by 

students include: (1) 29% of students could not identify the 

data or information needed to solve mathematical problems, 

(2) 61% of students did not use effective strategies and lead 

to solutions to solve mathematical problems, and (3) 83% of 

students did not provide an explanation of the strategies, 

related concepts, and mathematical procedures; not using 

mathematical representations to solve problems and did not 

interpret and communicate solutions of mathematical 

problem solving obtained. 

The low ability of mathematical problem solving 

caused by several factors, among others, lecturers still use 

lessons with lectures and less independent in learning. The 

lessons used by the lecturer with the sequence explaining, 

giving examples, asking questions, exercises, and assigning 

mailto:atick_fdl@yahoo.co.id
mailto:wahyudi.kakap@gmail.com


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Volume 2 Number 1 March 2017. Page 47-52 

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tasks to make the students accustomed to accept the concept 

directly from the lecturer without trying to find out the 

process of finding the concept. Therefore, it is required a 

learning model that can improve students’ independence 

learning and train students in solving problems that require 

mathematical concepts. 

According to Santyasa [2] the efforts to improve the 

quality of process and learning outcomes are through the 

implementation of constructivist learning paradigm. The 

change in the paradigm of learning leads to a change of 

learning focus from learner-centered learning into student-

centered learning. Learning conditions that make the 

students only receive the material from the teacher, record, 

and memorize it must be converted into knowledge sharing, 

inquiry, find knowledge actively so that there is an increase 

of understanding not memorizing. In addition, learning 

based on constructivist paradigms focuses on solving 

problems, developing concepts, constructing solutions and 

algorithms rather than memorizing procedures and using 

them to get one correct answer. The appropriate approach for 

this demand is inquiry approach. 

An inquiry approach is a form of teaching that 

emphasizes the active role of students both physically and 

mentally in the learning process. Kindsvatter, Wilen, and 

Ishler in Suparno [3] explain that inquiry is a teaching model 

that involves students' critical thinking skills for 

systematically analysing and solving problems. Through 

inquiry, can train students ability in solving problems both in 

solving problems and problems encountered in everyday life. 

Several studies have shown that the inquiry approach 

is well applied in learning. Brickman, et al [4] suggests that 

the inquiry approach can develop student skills, increase 

self-confidence and scientific skills. In addition, McBride, et 

al [5] found that physics teachers were more successful in 

teaching their students through an inquiry approach. 

Kurniawati, et al [6] showed that mastery of concept and 

critical thinking ability of students who learn with inquiry 

learning guided peer instruction integration higher than 

conventional learning. Similarly, Wahyudin, et al [7] 

concluded multimedia-assisted learning using guided inquiry 

can increase students' interest and understanding. 

This study uses an inquiry approach to improve 

students' mathematical problem-solving skill in 

mathematical physics course. To carry out teaching and 

learning process using inquiry approach, a textbook that is 

oriented to the approach is needed. Therefore, this research 

aims to develop a textbook of physics mathematics-based 

inquiry approach, in order to improve students' mathematical 

problem-solving skill. Besides developing textbooks, this 

research also develops supporting documents such as 

Semester Learning Activity Plan (SLAP), Lesson Plan (LP), 

and Mathematical ProblemSolving (MPS) test. 

II. RESEARCH METHOD 

This research is a research and development approach 

(R & D) which aims to develop a product of physics-based 

mathematics instructional books inquiry approach. The 

textbook development process uses the ADDIE model 

consisting of four stages: analysis phase, design stage, 

development, and production stage, implementation stage, 

and evaluation stage [8]. This research uses descriptive, 

evaluative, and experimental methods. Descriptive methods 

are used to describe the initial analysis of existing 

conditions. Evaluative methods are used to evaluate the 

product validation and testing process. The experimental 

method is used to test the efficacy of the resulting product. 

The sample of this research was two classes of 

Physics education study program of IKIP PGRI Pontianak 

selected as control class (Class A) and experiment class 

(Class B). For the experimental class, it is done using 

mathematical physics instruction based on inquiry approach. 

While the control class using Mathematical Physics textbook 

which was not based on inquiry approach. 

In the analysis phase, it describes the needs analysis 

of textbooks. From the results of preliminary studies on the 

need for textbooks to improve the problem-solving skills of 

mathematics has taken the action of designing textbook of 

mathematical physics based on inquiry approach. At this 

stage of design is also designed supporting document for a 

textbook. Furthermore, after going through the stage of 

analysis and design, the next stage was the development 

stage. At this stage, it is described the quality of physics-

based mathematics instruction book based on an inquiry 

approach assessed by a team of experts and improvements 

made by researchers based on experts input. 

The aspects assessed from the textbook consist of five 

such as: (1) the accuracy of the scope of the content, 

including the suitability of the textbook content to the 

purpose of the lecture to be achieved, and the breadth or 

depth of the textbook content, (2) the textbook digestibility, 

Systematic, orderly and consistent format, (3) language 

usage, such as language or editorial used in clear, proper, 

and communicative textbooks, (4) the appearance of the 

textbook, and (5) the use of clear illustrations and right. 

In addition to being asked to assess the quality of 

textbooks, the experts were also required to assess the 

quality of SLAP and LP. SLAP and LP were arranged based 

on course with reference to the standard format established 

by the instructional analysis development centre. 

Assessment in SLAP consists of five aspects: (1) 

development of the course identity, (2) development of 

learning activities, (3) time allocation, (4) library resources, 

and (5) language use. 

Aspects of assessment for the LP were four aspects: 

(1) development of expected end-capabilities and indicators 

based on inquiry approach, (2) development of inquiry-based 

learning activities, (3) development of assessment based on 

inquiry approach, and (4) LP.The assessment of each aspect 

in textbooks, SLAP and LP was done using Likert scale, 

namely SB (very good), B (good), C (enough), K (less) and 

SK (very less). Very well worth 5, good 4, enough 3, less 2, 

and very less 1. Next is calculated the average value of each 

aspect assessment of all expert team assessment and 

categorized with the provisions: the value of textbook 

quality /SLAP/LP was very good if 4<value<5; good if 

3<value< 4; enough if 2<value<3, less if 1 <value< 2. 



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The research instrument was developed in this 

research to assess the effectiveness of the lecture by using 

mathematical physics instructional book based on inquiry 

approach in improving students’ problem-solving abilities in 

mathematics. The instrument was a set of MPS test. MPS 

test was analysed quantitatively through a try-out to 39 

students of Physics education study program that have taken 

the subject of mathematical physics. Quantitative analyses of 

MPS tests include empirical validity, distinguishing power, 

difficulty index and reliability test. 

Results obtained from validation have been followed 

up with revisions of validation results. Furthermore, in the 

development stage, a limited trial conducted on some of the 

subjects of the textbook. Similar to the validation stages, 

these test results were reviewed and followed up with 

revisions. In order to improve the product trial result, the 

implementation of the textbook in the experimental class (23 

students) and compared with the control class (19 students) 

using the textbook used by the lecturer in the mathematics 

physics lecture. At this stage was also conducted MPS test to 

determine the problem-solving ability of mathematical 

students after obtaining learning by using developed 

textbook. 

From the result of the application of textbook, 

evaluation of mathematics instruction book based on inquiry 

approach and effectiveness level on students' mathematical 

problem-solving ability. 

III. RESULT AND DISCUSSION 

The results of the research presented in this paper are 

the results of each stage of development of physics 

mathematics textbooks based on inquiry approach and its 

supporting tools and research instruments, from the analysis 

phase to the evaluation stage. 

Activities undertaken at the analysis phase are needs 

analysis, student analysis, context analysis, and task 

analysis. The activity in requirement analysis stage is to 

determine the basic problem that is needed in the 

development of textbook by conducting a study on the 

relevant curriculum and learning theory so that the 

description of the text book is considered appropriate. At this 

stage defined and defined the needs of the mathematical 

physics lecture is expected after following this course 

students can explain the concepts and principles of ordinary 

integral and integral folding, matrix, derivative, and 

differential equations, and can use it in various problem-

solving process, both related issues Mathematics itself as 

well as related to the problems of physics. 

Mathematical physics is not a new subject matter for 

the students. In Senior high school level, they have studied 

mathematical physics subject matter such as integral, 

differential function, and matrix, therefore, they already have 

initial knowledge about it. At the beginning of the semester, 

the students have also acquired basic physics courses which 

are a prerequisite for taking a course in mathematical 

physics. With their initial knowledge, it certainly enables 

students to analyse and solve problems systematically. This 

is in line with the inquiry approach since it is a learning 

approach that involves students' critical thinking skill to 

analyse and solve problems systematically [3]. 

Student analysis was a study of student characteristics 

in accordance with the development of the textbook model 

design. From the preliminary study that researcher 

conducted it was revealed that the initial ability of students 

in Physics education study program of IKIP PGRI Pontianak 

in the academic year of 2014/2015 classified as low. Based 

on the analysis of the students it is determined that lectures 

did not directly use the inquiry approach, but in each subject 

preceded by lectures using expository methods to explain the 

mathematical concepts, then on the application of problem-

solving physics used inquiry approach. 

Context analysis is an act of identifying, detailing, 

and systematically compiling relevant mathematical 

concepts to be formed into appropriate textbooks. From this 

analysis it is found that the composed teaching material 

consists of four subjects: (1) matrix consisting of three 

learning activities namely: definition, types, and matrix 

count operation, determinant and inverse matrix, and 

application of matrix in solution of problem physics; (2) a 

derivative consisting of three learning activities: algebraic 

functions and trigonometric functions, high-level 

derivatives, and derivative applications in the completion of 

physics; (3) partial differential consisting of four learning 

activities namely: partial differential definition, total 

differential and chain derivative, and implicit and extreme 

price function, and differential application in the completion 

of physics problem; and (4) the ordinary integral and folding 

integral consisting of four learning activities: the regular 

integral, the two-fold integral, the triple integral, and the 

integral application in the completion of the physics 

problem; 

The activity in this task analysis is to identify the 

basic competency and standard competency that will be 

achieved through the mathematics physics lecture by using 

textbook based on inquiry approach. The last activity of the 

analysis phase was the conversion of standards competency 

and basic competency of task analysis and context analysis 

into lecture objectives. The purpose of the lecture is 

contained in every chapter and in every learning activity in 

the mathematics physics textbook. 

The next is the design stage. This stage was an early 

stage of the design of textbooks of mathematical physics 

based on inquiry approach that was used in lectures. At this 

stage, an early draft of the textbook has been produced and 

used for fourteen times face to face. The designed textbook 

consisted of four chapters and fourteen learning activities. 

The textbook was embedded with SLAP and LP. In addition 

at this stage also has produced the initial draft of MPS test 

instrument. 

The textbooks, supporting tools, and research 

instruments that have been designed at the design stage were 

validated by five experts who were deemed proficient in 

order to obtain information in the form of input, evaluation, 

and revision of the textbook model, supporting documents 

and research instruments that have been designed. 



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The results of the textbook quality assessment on the 

five aspects of assessment by five experts are shown in 

Table I. 

Table I 

Result of Textbook Analysis by Expert Team 

No 
Assessment 

aspects 

Mean 

score 

Mean 

of total 

score 

Scoring 

criteria 

1 The accuracy of 

content 

coverage 

4.30 

3.92 Good 

2 The legibility of 

textbook 

3.90 

3 The use of the 

language 

4.20 

4 Cover/appearan

ce 

3.20 

5 The use of 

illustration 

4.00 

 

The result of the analysis shows that the developed 

textbook has anaverage score of assessment is 3.92 it 

belongs to thegood criterion. Belawati, et al [9] said that 

several factors that influence the quality of textbook, among 

others: the scope of textbook content, digestibility, language, 

appearance, and illustration. The quality of textbook 

developed is dependent on the accuracy of textbook 

developers in taking into account these factors in developing 

textbook. With the assessment of the quality of textbook by 

a team of experts who categorized well, this textbook 

prototype can be used in the next step of the development of 

field trials (implementation) 

In general, the five experts stated that the 

mathematical physics textbook is well-constructed, but there 

were some things that need to be fixed before they are tested 

in the classroom. Some of the improvements that need to be 

improved include: (1) consistency in image numbering, 

examples, exercises, and competency tests; (2) error in 

typing;(3) error in calculation; (4) the exercise was put at the 

end of the activity;            (5) textbook was equipped with 

key answer for odd-numbered / even-numbered questions; 

and (6) improvements in some graphic images. 

The use of textbook will be more easily equipped with 

supporting documents such as SLAP and LP. The results of 

the SLAP quality assessment on the five assessment aspects 

are shown in table II. 

Table II 

The Result of SLAP Analysis by Expert Team 

No 
Assessment 

aspects 

Mean 

score 

Mean 

of 

total 

score  

Scoring 

criteria 

1 The development 

of course identity 

4.20 

4.40 

Very 

good 

2 The development 

of learning 

activities  

4.40 

3 Time allocation 

in the design 

4.50   

4 The use of 

literature 

4.20 

5 Language 

aspects 

4.70 

 
The results of the analysis show that the developed 

SLAP has an average score of each aspect of the assessment 

of more than four and a total average score of 4.40 is 

considered very good. Some expert team suggestions for 

SLAP are the addition of used literature sources and a more 

customized grammar with the format set by the instructional 

analysis development centre. 

The results of the analysis on the LP by the expert 

team showed that overall the LP was also very well 

classified with a mean score of 4.15. The LP is designed 

based on an inquiry approach with four aspects of 

assessment. The result of the quality assessment of the LP by 

the expert team is presented in Table III. The suggestion 

from the expert team on the lesson plan is on the more 

detailed learning steps of the inquiry instruction syntax in 

the LP. 

 

 

 

Table III 

The Result of LPAnalysis by Experts Team 

No Assessment aspects 
Mean 

score 

Total 

mean 

score 

Scoring 

criteria  

1 Expected capability 

development. 

4.40 

 

4.15 

 

Good 

2 The development of 

learning activities 

3.95 

3 Development of 

assessment 

3.77 

4 Language Usage 4.50 

 
A textbook that has been developed, of course, cannot 

be said well if not tested its use in the field, therefore this 

research develops research instruments to measure the 

effectiveness of the use of textbooks in classroom lectures. 

The developed instrument is the MPS test. This is in line 

with the opinion of Triyono [10] who said that the 

conclusions of a study were drawn based on empirical data 

collected. If the data collected does not provide a true picture 

of the actual situation, then the conclusion of the results of 

his research is also difficult to be trusted. 

 The results of the analysis by the expert team on the 

MPS test conclude that of the four MPS test questions given, 

three questions are declared valid and one is invalid. One 

problem with the valid category still needs to be fixed the 

redaction of the sentence is less clear. An invalid problem is 

replaced because it does not match the indicator of the grid 

problem. The replaced questions are then returned to the 

experts and are considered valid. After the next validated the 

problem is tested for being analysed. 



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The MPS test results show that there is no validity 

with a low level of validity. The first question (Rxy = 0.745), 

the third question (Rxy = 0.808) and the fourth question (Rxy = 

0.758) have a high degree of validity while the second (Rxy = 

0.857) has a very high degree of validity. From the reliability 

test resulted the fourth reliability index question is 0.802 is 

high. 

Analysis of distinguishing power and indices of 

difficulty on KMPS test questions indicates that the KMPS 

test has sufficient and good distinguishing features, as well 

as a moderate and easy difficulty index. The results of 

distinguishing power analysis and difficulty indices are 

presented in Table IV. 

 
Table IV 

The Result of Discriminating Power and Difficulty Index 

Analysis of MPS Test 

No  

MPS 

Test 

Discriminating Power Difficulty Index 

Score Criteria Score Criteria 

1 0.311 Good 0.621 Moderate 

2 0.304 Good 0.740 Easy 

3 0.241 Enough 0.743 Easy 

4 0.303 Good 0.604 Moderate 

 

Problem number three has considerable distinguishing 

power with easy index indices. This issue will still be used 

but will be revised on the content aspect. Revisions made to 

keep in mind the indicators to be achieved in the test 

questions. 

From the overall analysis of MPS test results showed 

that all items on the MPS test can be used as research 

instruments. 
From three stages of development has been produced 

prototype textbooks of physics mathematics-based approach 

inquiry and supporting documents. The next step is to test 

the prototype of the course to get input to refine the textbook 

before it is used more widely. 

Mathematical physics lecture by using textbook based 

on inquiry approach done in one semester. The result of 

mathematical problem-solving ability is shown in Table V. 

Table V 

Student Mathematical Problem Solving Abilities 

Class Mean Standard 

Deviation 

Exsperiment 56.34 18.07 

Control 4.20 15.29 

 
The result of hypothesis testing shows that there is a 

difference of the problem-solving ability of amathematic 

student who gets the learning by using physics mathematics 

instructional book based on inquiry approach with students 

who get the learning by using a textbook which is used by 

the lecturer, with significance level 0.029 smaller than 0.05. 

Judging from the average problem-solving abilities, the 

experiment class is higher than the control class. This shows 

the result of learning of students who get the learning by 

using textbook of physics of mathematics based on inquiry 

approach better than a student who gets the learning by using 

a textbook which usually used by the lecturer. 

The use of guided inquiry approach is very supportive 

in improving students 'mathematical problem-solving skills, 

in line with Kinsvatter, Wilen, and Islher[3] opinion that 

inquiry learning is a learning that involves students' critical 

thinking ability to analyse and solve problems 

systematically. In student inquiry learning is directed to 

answering questions and solving problems, learning is based 

on logical testing of facts and observations. Through inquiry 

learning, students can develop intellectual thinking and other 

abilities such as asking questions and skills to find answers 

that begin with their curiosity. This course can support the 

improvement of students' mathematical problem-solving 

skills 

Usman [11] in his research concludes that in solving a 

problem, students need meta-cognition activities in the form 

of: (1) when understanding the problem, the subject 

performs meta-cognition activities, namely: realizing the 

importance of thinking about how to understand the 

problem, monitoring the understanding of the problem, and 

evaluating the understanding of the problem, (2) when 

making the completion plan, the subject performs meta-

cognition activities, namely: be aware of the importance of 

planning the completion steps, monitoring the plan of 

completion steps, and re-evaluating the plan of completion 

plan steps, (3) Meta-cognition activities, namely: realizing 

the importance of thinking about the implementation of the 

completion plan, monitoring the implementation of the 

completion plan, and evaluating the implementation of the 

completion plan, (4) when re-examining the completion, the 

subject performing meta-cognition activities, Namely: 

realizing the importance of thinking about re-examining the 

settlement, monitoring the truth of the outcome, and 

evaluating the truth of the outcome. 

These meta-cognition activities are most likely to be 

developed using inquiry learning, since inquiry learning has 

learning steps: the first stage is the orientation stage, creating 

a responsive atmosphere or learning climate. Students are 

conditioned to be ready to receive lessons. Students are 

stimulated to think about solving problems. This stage can 

develop a meta-cognition activity that is aware of the 

importance of thinking about how to understand the 

problem, monitor the understanding of the problem, and 

evaluate the understanding of the problem. 

The second stage is the stage of problem formulation, 

which begins when asking questions of the phenomena 

learned at the beginning of the lesson so that it leads to the 

hypothesis (temporary answer to the problem under study). 

All students are entitled to submit a hypothesis but selected 

one of the hypotheses relevant to the concept being studied. 

At this stage meta-cognitive activities that can be developed 

are aware of the importance of thinking about the plan of 

completion steps, monitoring the plan of completion steps, 

and re-evaluate the steps of the settlement plan. 

The third and fourth stages of inquiry learning are 

data collection and hypothesis testing. Data collection is an 

activity in gathering the information needed to test the 



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hypothesis. At this stage of data collection, students are 

given the freedom to experiment or study literature. The 

process of determining the answers based on data collection 

performed is called the hypothesis testing stage. At both 

stages, it can develop meta-cognition activities that are 

aware of the importance of thinking about implementing the 

completion plan, monitoring the implementation of the 

completion plan, and evaluating the implementation of the 

settlement action plan. 

IV. CONCLUSIONS 

The product of this development research is a 

physics-based mathematics instruction book based on 

inquiry approach with its supporting documents in the form 

of SLAP, LP, and MPS test. The use of the textbook in 

teaching and learning process revealed that the use of 

mathematics physics textbook based on inquiry approach 

can improve students' mathematical problem-solving ability. 

For future improvement, it is necessary to evaluate the 

textbook by rearranging the textbook to make it simpler and 

easier to understand. 

ACKNOWLEDGMENT 

Our deepest gratitude goes to the Directorate of 

Research and Community Service, Ministry of Research, 

Technology and Higher Education for funding assistance 

through the Competitive Grants research program with 

contract number 026 / L.202.203/ HB/ IV/ 2015. 

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