Corresponding Author: Endah
Zulfah
E-mail: [email protected]
INTRODUCTION
The low mathematical
problem-solving ability of students can also be seen from the results of
diagnostic tests in the form of story problems conducted by Siagian solving ability is an important aspect for
every learner in order to solve problems in the learning process and everyday
life (Ruswati
et al., 2018).
Many parties have
realized the importance of developing problem-solving skills, as evidenced by
the inclusion of problem-solving skills in the learning objectives of
mathematics in Indonesia since the 2004 curriculum (Wirdaningsih et al. 2017). However, in reality, students' mathematical
problem-solving skills are still below the expected standard. This can be seen
from several studies that have been conducted previously, including research
conducted (Putra, 2017) in class VIII SMP 1 Pulau Panggung, which showed
that out of 32 students, only 9 students reached the KKM.et al. (2019). Based on the results of interviews with one of the mathematics
teachers of MTs Negeri 5 Jambi City also said that students still have
difficulty in answering problem-solving questions in the form of story
problems. This was evidenced when conducting a mathematical problem-solving
ability test on ajargenjang material at SMPN 16 Jambi City and MTs N 5 Jambi
City, where the average problem-solving ability result was 47.74. Based on the
tests of the two schools, it was found that most students had relatively low
mathematical problem-solving skills. This is caused by learning that has so far
focused on developing mathematical abilities in quantity rather than in
quality. Whereas in mathematics learning, it is expected that students are
involved in learning so that they not only use certain formulas and procedures
to solve problems, but more than that, students are also expected to be able to
solve some mathematical problems related to real life (Matang & Owens, 2004).
Based on the above problems, it is hoped that students will have the
opportunity to be guided into situations to find concepts in their way so that
learning becomes more meaningful (Wijaya, 2013). The role of the
teacher can be maximized by developing a learning design. The design in
question is a Hypothetical Learning
Trajectory (HLT), and after being tested, it will become Local Instructional Theory (LIT) (Hidayat
& Riyana, 2021). LITs can help to
support learning achievement and can also help teachers evaluate and rethink
teaching, possibly before they start teaching (Andrews-Larson et al., 2017). In learning design, an approach is needed, namely the Realistic Mathematics Education (RME)
approach (Afriansyah, 2017). RME is an approach that connects subject matter with real-world
problems (Wahyudi, 2016). So that RME can help improve students' ability to solve
mathematical problems (Gee, 2019); (Kelen, 2020). Based
on these problems, the purpose of this study is to develop a local instructional theory based on realistic mathematic education (RME) in
class VII SMP / MTs that is valid and practical. This research is expected to
improve students' mathematical problem-solving skills through the development
of local instructional theory (LIT) based on realistic mathematics education
(RME). The RME approach relates mathematical material to real-world situations,
helping students understand mathematical concepts better and apply them in
everyday life. In addition, with the RME approach, mathematics learning is
expected to become more meaningful and relevant to students, increasing their
involvement in the learning process.
METHOD
This research is a
design study that uses two development models: the Gravemeijer & Cobb model
and the Plomp model (Hered et al., 2021). Gravemeijer and Cobb's design is used in the prototype
development stage or learning flow in the Plomp design. To implement the
learning flow, a teacher's book and student book were designed with the Plomp
design. Furthermore, the learning flow is developed using the Gravemeijer and
Cobb design.
Through the
combination of the two models, the research phase consists of preliminary
research, development or prototyping phase, and assessment phase. In the
preliminary research stage, which is reviewing the literature related to
concept discovery and clarifying theoretical intentions, then some needs
analysis is carried out as a basis for designing a learning flow that is in
accordance with the Plomp model. Based on the results of the analysis at the
preliminary research stage, a realistic mathematics education-based learning
path was designed. At the prototyping stage, the developed prototype was
evaluated based on formative assessment.
The formative
evaluation carried out on the prototype that has been designed is a
self-evaluation, validation by experts (expert review), and was conducted by
three mathematics lecturers, one Indonesian lecturer, and one educational
technology lecturer. After the developed product is declared valid, a
one-to-one evaluation, small group evaluation, and field test are conducted to
determine its practicality. The test subjects in this study were students of
class VII MTs N 5 Jambi City. Research data collected through validation sheets
was used to see the feasibility of instruments and products assessed by experts
at the expert review stage; teacher and learner response questionnaires were
used to see the practicality of products tested at the one-to-one, small group,
and field test stages, local instructional theory implementation observation
sheets used to see the implementation of the learning process using teacher
books and realistic mathematic education (RME)-based student books, interview
sheets are also used to ask students' opinions on student books at the one to
one, small group and field test stages. Data from the interview results were
described to revise the developed learner book, and the test of students'
mathematical problem-solving ability was used to see the effect of the tested
book on students' mathematical problem-solving ability.
RESULTS AND DISCUSSION
The results of research on the development of local instructional theory based on RME
in an effort to improve mathematical problem-solving skills from the
preparation stage to retrospective analysis are explained, namely:
Initial Investigation
Stage
At the initial investigation stage, several
activities were carried out to gather information about the problems found in
learning mathematics. At this stage, needs analysis, curriculum
analysis, learner analysis and literature review analysis are carried out.
Based on the results of this initial investigation, a learning design was
designed in the form of a local
instructional theory based on RME to improve the mathematical
problem-solving skills of seventh-grade students.
Development Stage
Design of Hypothetical
Learning Trajectory
At this stage, HLT will be
developed to contain contextual problems that are adapted to the daily lives of
students. Then, some activities will help students construct their knowledge
and find the concept of parallelogram. This HLT consists of three parts, namely
learning objectives, learning activities and prediction of students' answers
and educators' anticipation. The learning flow consists of three HLTs
consisting of
Activity 1: Listing parallelogram-shaped
objects in daily life. This activity is designed for students to explore their
knowledge of various parallelogram-shaped objects in daily life. In this
activity, students are asked to determine the shape of a plane from the roof of
a modern house, which is a parallelogram. Then, students record objects that
are in the shape of a parallelogram in everyday life.
Activity 2: Students
discover the concept of area of a parallelogram by comparing two cartons that
have different shapes: rectangle and parallelogram. In this activity, students determine which
carton is wider and conclude the comparison of the two carton sizes.
Activity
3: Determining the concept of the perimeter of a parallelogram through objects
in the daily environment. In this activity, students are asked to determine the
perimeter of an object in their daily environment that is in the shape of a parallelogram
based on their experience. Informally,
students will discover the concept of the perimeter of a parallelogram.
Teacher's book and
Learner's book
The teacher's book and learner's book are
designed based on RME. The teacher's book has several components, namely cover,
learning objectives, time allocation, material summary, learning activities,
predicted learner answers, teacher anticipation and assessment. As for the
student book, the components are covered, learning objectives, learner
activities, contextual problems, and let's practice.
Validation of HLT,
Teacher's Book and Learner's Book
The
validation stage was conducted after the self-evaluation
stage of the HLT, teacher's book, and learner's book were conducted.
Activities carried out at the self-evaluation
stage include looking at typing errors, sentences that are not clear in
meaning, and punctuation errors, as well as choosing the right colour and font
size. This was followed by the validation stage carried out by five experts,
namely, three mathematics lecturers, 1 Indonesian lecturer, and one lecturer in
educational technology. In the HLT, the aspects assessed in the validation were
content and language aspects. The aspects assessed in the HLT validation were
content and language aspects.
Table 1. Average overall HLT validation results
|
No.
|
Assessed Aspect
|
Average
|
Category
|
|
1
|
Contents
|
3,52
|
Very Valid
|
|
2
|
Language
|
3,39
|
Valid
|
|
Overall
Average
|
3,45
|
Valid
|
Based on the results shown in Table 1, it
can be concluded that the HLT is valid and suitable to be tested on students.
The HLT on the topic of parallelogram that has been implemented into the
teacher's book and learner's book is also validated with the aspects assessed,
which are content, language, didactic or presentation, and graphical or display
aspects.
Table 2: Average Results of Teacher's Book
Validation by Experts
|
No.
|
Assessed
Aspect
|
Average
|
Category
|
|
1
|
Contents
|
3,52
|
Very valid
|
|
2
|
Language
|
3,71
|
Very valid
|
|
3
|
Didactics / presentation
|
3,61
|
Very valid
|
|
4
|
Graphics/display
|
3,46
|
Valid
|
|
|
Overall average
|
3,58
|
Very valid
|
Table 3. Average Results of Learner Book
Validation by Experts
|
No.
|
Assessed
Aspect
|
Average
|
Category
|
|
1
|
Contents
|
3,58
|
Very valid
|
|
2
|
Language
|
3,75
|
Very valid
|
|
3
|
Didactics / presentation
|
3,50
|
Very valid
|
|
4
|
Graphics/display
|
3,42
|
Valid
|
|
|
Overall average
|
3,56
|
Very valid
|
The overall validity value of teachers'
and learners' books is in the very valid category. Thus, it can be concluded
that RME-based teachers' and learners' books can be used.
After all the products are valid, a one-to-one or individual test is
carried out. The subjects of this activity were three students of class VII MTs
N 5 Jambi City with high, medium and low abilities. In this activity, students
are asked to try to do the activities in the student book. The implementation
of one-to-one communication was carried out to see the obstacles faced by
students in finding the concept of the area and perimeter of the parallelogram
through RME-based student books. Then, learners are asked to provide feedback
on the learner book that has been used in terms of spelling, punctuation,
activity instructions, and ease of use.
The revised product based on the results of the one-to-one
evaluation was named Prototype 4 and continued at the small group stage. At the
small group stage, the evaluation was carried out on six students who were
divided into two heterogeneous groups. In the problems in each activity,
students are able to understand and find the concept of the area and perimeter
of the parallelogram. Furthermore, students are given a practicality
questionnaire to see the ease of the student book used.
Table 4.
Practicality Results of the Student Book at the Small Group Stage
|
No.
|
Assessed
Aspect
|
Average (%)
|
Category
|
|
1
|
Ease of Use
|
84,72
|
Practical
|
|
2
|
Time
Efficiency
|
83,33
|
Practical
|
|
3
|
Attractiveness
|
86,11
|
Very
Practical
|
|
4
|
Ease of
Understanding
|
82,3
|
Practical
|
|
5
|
Benefits
|
80,83
|
Practical
|
|
|
Practicality Score
|
83,45
|
Practical
|
After the small group evaluation is complete, a field test is then conducted. The
evaluation was carried out by testing the product on one class consisting of 30 heterogeneous learners. This learning begins with a class discussion; students
sit in groups of 5 learners. This class discussion not only aims to build and
develop student interactivity in accordance with the characteristics of RME but
also to stimulate students' basic knowledge of the concept of the area and
perimeter of a parallelogram.
Table 5.
Practicality Results of the Learner Book at the Field Test Stage
|
No.
|
Assessed
Aspect
|
Average (%)
|
Category
|
|
1
|
Ease of Use
|
92,5
|
Very
Practical
|
|
2
|
Time
Efficiency
|
87,3
|
Very Practical
|
|
3
|
Attractiveness
|
82,3
|
�Practical
|
|
4
|
Ease of
Understanding
|
84,5
|
Practical
|
|
5
|
Benefits
|
88,3
|
Very
Practical
|
|
|
Practicality Score
|
86,9
|
Very
Practical
|
Table 6: Practicality Results of Teacher's Book
|
No.
|
Assessed
Aspect
|
Average
(%)
|
Category
|
|
1
|
Ease of Use
|
95,8
|
Very
Practical
|
|
2
|
Time
Efficiency
|
84,5
|
Practical
|
|
3
|
Attractiveness
|
82,3
|
�Practical
|
|
4
|
Ease of
Understanding
|
88,9
|
Very
Practical
|
|
5
|
Benefits
|
87,5
|
Very
Practical
|
|
|
Practicality Score
|
87,8
|
Very
Practical
|
From the results of Tables 5 and 6, the student book and teacher
book have a practical value with a very practical category. The results of the
interview also showed that the instructions and problems presented in the
student book were clear overall. Learners also said that the colourful and
illustrated design makes students interested in reading and understanding it.
Most of the work on student books can be carried out according to the time
allocation provided. Thus, the student book used in terms of ease of use,
readability, and presentation, as well as the time used, is very practical.
The effectiveness of the HLT on the topic of parallelogram based
on RME was seen from the test results of students' mathematical problem-solving
ability. The effectiveness test was conducted after the students participated
in the small group and field tests. Of the six students who took the test during the small group, 4 of them
completed it with an average score of 81. While the test results during the field test with 30 students, on average, obtained a score of 80,
and only five people were below the KKM. In accordance with the effectiveness
criteria, the RME-based mathematics learning design is effective if the number
of students who reach the KKM is more than 65%. Thus, because the number of
students who reach the KKM is more than 65%, the local instructional theory on the topic of parallelogram based on
RME can be effective.
This is in accordance with the research expectation that LIT can
improve mathematical problem-solving skills. Research has revealed that
learning mathematics through local
instructional theory based on RME can further improve mathematical
abilities (Harnas & Hidayati, 2021). Other research results also show that students can understand
the concept of perimeter and area by using RME-based learning trajectories (Simamora, 2021).
CONCLUSION
Based on the results of the research
that has been done, it can be concluded that the local instructional theory on
the topic of parallelogram based on realistic mathematic education (RME) to
improve the mathematical problem-solving skills of students in grade VII MTS,
which is implemented into the teacher's book and student book has been valid,
practical and effective. Based on the above results, the local instructional
theory on the topic of parallelogram learning grade VII SMP/MTs can be used as
a guide for teachers in implementing learning to improve students'
problem-solving skills.
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