!Volume 3, No. 3, January 2022
p- ISSN 2777-0915 | e-ISSN 2797-6068
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250 http://devotion.greenvest.co.id
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Yulia Dahlan
1
and Nurhasanah Siregar
2
Medan State University, Indonesia
1 and 2
Email: [email protected]
1
and [email protected]
2
Keywords
!!
Mathematical
communication skills,
Reciprocal Teaching
Models, Relations
and Functions
Article.Info.
Accepted:
December, 23
rd
2021
Revised:
January, 4
th
2021
Approved:
January, 14
th
2021
Abstract!
This study aimed to determine the improvement of students'
mathematical communication skills in relation and function
materials through the Reciprocal Teaching learning model
in class VIII of SMPS National Development Pangkalan
Susu. The researchers used classroom action research
(CAR) which is carried out in 2 cycles, each cycle was
carried out in 2 meetings. The subjects in this study were
students of class VIII of SMPS National Development
Pangkalan Susu, totaling 22 people. Data collection
techniques used were teacher and student observation
sheets, and tests of mathematical communication skills. The
test was carried out 3 times, namely a diagnostic test, a test
for mathematical communication skills I, and a test for
mathematical communication skills II. The results of the
research at the time of the diagnostic test showed that the
students' mathematical communication skills in
explaining/writing the elements were known, the elements
were asked and concluded correctly and completely
(33.4%), painting pictures, diagrams, graphs, or tables
completely and correctly (38%), and express mathematical
ideas using symbols or mathematical language in writing as
a complete and correct representation of an idea or ideas
(32%). After being given action in Cycle I and Cycle II, the
students were able to explain/write known elements, ask
questions and conclusions correctly and completely,
describe pictures, diagrams, graphs, or tables completely
and correctly, and state mathematical ideas using symbols
or mathematical language in writing as a complete and
correct representation of an idea or idea. The results of the
mathematical communication ability test given in the
classical cycle I obtained that students who completed were
10 students (45.45%) out of 22 students with an average of
58.09, in the second cycle who completed increased to 16
students from 22 students (81 ,81%) with an average of
74.18 and has achieved the classical completeness criteria
because 80% of the number of students have mathematical
communication skills in the sufficient category, namely 70.
Based on the results of the study, it can be concluded that
the Reciprocal Teaching model can improve students'
Yulia Dahlan
1
and Nurhasanah Siregar
2
Efforts to Improve Students' Mathematical Communication Ability Through
Reciprocal Teaching Learning Model For Class VIII SMPS Development National
School of Milk Base 251
Introduction.
The most fundamental is mathematics, where mathematics plays a very important
role in knowledge and technology. (Leung & Hasratuddin, 2018) stated that mathematics
is a science that supports human potential and can increase logical, critical thinking
patterns, and the value of human potential and rational thinking patterns. Thus, one of the
benchmarks and the original goal of learning mathematics is the ability to communicate
mathematically to gain more interest in learning (Litkowski, Duncan, Logan, & Purpura,
2020). (Harahap, 2012) states that communication plays an important role, because using
good communication among students, teachers, and the environment can exchange
inspiration (Li & Peng, 2012). So it is necessary to know more about understanding
mathematical communication skills (Rohid, 2019).
According to (Purwandari, Astuti, & Yuliani, 2018), mathematical communication
is a dialect in the classroom with the topic of mathematical material on that day.
Mathematical communication ability can also be interpreted as a student's ability to
express mathematical ideas either orally or in writing (Sarah, Mursalin, Muliana, Nuraina,
& Rohantizani, 2021), and is included in pictures, tables, symbols, diagrams, and algebra
(Awiria, Santosa, & Yuhana, 2021).
Mathematical communication can be expanded with the process of learning
mathematics in schools (Kusuma, 2021). It happens because of the ability of students to
think which is developed from the science of logic. Thus, learning mathematics is crucial
for mathematical communication that is developed (Hodiyanto, 2017).
Mathematical communication skills can be measured from six criteria:
a. Expressing conditions, pictures, diagrams, or other into language, symbols, ideas or
mathematical models
b. Mathematical ideas, conditions and relations are explained orally or in writing
c. Listening and discussing and writing related to mathematics
d. Reading with understanding a written mathematical representation
e. Making conjectures, compiling arguments, formulating definitions, and generalizing
f. Restate a mathematical description or paragraph in your own language
However, in the learning process mathematical communication skills have not been
fully developed explicitly. The reality in the field shows that students' mathematical
communication skills are still low and many students have difficulties in learning
mathematics.
As happened in class VIII-1 of the Pangkalan Susu National Development Junior
High School, researchers conducted an initial test on February 26, 2021 with a total of 21
students. From the results of the initial test conducted. Based on the results of the initial
test, it was obtained that the skills of students who were able to explain/write mathematics
(Known elements, were asked and conclusions) only 11 students (33.4%) belonged to the
very low category, students who were able to describe mathematics (Described) pictures,
diagrams, graphs, or tables completely and correctly) only 9 students (38%) belong to the
very low category and students who are able to express mathematics/mathematical
representations (Stating mathematical ideas using symbols or mathematical language in
writing) only 8 students (47 ,61%). Rate. average. ability. student mathematical
communication. on. test. ability. beginning. is 72.73% with 16 students who are not
capable of mathematical communication (value 70). So that the value has not reached
classical completeness because the number of students who have completed (the score
65) has not reached 85% of the total number of students.
mathematical communication skills in SMPS National
Development of Pangkalan Susu.
Volume 3, No. 3, January 2022, pp. 250-260
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Efforts to build students' mathematical communication skills, one of which is
influenced by the learning model applied by the teacher in order to create effective
learning in learning mathematics, it is necessary to have a learning model involving the
teacher, namely the teacher and students or students. The monotonous learning process
will make students feel bored, the teacher must actively adapt the learning model to the
material being taught.
One of the learning models of Reciprocal Teaching which is expected to improve
students' mathematical communication skills. This learning model supports student
involvement in learning activities.
(Meilia, 2021) argues that:
Reciprocal Teaching is an upgrading approach that practices 4 independent
description strategies (Said, 2021), namely formulating learning materials, organizing
problems and solving them, re-explaining the insights that have been obtained (Hidayah,
Ulfah, & Suryaningsih, 2021), after that predicting the next problem from the case
presented to students. The benefit is that it can increase the enthusiasm of students in
upgrading because students are demanded to actively share ideas and explain their
professional results well so that the ability to design something especially the language of
mathematics can be achieved. So it can be concluded that Reciprocal Teaching is a form
of upgrading where students are given the opportunity to work on the module first. After
that, students re-explain the modules they have learned to other students. The teacher only
works as a provider and mentor in upgrading, which is to straighten or provide a
description of module matters that cannot be solved independently by students.
Research.Method....
This type of research is classroom action research (Classroom Action Research)
which aims to improve students' mathematical communication skills by applying the
Reciprocal Teaching learning model to the material Relations and Functions in class VIII-
1 students. Classroom Action Research is defined as research conducted in the classroom
and aims to overcome various problems that occur in the classroom.
The subjects in this study were students of class VIII-1 SMPS National
Development Base Milk, as many as 21 people. The object of this study is to improve
students' mathematical communication skills in relation and function material by using
the Reciprocal Teaching learning model in class VIII of the Pangkalan Susu National
Development Middle School for the 2021/2022 Academic Year.
Picture 1. Classroom Action Research.
Yulia Dahlan
1
and Nurhasanah Siregar
2
!
Efforts to Improve Students' Mathematical Communication Ability Through
Reciprocal Teaching Learning Model For Class VIII SMPS Development National
School of Milk Base 253
Result.and.Discussion.
This research was conducted at SMPS National Development Pangkalan Susu
Class VIII-1, which consisted of 21 students. The problem in this study is in accordance
with the background of the problem, namely the low mathematical communication skills
of students. The problem was obtained from the results of the initial ability test on
students' mathematical communication skills given during observation. The results are
described in the following table.
Table 1. Improving Students' Mathematical Communication Understanding Ability in
Cycle I and Cycle II.
Ability Indicator
Cycle I
Cycle I
Improvement
Write/explain the known elements,
ask questions and draw conclusions.
62,68
77,84
15,16
describe pictures, diagrams, graphs, or
tables completely and correctly.
45,90
74,95
29,05
express mathematical ideas using symbols or
mathematical language in writing.
44,09
77,84
33,75
Grade average
58,09
77,11
19,02
Classical completeness
45,45%
81,81%
36,36%
The average value obtained by students classically on the steps of mathematical
communication on each test of mathematical communication skills II has increased. The
following is a description of the students' mathematical communication steps:
Picture 2. Description of the Increase in the Average Score of Ability.
Based on the test results of students' mathematical communication skills in the
initial ability test, the average test score from 40.00 increased to 58.09 in the first cycle
and increased to 77.11 in the second cycle the percentage of students who have been able
to communicate mathematically from 27.27 % in the initial ability test increased to
Volume 3, No. 3, January 2022, pp. 250-260
254 http://devotion.greenvest.co.id
45.45% in the first cycle and increased to 81.81% in the second cycle. More details can
be seen in table 2.
Table 2. Level of Mathematical Communication Ability Each Cycle.
Value Interval
Mathematical
Communication
Ability Level
Beginning
90 ≤ TKKM ≤
100
Very High
-
80 ≤ TKKM < 90
Tall
-
65 ≤ TKKM < 80
Enough
6
56 ≤ TKKM < 65
Low
16
∑
22
Class Average
40,00
The results are presented in a graph in Picture 3.
Picture 3. Graph of the Average Value of the Communication Ability Test in Each Cycle.
The students' ability in writing/explaining known elements, asked elements, and
drawing conclusions on the questions in the first cycle obtained an average value of 62.68
and in the second cycle of 77.84 with an increase of 15.16. More details can be seen in
table 3.
Table 3. Mathematical Communication Ability Level Cycle.
Value Interval
Mathematical
Communication
Ability Level
Cycle I
Cycle II
90 ≤ TKKM ≤ 100
Very High
-
-
80 ≤ TKKM < 90
Tall
5
8
65 ≤ TKKM < 80
Enough
10
12
56 ≤ TKKM < 65
Low
7
2
∑
22
22
Awal siklus I siklus II
Nilai rata-rata
40 58.09 77.11
0
10
20
30
40
50
60
70
80
90
Average value
Average Value
Yulia Dahlan
1
and Nurhasanah Siregar
2
Efforts to Improve Students' Mathematical Communication Ability Through
Reciprocal Teaching Learning Model For Class VIII SMPS Development National
School of Milk Base 255
The results are presented in a graph in Figure 2
Picture 4. Graph of Mathematical Communication Ability Level Each indicator of ability
to write/explain known elements, asked elements, and draws conclusions.
The ability to paint pictures, diagrams, graphs, or tables completely and correctly
in the first cycle was 45.90 and in the second cycle the average value was 74.95 with an
increase of 29.05. More details are noted in table 4.
Table 4. Level of Mathematical Communication Ability Each Cycle Indicator of ability to
paint pictures, diagrams, graphs, or tables completely and correctly
Value Interval
Mathematical
Communication
Ability Level
Cycle II
90 ≤ TKKM ≤ 100
Very High
-
80 ≤ TKKM < 90
Tall
4
65 ≤ TKKM < 80
Enough
14
56 ≤ TKKM < 65
Low
4
∑
22
Average Class
74,95
Class Average
62,68
77,84
62.68
77.84
Siklus I siklus II
Nilai Rata-rata
Nilai Rata-rata
Average Value
Average Value
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The results are presented in a graph in Picture 5.
Picture 5. Graph of Mathematical Communication Ability Level Each Indicator depicts a
complete and correct picture, diagram, graph, or table.
The ability to express mathematical ideas using symbols or mathematical language
in writing in the first cycle was 44.09 and in the second cycle the average value was 70.04
with an increase of 29.14. More details are noted in table 5.
Table 5. Level of Mathematical Communication Ability Each Cycle Indicator states
mathematical ideas using symbols or mathematical language in writing.
Value Interval
90 ≤ TKKM ≤ 100
80 ≤ TKKM < 90
65 ≤ TKKM < 80
56 ≤ TKKM < 65
Average Value
Average Value
Yulia Dahlan
1
and Nurhasanah Siregar
2
Efforts to Improve Students' Mathematical Communication Ability Through
Reciprocal Teaching Learning Model For Class VIII SMPS Development National
School of Milk Base 257
The results are presented in a graph in Picture 6.
Picture 6. Graph of Mathematical Communication Ability Level Each Indicator expresses
mathematical ideas using written mathematical symbols or language.
From the description of the research results, it can be seen that through the reverse
learning model (reciprocal teaching) can increase student activity because the principle of
this learning is a learning that applies four cognitive strategies that direct students to be
independent, active in understanding a material. So in every learning the more active role
is the students.
In the first cycle, the observations showed that the students were quite happy and
enthusiastic about learning with the application of the reciprocal teaching model to
inform that this learning model could create a positive response for students to learn
mathematics. Students also look smarter and bolder in applying the reverse learning
model.
The results of the study after being given an action that was carried out in 2 cycles
to see students' mathematical communication skills, namely in the first cycle, student
learning was carried out according to the lesson plans that had been made in the material
being studied and after learning was completed, students presented the results of their
discussions. Cycle I was carried out in 2 meetings, after completing the first cycle at the
end of the meeting students were given a test to measure mathematical communication
skills by being given questions that matched the indicators of mathematical
communication. The results of the implementation of the first cycle is 50.89 with the
level of mathematical communication skills in the low category.
After the results obtained from the first cycle, it can be seen what problems have
not been resolved in the learning process or at the time of giving the mathematical
communication ability test. In the second cycle of group learning, there were still some
groups that were not compact and not yet active. Researchers provide understanding to
students about the importance of cooperation. The researcher determined that one of the
students was the leader of the group who was encouraged to invite his friends to do an
investigation together so that each member of the group could participate properly.
Researchers guide students to divide tasks to each group member when presenting the
results of the discussion in order to make time efficient.
Increasing indicators of mathematical communication skills, namely writing
mathematics from cycle I to cycle II, increased from cycle I students who completed
writing/explaining known elements, asked elements, and drawing conclusions there were
Average Value
Average Value
Volume 3, No. 3, January 2022, pp. 250-260
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15 students (68.19%) and cycle II increased to 20 students (90.0%). The ability to paint
pictures, diagrams, graphs, or tables completely and correctly also increased from 8
students (36.36%) to 18 students (81.82%). The ability to express mathematical ideas
using symbols or written mathematical language has increased from 7 students (31.81%)
to 17 students (77.28%).
Of the 4 indicators of mathematical communication skills that have the lowest
average value is the ability to express mathematical ideas using symbols or written
mathematical language. Because students do not really understand giving mathematical
ideas in the form of symbols or mathematical language. Therefore, teachers should teach
students various examples related to mathematical symbols.
Based on the results of the research that has been stated above, it shows that the
application of the Reciprocal Teaching model can improve students' mathematical
communication skills.
Based on the results of data analysis, learning mathematics on the material
Relations and Functions using the Reciprocal Teaching model in cycle I can be said to be
ineffective because it does not meet one of the indicators of learning effectiveness,
namely classical mastery of students' mathematical communication ability tests that do
not reach 80%, namely 58.09%. While in the second cycle of learning is said to be
effective because: the classical mastery of the second mathematical communication skill
test of students reached 81.81% and the process of implementing learning is in the good
category.
Based on the description above, it can be concluded that the Reciprocal Teaching
model is an alternative that can be used in improving students' mathematical
communication skills (Iskandar, Jannah, & Wicaksono, 2021), especially the material on
relations and functions at the Milk Base National Development Junior High School
(Kilelu, van der Lee, Koge, & Klerkx, 2021).
Conclusion.
The Reciprocal Teaching model is able to improve students' mathematical
communication skills. The increase in students' mathematical communication skills is
also supported by the increase in students' mathematical communication ability test
results. The results of the student's mathematical communication ability test given in the
classical cycle I obtained that students who completed were 10 students (45.45%) out of
22 students with an average of 58.09 and had not achieved classical completeness, in the
second cycle students who completed increased to 16 students (72.72%) of 22 students
with an average of 74.18 and have reached the classical completeness criteria. Based on
the results of this study, it was concluded that the application of the Reciprocal Teaching
model could improve the mathematical communication skills of class VIII students of the
National Development SMPS Pangkalan Susu T.A 2021/2022 on the material of
Relations and Functions.
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