Corresponding Author: Nasruddin
E-mail: [email protected]
INTRODUCTION
Learning mathematics as part of the educational
process in schools plays a vital role in increasing students' potential. This
is following the regulation of the minister of national education number 22 of
2006 concerning content standards that mathematics subjects need to be given to
all students starting from elementary school to equip students with the ability
to think logically, analytically, systematically, critically and creatively, as
well as the ability to work together (Masuri, 2019). The development of science begins with human nature,
which wants to know everything (Arifin, 2020). So far, in learning mathematics, students have never
or rarely been allowed to present their representations (Djidu et al., 2021). Students tend to imitate the teacher's steps in
solving problems. As a result, students' mathematical representation abilities
still need to develop. In addition, the resources that can support the student
learning process could be more extensive. So, global competition arises between
various nations to obtain supporting sources to succeed in this learning (Jahring et al., 2022).
Referring to the National Council of Teachers of
Mathematics states that five basic mathematical abilities are standard, namely
problem-solving, reasoning and proof, communication, connections, and
representation (HL et al., 2023). One of the abilities that students must possess is the
ability to represent. Representational ability is the ability of students to
express their ideas in mathematical models to plan a problem-solving through
mathematical representations; students can develop and deepen their
understanding of mathematical concepts and help students communicate their
thoughts. Based on this description, the ability to represent is an essential
element in learning mathematics (Yusnani, 2016).
Based on the results of observations and interviews
conducted at the school, it was found that most students' mathematical
representation abilities were at a low level (Sejati et al., 2021). This is due to several factors, including the lack
of students' ability to express ideas or ideas, the lack of student involvement
in the teaching and learning process, and the use of the learning model used is
not appropriate, the learning that teachers often apply is discussion, lecture,
and question and answer. This resulted in students needing more motivation to
obtain sources of information other than the teacher and students not
accustomed to discovering mathematical concepts.
Recognizing the importance of mathematical
representation abilities, teachers must seek learning by applying learning
models that usually involve students fully in the learning process, encouraging
students to be able to communicate the ideas they have (Ovan et al., 2023). By choosing the suitable learning model, existing
learning can provide opportunities and encourage students to practice students
mathematical abilities (Jahring et al., 2022).
Observing this, it is better to renew innovation and
mindset toward learning goals of mathematics that are more varied with learning
methods or models that can optimize students' abilities (Hariyati et al., 2013). An exciting and effective learning model or method
is needed so students can participate in the learning process (Nasruddin et al.,
2019).
The Team Assisted Individualization (TAI) type of
cooperative learning model was initiated to design a particular teaching form
that could solve problems that could make individual teaching methods
ineffective. By having students work in cooperative learning teams and taking
responsibility for managing and checking routines, helping each other with
problems, and encouraging each other to progress, teachers can free themselves
from giving one-on-one instruction to small groups�homogeneous students from
heterogeneous teams (Hakim, 2023). As teachers, we dream of reviving the joy of
learning.
The TAI is a group learning model with a guidance
strategy between friends. In this lesson, students are given worksheets to work
on in groups so that students can easily understand the concept of the
material. Students are invited to study independently, trained to optimize
their ability to absorb the scientific information they seek, explain their
findings to other parties, solve problems, and use their representations. So
through this learning model, the students' activeness, independence, and skills
in expressing their ideas can be developed. In addition, this model is expected
to improve students' mathematical representation abilities.
The aims of this study were 1) to find out how the
pretest and posttest results of the students' mathematical representation
abilities were taught by using the TAI cooperative learning model and
conventional learning models; 2) to find out whether the average increase in
students' mathematical representation abilities after being taught with the TAI
type cooperative learning model with a constructivism approach and conventional
learning models; and 3) to find out whether the students' mathematical
representation skills taught by the TAI type cooperative learning model with a
constructivism approach are more effective than conventional learning models.
METHODS
This type of research is True Experiment
research involving two classes, namely TAI learning with a constructivism
approach given to experimental class students and conventional learning given
to control class students. Experimental research is a method used to seek the
effect of specific treatments on others under controlled conditions (Sugiyono, 2013). This research was conducted at Samaturu 3 Public Middle
School in class VIII, even semester, in Liku Village, Samaturu District, Kolaka
Regency. This
study used two classes, namely the first class, taught by the TAI learning
model with a constructivism approach, and the second class, which was taught by
conventional learning. This study used pretest and posttest to measure
students' initial and final abilities. The experimental design used a
pretest-posttest control group design. According to Arikunto, the population is
the entire research subject (Arikunto, 2002). Meanwhile, according to Sugiyono, the population is a
generalization area consisting of objects/subjects with specific qualities and
characteristics determined by researchers to be studied and then conclusions
drawn (Sugiyono, 2013). The population in this study were all class VIII students
at SMP Negeri 3 Samaturu, which consisted of 3 classes with 86 students.
The sample in this study was selected using cluster
random sampling. Sukardi states that random cluster sampling is a sample
selected based on groups, regions, or subjects that naturally come together (Sukardi, 2021). At
the same time, Bintari stated that
cluster random sampling is sampling based on groups as members of the
population. This study used simple cluster random sampling (Bintari et al., 2014).
RESULTS AND DISCUSSION
Descriptive Analysis
Descriptive analysis in this study consisted of an analysis of students' mathematical representation
abilities, an analysis of teacher observation sheets, and an analysis of student
activity observation sheets as well as an analysis of students' mathematical
representation abilities.
Analysis of Students' Mathematical
Representation Ability
Analysis of students' mathematical representation abilities is intended
to provide an overview of the characteristics and differences in the average value of the Team Assisted Individualization cooperative
learning model. (TAI) with
the constructivism approach
and the conventional learning model,
which can be seen through the average or
mean and
standard deviation values in
Table 1 below.
Table 1 . Descriptive Analysis of Students' Representational
Ability
|
Statistics
|
Learning model
|
|
TAI
|
conventional
|
|
Pretest
|
Posttest
|
N-Gains
|
Pretest
|
Posttest
|
N-Gain
|
|
N
|
19
|
19
|
19
|
17
|
17
|
17
|
|
Average
|
14.08
|
58.72
|
0.525
|
15
|
55.52
|
0.478
|
|
Save. raw
|
5.78615
|
7.332761
|
0.07060
|
6.78923
|
7.20368
|
0.06694
|
|
Variance
|
33.47953
|
53.76938
|
0.005
|
46.09375
|
51.89306
|
0.004
|
Based on Table 1, we obtained an average
increase in the ability of
mathematical representation (KRM)
of students taught with the TAI-type
cooperative learning model of 0.525. In contrast, the average increase in KRM
taught with a conventional learning model was 0.478; the interpretation of the N-gain
value for both learnings was included in the medium category. So the average
increase in students in TAI learning with a constructivist approach is higher
than the average increase in students taught with conventional learning.
Analysis of Teacher Activity Observation Sheets
������������ The teacher's observation sheet is used to see whether
the teacher can carry out the learning process according to the existing
syntax. The results of the observation sheet are presented in Table 2 and Figure 1 below:
Table 2.
Results of Teacher Activity Observation
Sheet
|
Observation of Teacher Activities
|
Meeting
|
|
1
|
2
|
3
|
4
|
|
Experiment Class
|
81.25%
|
86.67%
|
86.67%
|
93.33%
|
|
Control Class
|
80%
|
81.818%
|
90.909%
|
90.909%
|
|
Average Percentage of Experiment Class Teacher Activities
|
86.98%
|
|
Average Percentage of Activity
Control Class Teacher
|
85.909%
|
From the results
of the analysis in Table 2 above, it can be seen that the percentage of the
average value of teacher activity in the learning process using the TAI
learning model with a Constructivism approach in the experimental class is
86.98%. While the percentage of the average value of teacher activity in the
learning process using conventional learning in the control class is 85.909%.
The results of the analysis of the observation sheet can be seen in Figure 1 below:
Figure 1. Results of Analysis of Teacher Activity Observation
Sheets
Analysis of Student Activity Observation Sheets
Student activity observation sheets determine student activity during
the learning process. The results of the observation sheet are presented in
Table 3 and Figure 2
below:
Table 3. Results of Student Activity Observation Sheets
|
Observation Student Activities
|
Meeting
|
|
1
|
2
|
3
|
4
|
|
Experiment Class
|
76.67%
|
76.67%
|
80%
|
83.33%
|
|
Control Class
|
63.64%
|
75%
|
78.33%
|
83.64%
|
|
Average Percentage of
Experiment Class Student Activities
|
79.18%
|
|
Average Percentage of
Activity
Control Class Students
|
74.70%
|
From the analysis results in
Table 3 . above, it can be seen that
the percentage of the average value of student activity in the learning process
using the TAI learning model with a
constructivism approach in the experimental class is 79.18%. While the percentage
of the average value of student activity in the learning process using
conventional learning in the control class is 74.70%. The results of the student observation sheet analysis can
be seen in Figure 2 below:
Figure 2 Results of Analysis of Student Activity
Observation Sheets
Inferential Analysis
The difference in increase using
independent sample t-test, with the following statistical hypotheses:
�
The test criteria used are if the t hit value > t table,
then H 0 is rejected, and if the t hit value < t
table, then H 0 is accepted. The significance test is
used to test the increase in students' mathematics learning outcomes taught by the TAI
cooperative learning model, and the conventional learning model uses the Independent Samples T-Test, presented in Table 4.
Table 4.
Results of the Analysis of the
Significance Test of Differences in
Students' Mathematical Representation Ability in
Both Learning
|
|
n
|
|
|
|
tcount
|
t table
|
Conclusion
|
|
Experiment
|
19
|
0.525
|
0.00498
|
0.069
|
2039
|
1.6918
|
H0 is rejected
|
|
Control
|
17
|
0.478
|
0.00448
|
Based on the table above, it is found that the value of tcount =
2.039 > ttable = 1.6918, then H0 is rejected, and H1
is accepted. By accepting H1, it can be concluded
that the increase in the mathematical representation abilities of students who
use the TAI learning model with a constructivist approach is higher than the
increase in the mathematical representation abilities of students who use
conventional learning in class VIII students of SMP Negeri 3 Samaturu.
From the results of the research
that has been described previously, the discussion in this study includes 1) Students'
mathematical representation abilities; 2) the teacher's ability to manage to
learn; 3) student activity in the learning process, and 4) The effectiveness of
the learning model. The discussion is described as follows:
Students' Mathematical Representation Ability
From the results of the study, it was found that the increase in
students' mathematical representation abilities ( N-gain ) who were taught
using the TAI type cooperative learning model with a constructivism approach
consisting of 19 students obtained an average value (mean) of 0.525, with a
variance of 0.005 and a standard deviation 0.07060. While improving students'
mathematical representation abilities (N-gain) taught using conventional
learning consisting of 17 students obtained an average value (mean) of 0.478,
with a variance of 0.004 and a standard deviation of 0.06694.
The results of testing the hypothesis using a single t-test at a
significance level of α = 0.05 obtained a sig. (0.000) < α = 0.05
means H 0 is rejected, and H 1 is accepted. This means
that there is an increase in students' mathematical representation abilities
after being taught using the TAI learning model and conventional learning.
While the results of testing the hypothesis using the t-test at a significance
level of α = 0.05 obtained a value of tcount (2.03985) > ttable (1.6918). Because tcount > ttable, then testing the hypothesis
with the t-test shows that H0 is rejected, increasing the
mathematical representation abilities of students who use the TAI-type
cooperative learning model with a constructivism approach is more effective
than increasing the mathematical representation abilities of students who use
conventional learning.
Teacher Ability to Manage Learning
The teacher's ability to manage learning both in the experimental and
control classes was generally carried out well; this is in accordance with the
observer's observations during 4 (four) consecutive meetings. The average
percentage of teacher activity in the learning process in the experimental
class was 86.98%. Meanwhile, the average percentage of teacher activity in the
learning process in the control class was 85.909%. The average percentage of
teacher activity in the learning process shows that teacher activity in the
learning process in both the experimental class and the control class is
included in the very active category.
Student Activities in Following the Learning
Process
Observer results on student activities in the learning process, both in
the experimental and control classes, show that all aspects observed are
generally carried out well. The average value of the percentage of student
activity in the learning process in the experimental class was 79.18%. At the
same time, the average value of the percentage of student activity in the
control class was 74.70%. From the average value of the percentage of student
activity in the learning process in the experimental class, it is included in
the very active category. In contrast, the control class is included in the
active category.
Learning Effectiveness
The
effectiveness of learning in this study can be concluded that the achievement
of learning effectively both in the TAI cooperative learning model and conventional
learning models is adequate for applying cube and block learning materials for
class VIII junior high school students. However, after further analysis by
comparing the average value of the increase in mathematical representation
ability (N- gain), it shows that the average
increase in the mathematical representation ability of students who are taught
with the TAI-type cooperative learning model with a constructivism approach higher
than the average increase in the ability of students' mathematical
representations taught using conventional learning models. This means that
improving students' mathematical representation abilities by applying the TAI-type
cooperative learning model with a constructivist approach is more effective
than conventional learning models.
CONCLUSION
Based on the results of data analysis
and discussion that has been carried out, the results of this study can be
concluded that the average ability of students' mathematical representations
before being taught using the TAI learning model with a constructivist approach
is still meager, equal to 14.08. while the average pretest results of students
taught using conventional mathematics is 15.00. Meanwhile, the average
mathematical representation ability of students after being taught using the
TAI learning model with a constructivism approach is better than the average
mathematical representation ability of the previous students, which was equal
to 58.72. Meanwhile, the average posttest results of students taught using
conventional learning were better than the average results of students' pretest
mathematics, which was 55.2.
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