JURNAL PENDIDIKAN MATEMATIKA DAN IPA
Vol.
No.
459 - 468
http://jurnal.
id/index.
php/PMP THE EFFECTIVENESS OF THE TEACHING AT THE RIGHT LEVEL (TaRL) APPROACH ON LEARNING OUTCOMES IN THE TOPIC OF RELATIONS AND FUNCTIONS AMONG GRADE Vi STUDENTS Christelita Chelcilia Edy1.
Nicky Kurnia Tumalun2.
Vivian Eleonora Regar3
1,2,3
Department of Mathematics Education.
Faculty of Mathematics.
Natural Sciences, and Earth Sciences.
Universitas Negeri Manado.
Jl.
Kampus Unima.
Tondano.
Minahasa.
Sulawesi Utara 95618 Email Corresponding: christelitachelci6@gmail.
DOI: https://dx.
org/10.
26418/jpmipa.
Abstract This research aimed to evaluate the effectiveness of the Teaching at the Right Level (TaRL) approach on student learning outcomes regarding relations and functions.
This experimental study employed a pretest-posttest control group design at State Junior High School 5 Manado.
The experimental class was taught using the TaRL approach, while the control class received Direct Instruction.
Results indicated that the average learning outcomes of the experimental class .
significantly outperformed the control class .
Hypothesis testing via t-test yielded tcount = 3.
ttabel = 2.
011 at a significance level of 0.
05, confirming significant Furthermore.
TaRL met all effectiveness criteria: .
the average score exceeded the learning objective attainment threshold (KKTP) of 75.
classical mastery was achieved.
student responses to the learning process were positive.
In conclusion, the TaRL approach is effective in improving student learning outcomes for relations and functions material among eighth-grade students.
Keywords: Effective.
Teaching at the Right Level.
Relations and Functions.
INTRODUCTION
A fundamental system that is essential and inherent in the life of every individual is referred to as education .
Education constitutes a knowledge, enhance skills, and provide benefits for individuals in mastering theories, making decisions, and solving various contextual problems .
Therefore, education plays a crucial role in improving the quality of human resources and achieving national aspirations .
line with the objective of enhancing human resource quality, mathematics is regarded as an important subject.
Received Revised Accepted : 2025-12-09
: 2026-05-07
: 2026-05-21
This work is licensed under a Creative Commons Attribution 4.
0 International License Jurnal Pendidikan Matematika dan IPA Vol.
No.
particularly in fostering logical and analytical thinking skills .
As an essential discipline, mathematics is a compulsory subject at every level of education in Indonesia, ranging from the most basic to higher education .
However, the majority of students perceive mathematics as a difficult and uninteresting subject .
Despite these challenges, which often reduce learning interest, they do not diminish the inherent importance of mathematics itself .
Mathematics instruction from the primary school level is necessary to improve the quality of education and to develop studentsAo abilities in logical, analytical, systematic, critical, and innovative thinking .
Observations and interviews conducted at SMP Negeri 5 Manado achievement of Grade Vi students in mathematics, particularly in the topic of Relations and Functions, which is perceived as abstract and difficult.
The relationships, representing them in diagrams, and relating the concepts to real-life contexts.
This condition is exacerbated by the implementation of predominantly conventional teaching methods and the lack of in-depth instructional support from teachers.
Based on interviews with the mathematics teacher, the majority of studentsAo learning outcomes fall below the Minimum Mastery Criteria (KKTP) of 75, with an average recorded score of only 55.
A relation is defined as Aua rule that maps elements of set A to elements of set B, which can be represented in arrow diagrams.
Cartesian diagrams, or sets of ordered pairs.
Ay Meanwhile.
Aua function from A to B is a special type of relation that requires each element of A to be mapped to exactly one element of BAy .
This topic demands strong reasoning abilities.
therefore, its mastery is highly important for students .
The high level of difficulty underscores the need for an adaptive, comprehensive, and structured approach to effectively internalize the concepts of Relations and Functions .
Teaching at the Right Level (TaRL) is an approach oriented toward studentsAo actual abilities, without being constrained by formal grade levels .
TaRL emphasizes the adaptation of instructional materials and methods according to studentsAo levels of understanding to optimize their .
The effectiveness of this approach depends on the systematic implementation of two main components, namely grouping students based on their initial ability levels and focusing on skills appropriate to those levels .
This student-centered supports the development of each learnerAos specific competencies .
TaRL is considered a solution to the problem of diverse learning paces within the classroom .
, recognizing that each student possesses varying levels of understanding .
The TaRL syntax includes: .
diagnostic assessment to map studentsAo initial abilities, .
communication of learning objectives, .
grouping students based on ability levels .
igh, medium, lo.
, .
provision of core conceptual understanding to enable independently, and .
guidance and monitoring throughout the learning Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
process, followed by reflection and consolidation of the material .
Support from previous studies strengthens the rationale for selecting TaRL as a solution.
Study .
demonstrated the effectiveness of TaRL in improving mathematics learning outcomes, evidenced by a significant increase in the average score from 63.
21 to 82.
Study .
also concluded that TaRL is effective because instruction is tailored to studentsAo levels of understanding and encourages their active participation during the learning process.
Therefore, it has the potential to serve as an effective solution to address the issue of low student learning achievement .
Based discussion, this study aims to investigate the effectiveness of the Teaching at the Right Level (TaRL) approach on studentsAo learning outcomes in the topic of Relations and Functions at SMP Negeri 5 Manado.
METHOD
This study employed a quasiexperimental design in the form of a pretestAeposttest control group with a quantitative approach, conducted at SMP Negeri 5 Manado in the first semester of the 2025/2026 academic year, involving the entire population of Grade Vi students.
The sample was selected using a simple random sampling technique, resulting in Class Vi.
1 as the experimental group .
cu = .
and Class Vi.
3 as the control group .
cu = .
Instruction using the TaRL approach in the experimental class was conducted over two sessions with a time allocation of 3 y 40 minutes .
minutes per sessio.
The intervention procedure included: .
an initial .
grouping students based on their levels of and .
instruction tailored to the ability level of each The consisted of an essay test .
retestAe posttes.
to measure learning outcomes in relations and functions, as well as a Instrument validity was ensured through content validity testing conducted by two expert lecturers from the Department of Mathematics at Manado State University .
xpert Based on the expertsAo evaluation, the test items were deemed valid and appropriate for data collection in this study.
Posttest data were analyzed through prerequisite tests, namely the normality test (Liliefor.
and the homogeneity test (F-tes.
, followed by Independent Samples t-test.
The data were considered normally distributed if yaycaycaycoycaycycoycaycyceycc < yaycycaycaycoyce .
u = 0,.
and were considered homogeneous .
qual variance.
if yaycaycaycoycaycycoycaycyceycc < yaycycaycaycoyce .
u = 0,.
Hypothesis conducted at a significance level of = The null hypothesis (HCA) states that the mean learning outcomes of the class implementing the TaRL approach are equal to those of the class Meanwhile, the alternative hypothesis (HCA) states that the mean learning outcomes of the TaRL class are superior to those of the class using direct instruction.
The criterion for rejecting HCA is if ycycaycaycoycaycycoycaycyceycc > ycycycaycaycoyce in which case HCA is rejected and HCA is accepted, indicating that the TaRL Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
approach is proven to yield superior .
ore effectiv.
learning outcomes compared to direct instruction, and vice versa.
The effectiveness of the TaRL approach in the experimental class was measured using three main criteria.
Criterion 1 is individual learning achievement, in which TaRL is considered effective if studentsAo posttest scores exceed the Minimum Mastery Criterion (KKTP) established by SMP Negeri 5 Manado, namely 75.
Criterion 2 is classical learning this approach is deemed effective if the percentage of students achieving the KKTP reaches at least 80% of the total number of students in .
Furthermore.
Criterion 3 examines studentsAo responses to the instruction.
The response questionnaire data were analyzed descriptively and classified as presented in Table 1.
Table 1.
Student Response Criteria Percentage .
yc Ou ynya yiya O yc < ynya yeya O yc < yiya yaya O yc < yeya yc < yaya Criteria Very Positive Positive Moderately Positive Less Positive Very Less Positive Sumber: .
RESULT AND DISCUSSION The data presented in the following table represent the studentsAo learning outcomes from both classes instructional models, serving as the primary data used to analyze and test two effectiveness criteria: Criterion 1 (Individual Learning Achievemen.
, based on the comparison of the average posttest score with the KKTP, and Criterion 2 (Classical Master.
, based on the percentage of students achieving mastery in the experimental class.
These data are presented in detail in Table 2.
Table 2.
Learning Outcomes of the Experimental and Control Classes Number of Students Average Pretest Score Average Posttest Score KKTP Score Number of Students Achieving Mastery (Ou yiy.
Percentage of Mastery Number of Students Not Yet Achieving Mastery (< yiy.
Percentage Not Yet Achieving Mastery Experimental Class
58,440
81,800
Control Class
58,640
71,480
Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
Table 2 illustrates that 20 students .
%) in the experimental class achieved scores exceeding the KKTP .
, while 5 students .
%) scored below the KKTP.
Thus.
Criterion 1 of TaRL effectiveness is fulfilled, as the average student learning achievement surpasses the KKTP value .
Furthermore, with a mastery percentage of 80%, the experimental class also meets Criterion 2 (Classical Master.
required to determine the effectiveness of the TaRL approach.
This instructional grouping.
As explained by (Banerjee et al.
, 2.
, the core of TaRLAos effectiveness lies not merely in the content, but in the appropriateness of the instructional AudosageAy provided according to studentsAo initial ability In the topic of Relations and Functions, which is inherently abstract, this grouping enables lower-level students to build a foundational understanding of concepts without feeling intimidated by the complexity of Grade Vi material.
This approach helps prevent the widening of learning gaps, which often occur conventional instructional models (Sari et al.
, 2.
Practically, indicate that mathematical content perceived as difficult can be made accessible to students if instruction is not rigidly driven by curriculum targets alone, but is instead aligned with learnersAo cognitive readiness.
Furthermore, the effectiveness of the TaRL approach was also evaluated through Criterion 3, namely studentsAo positive responses to the instruction.
The analyzed data from the student response questionnaire are presented in detail in the table 3.
Table 3.
Results of the Analysis of Student Response Questionnaires toward the Implementation of Instruction Indicator Grouping based on ability level Instructional components Student engagement Teacher monitoring Average Based on Table 3, it was found that overall, 82 percent of students provided positive responses, indicating that they perceived beneficial impacts and agreed with the instructional method using the TaRL approach.
This is supported by qualitative data from student comments, which consistently reinforce improvements in cognitive understanding, the perception that the instructional method is effective and Percentage Criteria Very Positive Very Positive Very Positive Positive Very Positive engaging, and appreciation for the collaborative learning aspect.
From the questionnaire results, both in terms of percentage scores and comments, it can be inferred that students responded positively to the implementation of the TaRL instructional model, thereby fulfilling Criterion 3 of research The first stage in the data analysis process began with prerequisite testing to determine the Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
type of statistical analysis to be used.
The normality test of the sample data distribution employed the Liliefors method, as presented in Table 4.
Table 4.
Results of the Normality Test Posttest Data Mean Experimental 81,800 Standard Deviation .
10,111 Control
71,480
10,033
The results of the normality test show that yaycaycaycoycaycycoycaycyceycc = 0,096 .
, both of which are less than yaycycaycaycoyce .
Therefore, based on the testing criteria, it is confirmed that the sample data are normally distributed.
After the normality assumption was satisfied, the analysis proceeded ycyeOyeOyeiyenyeayeO ycyeiyeCyeEyeIyes Conclusion 0,096 0,180 0,089 0,180 Normally Distributed Normally Distributed with the homogeneity of variance test, which aims to examine the equality of variances between the experimental and control groups.
If homogeneity is confirmed, statistical comparisons between the two groups can be validly The results of the homogeneity test are presented in Table 5.
Table 5.
Results of the Homogeneity Test Posttest Data Experimental Control Variance .
cya ) 102,250 100,677 ycyeOyeOyeiyenyeayeO ycyeiyeCyeEyeIyes 1,016 1,984 From Table 5, it is observed that Significance (Sig.
0,485
Conclusion Homogene purely influenced by the treatment rather than differences in the initial variance conditions.
Hypothesis testing constitutes the final stage to address the research problem, employing the Independent Samples t-test .
-tes.
The results of the t-test analysis are summarized in Table 6.
< yaycycaycaycoyce .
, further supported by the significance value (Sig.
) = 0.
485 > 0.
This finding leads to the conclusion that the variances of the data in both classes are homogeneous, indicating that any differences in the final outcomes are Table 6.
Results of the Hypothesis Test
Posttest Data
Mean
yeiyeOyeOyeiyenyeayeO
yeiyeiyeCyeEyeIyes Experimental Control
81,800
71,480
3,622
2,011
Sig.
0,001
yu Conclusion 0,05 There is a Significant Effect Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
Based on the results in Table 6, the value of ycycaycaycoycaycycoycaycyceycc = 3,622 > ycycycaycaycoyce = 2,011, at 48 degrees of freedom .
This is further supported by the significance value Sig.
-taile.
= 0.
001 < 0.
Referring to these values.
HCA is rejected and HCA is implementation of TaRL is more effective than the direct instruction The theoretical implications of these hypothesis testing results reinforce the differentiated instruction These findings affirm that the effectiveness of TaRL lies in reducing studentsAo cognitive load.
through the segmentation of material according to ability levels, students are able to achieve better mastery of the concepts of Relations and Functions.
The results of this study indicate a significant increase in the average student learning implementation of the TaRL approach.
This improvement is reflected in studentsAo enthusiasm and participation throughout the learning process.
Each student was provided with instruction aligned to their actual level of ability, with teachers facilitating learning activities focused on the mastery of fundamental skills.
This demonstrates that the implementation of the TaRL approach is capable of fostering an environment, as well as enhancing studentsAo confidence in mastering essential competencies.
These findings are consistent with .
, which define TaRL as a method that instructional material with studentsAo actual ability levels.
The improvement in learning outcomes can be directly associated with the steps embedded in the TaRL instructional syntax that was The initial diagnostic assessment enabled teachers to classify students into levels .
igh, medium, lo.
, as explained by .
This grouping ensures that each student receives appropriate intervention, thereby addressing the fundamental issue of differing learning paces among students, as highlighted by .
Findings from .
are also effectiveness of the TaRL approach in improving student learning outcomes.
The test results indicate that pretest scores prior to the implementation of TaRL showed a significant increase in the posttest.
Specifically, the study reported improvements in both the lowest and highest achievement scores following the implementation of TaRL.
Furthermore, the results of study .
likewise concluded that the TaRL approach is effective in enhancing learning outcomes.
This approach facilitates the development of numeracy skills by aligning instruction with studentsAo levels of understanding and encouraging active participation during the learning These findings confirm that the implementation of the TaRL
approach has a positive and significant studentsAo
CONCLUSION
The overall conclusion of this study is that the TaRL approach meets all established effectiveness criteria and demonstrates a statistically Christelita Chelcilia Edy.
Nicky Kurnia Tumalun.
Vivian Eleonora Regar The Effectiveness of The Teaching at The Right Level (TaRL) Approach on Learning Outcomes in The Topic of Relations and Functions among Grade Vi Students Jurnal Pendidikan Matematika dan IPA Vol.
No.
significant difference in learning The experimental class achieved an average score of 81.
exceeding the KKTP (Ou.
, with classical mastery attained and supported by predominantly Very Positive student responses .
verage of 82%).
Furthermore, there is a clear difference compared to the learning outcomes under the direct instruction model, with the control class average recorded at 71.
The t-test results show that tcalculated = 3,619 > ttable = 2,011 leading to the rejection of HCA and acceptance of HCA.
This indicates that the TaRL approach is statistically significantly more effective than direct instruction, particularly in the topic of Relations and Functions at SMP Negeri 5 Manado.
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