Jurnal Elemen, 11.
, 951-965.
October 2025 https:/doi.
org/10.
29408/jel.
Overcoming learning obstacles in cylinder and cone volume: A didactic design research approach Titin Suryani *.
Jamilah.
Reni Astuti Department of Magister of Mathematics Education.
Universitas PGRI Pontianak.
West Kalimantan.
Indonesia Correspondence: tbes955@gmail.
A The Author.
2025 Abstract Many students encounter learning obstacles when understanding the volume of cylinders and however, few studies have explicitly integrated these obstacles into didactic design.
This study aimed to develop a didactic design to address specific learning obstacles in understanding the volume of cylinders and cones.
Using a Didactic Design Research (DDR) approach grounded in BrousseauAos Theory of Didactic Situations, the study involved 28 seventh-grade students and a mathematics teacher from a junior high school in Pontianak, selected through purposive sampling.
Data were collected through observations, diagnostic tests, and interviews and then analyzed qualitatively using interpretative and critical techniques.
The didactic design consisted of four didactic situations: action, formulation, validation, and institutionalization, implemented in classroom practice.
The institutional phase revealed several limitations, particularly a lack of sufficient scaffolding and inadequate visual support for studentsAo spatial The findings indicate that addressing epistemological obstacles, such as misconceptions regarding the interpretation of height and base area in three-dimensional solids, can enhance studentsAo conceptual understanding.
The study suggests that integrating learning obstacle analysis into didactic design helps refine future implementations to better anticipate studentsAo cognitive development.
Keywords: cylinder and cone volume.
didactic design.
learning obstacles How to cite: Suryani.
Jamilah, & Astuti.
Overcoming learning obstacles in cylinder and cone volume: A didactic design research approach.
Jurnal Elemen, 11.
, 951965.
https://doi.
org/10.
29408/jel.
Received: 26 July 2025 | Revised: 5 October 2025 Accepted: 21 October 2025 | Published: 8 November 2025 Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Titin Suryani.
Jamilah.
Reni Astuti Introduction Diagnostic data revealed that 21 of 28 students .
%) exhibited procedural errors when solving cylinder and cone volume problems involving unit conversions and fraction operations (Agustini & Fitriani, 2.
Furthermore, students do not fully understand the underlying concepts and formulas related to these two solids (Solin et al.
, 2.
When teaching the volume of cylinders and cones, teachers tend to emphasize memorizing formulas rather than understanding their conceptual meanings (Aisyah et al.
, 2.
Consequently, students frequently make errors when solving related problems, which can be categorized as learning obstacles (Abouelenein & Elmaadaway, 2023.
Widodo et al.
, 2.
Learning obstacles refer to difficulties that hinder students from fully engaging in learning activities, preventing them from achieving the intended learning outcomes (Pebriyanti et al.
Suryadi, 2.
According to Suryadi .
, learning obstacles consist of three interrelated categories: didactic obstacles, which arise from mismatches between instructional methods and studentsAo learning conditions (Brousseau in Ramli and Sufyani .
obstacles, which relate to psychological or developmental factors influencing studentsAo readiness to learn.
and epistemological obstacles, which stem from a limited understanding or inappropriate conceptualization of mathematical ideas (Jamilah et al.
, 2.
These obstacles manifest as errors in applying formulas, misinterpreting geometric relationships, or lacking motivation and prior knowledge.
Although numerous studies have investigated learning obstacles in topics such as triangles (Sari et al.
, 2.
, geometric sequences (Andani et al.
, 2.
, and the volume of cubes and cuboids (Mahmud et al.
, 2023.
Priskila et al.
, 2023.
Purnama et al.
, 2.
, research addressing curved surface solids, particularly the volume of cylinders and cones, remains Prior Didactical Design Research (DDR) studies have predominantly focused on flat or polyhedral solids, leaving a gap in understanding how students conceptualize solids with curved boundaries and their composite relationships.
This study addresses this gap by focusing on the conceptual and procedural difficulties that arise in learning the volume of cylinders and Preliminary findings from Suryani et al.
, involving seventh-grade students at AlMumtaz Middle School in Pontianak, revealed persistent difficulties in solving problems related to cylinder and cone volumes, especially when involving fractions or formula The interviews indicated that these challenges stemmed from insufficient understanding of prerequisite concepts, computational inaccuracies, and limited variation in problem types.
These findings reflect the presence of didactic, ontogenic, and epistemological obstacles (Ramli & Sufyani, 2.
Developing a didactic design, a term derived from the French didactique des mathymatiques and distinct from the more general Auinstructional designAy is an essential step toward overcoming these barriers.
A didactic design aims not merely to plan teaching sequences but to model and analyze the dynamic relationship between the teacher, student, and mathematical knowledge (Brousseau, 1997.
Chevallard, 1.
Prior research has shown that didactic designs informed by learning obstacle analysis improve both learning effectiveness Overcoming learning obstacles in cylinder and cone volume: A didactic .
and studentsAo conceptual understanding (Habibah et al.
, 2021.
Jamilah & Winarji, 2021.
Rahmawati et al.
, 2.
To strengthen the theoretical foundation, this study systematically integrates SuryadiAos Learning Obstacle Framework with BrousseauAos Theory of Didactic Situations and ChevallardAos Didactic Transposition Theory (Brousseau, 1997.
Chevallard, 1985.
Suryadi.
Each type of learning obstacle informs the construction of classroom tasks and teacher For instance, didactic obstacles were addressed through action situations emphasizing the contextual exploration of real objects .
, estimating cylinder volume through measurable container.
, while epistemological obstacles were targeted in the formulation and validation phases, where students verbalized and justified their reasoning.
Ontogenic obstacles related to motivation and readiness were mitigated during the institutionalization phase through adaptive questioning and reinforcement of conceptual distinctions, such as recognizing the perpendicular height of cones.
This integration illustrates how each obstacle is systematically connected with corresponding didactic situations, thereby providing a coherent theoretical basis for the development of a Hypothetical Didactic Design (HDD) focused on the volume of cylinders and The present study also draws on SimonAos Learning Trajectory Theory (Simon, 1.
, emphasizing the iterative refinement between hypothetical and actual learning pathways (HLT and ALT, respectivel.
Moreover, global perspectives on geometric cognition (Battista, 2007.
Fischbein, 1.
highlight that understanding three-dimensional figures requires the reconstruction of spatial reasoning through visual and experiential engagement, an aspect directly aligned with this studyAos approach.
International applications of Didactical Design Research .
Even and Ball .
Pryvost et al.
) have demonstrated its effectiveness in fostering mathematical reasoning and conceptual fluency in diverse educational contexts.
By extending this framework to curvedsurface solids, this study contributes both theoretically and practically to the growing body of DDR literature in mathematics education.
Finally, the selection of Grade 7 students is pedagogically justified.
In the Indonesian Merdeka Curriculum, the concept of the volume of solids, including cylinders and cones, is introduced at this level, aligning with international benchmarks such as the Common Core State Standards for Mathematics (CCSSM), which also introduce measurement and volume reasoning for early secondary learners.
Therefore, this study aimed to develop and evaluate a hypothetical didactic design (HDD) that can help students overcome learning obstacles in understanding the volume of cylinders and cones through the Didactical Design Research (DDR) approach.
Methods This study employed the Didactical Design Research (DDR) method, a localized form of Design-Based Research (DBR) developed within the Indonesian mathematics education context (Suryadi, 2.
, as follows.
While DBR generally emphasizes iterative cycles of design, implementation, and reflection to improve learning environments (Gravemeijer & Titin Suryani.
Jamilah.
Reni Astuti Cobb, 2.
DDR focuses specifically on the didactical dimension, identifying, anticipating, and overcoming learning obstacles encountered by students.
The methodological legitimacy of DDR has also been recognized internationally, as seen in studies such as Pryvost et al.
which adapted DDR principles across diverse classroom contexts.
The DDR framework in this study consisted of three main stages: prospective, metapedadidactic, and retrospective analyses (Figure .
The term metapedadidactic analysis refers to a reflective process in which researchers and teachers analyze classroom interactions and instructional decisions from a meta-level perspective to understand how didactical relationships evolve during implementation (Suryadi.
Suryadi & Prabawanto, 2.
Although uncommon internationally, this concept serves a similar function to meta-didactical reflection, as discussed in the international DBR literature .
Prediger et al.
According to Suryadi (Sitanggang et al.
, 2.
, in the learning process, there are three types of relationships that must be established: the pedagogical relationship (HP) between the teacher and the students, the didactical relationship (HD) between the students and the learning materials, and the relationship between the teacher and the learning materials, known as didacticalAepedagogical anticipation (ADP).
Prospective Analysis Learning Obstacle Analysis Compiling HLT and DDH Metapedidactic Analysis Didactic Triangle Analysis (HP.
HD DDH Implementation Analysis and ADP) Retrospective Analysis Analysis of the Conformity between the Didactic Situation of DDH and the Suitability Analysis HLT and LT Implementation Figure 1.
Stages of didactical design research .
dapted from Suryadi, 2.
In the prospective analysis stage, the researchers designed a Hypothetical Learning Trajectory (HLT) and a Hypothetical Didactical Design, referred to as Desain Didaktik Hipotetik (DDH), based on diagnostic findings regarding studentsAo learning obstacles in understanding the concept of cylinder and cone volumes (Jamilah et al.
, 2.
The design aimed to reduce the emergence of didactic, epistemological, and ontogenic obstacles during instruction (Putra & Setiawati, 2018.
Shabrina et al.
, 2.
The implementation was carried out in two 90-minute sessions under the supervision of the researcher and the classroom teacher.
The metapedadidactic analysis stage examined the implementation of this design through the didactic triangle framework, focusing on the relationships between .
teacher and student .
, .
student and learning content .
, and .
teacher and content Overcoming learning obstacles in cylinder and cone volume: A didactic .
idactical anticipatio.
This framework is grounded in BrousseauAos Theory of Didactical Situations (Brousseau, 1.
and was later expanded by Suryadi .
to include anticipatory elements in DDR.
Data from classroom observations, teacher reflections, and video recordings were analyzed to explore how teachers responded to emergent learning difficulties.
The retrospective analysis stage compared the Hypothetical Learning Trajectory (HLT) with the Actual Learning Trajectory (ALT) observed during the implementation (Jamilah.
This comparison identified discrepancies between the intended and enacted learning processes, providing insights for refining didactic design for future classroom applications.
The participants included 28 seventh-grade students .
ged 12Ae.
and one mathematics teacher from SMP Al-Mumtaz Pontianak, a private Islamic junior high school located in an urban area of West Kalimantan.
Indonesia.
The school was selected through purposive sampling as it represents a typical urban Indonesian context implementing the Merdeka Curriculum, which emphasizes contextual, competency-based, and meaningful mathematics learning (Turner, 2.
According to teacher reports, students had prior experience with basic fraction operations but limited exposure to applying them in geometric or contextual problemsolving, which often led to procedural and epistemological obstacles.
Data were collected through classroom observations (Wahyono, 2.
, diagnostic tests (Triyono et al.
, 2.
, and semi-structured interviews (Kamaria, 2.
The instruments included observation guidelines, diagnostic test items and interview protocols.
To ensure validity, the diagnostic test items were validated by two doctoral-level mathematics education faculty members specializing in geometry instruction and didactical design.
Validation followed international standards using a content validity index (CVI) approach, in which each item was rated for relevance, clarity, and cognitive alignment.
Revisions were made based on expert feedback and the results of a small-scale pilot test with students of similar characteristics.
The sample test items and scoring rubrics are provided in the Appendix.
Data were analyzed qualitatively through three stages: .
data reduction and coding based on the types of learning obstacles .
idactic, ontogenic, and epistemologica.
thematic and constant comparative analysis across DDR stages to identify recurring patterns of student difficulties and teacher responses.
drawing conclusions through cross-verification of data from observations, tests, and interviews.
To ensure trustworthiness, this study employed data and theory triangulation (Alfansyur & Mariyani, 2020.
Nurfajriani et al.
, 2.
Additionally, intercoder reliability was established by involving two independent coders with expertise in mathematics education who discussed and reconciled differences in coding until reaching full consensus Prior to data collection, ethical clearance and informed consent were obtained from both students and their parents through written agreements outlining the study objectives, procedures, and confidentiality measures.
Participation was voluntary, and all the data were The researcher did not act as a classroom teacher during the implementation.
maintain implementation fidelity, the teacher received detailed instructional guidelines and short training for each phase of didactic design.
The researcher functioned solely as an observer, documenting the process through video recordings, field notes, and post-lesson reflective discussions to ensure alignment between the intended and enacted learning trajectories.
Titin Suryani.
Jamilah.
Reni Astuti Results The research results are presented based on the three stages of Didactic Design Research (DDR): prospective analysis, metapedadidactic analysis, and retrospective analysis.
Each stage is supported by rich empirical data from diagnostic tests, learning observations, student responses, and interviews.
Figures and tables are embedded to support the explanations.
Prospective analysis A preliminary study conducted by Suryani et al.
identified learning obstacles faced by seventh-grade students at Al-Mumtaz Junior High School in Pontianak on the topic of cylinder and cone volume.
Two diagnostic questions were administered:
A cylindrical paint can has a radius of 10 cm and a height of 15 cm.
What is the volume of the can? A cone-shaped ice cream container has a diameter of 14 cm and a volume of 1540 ml.
Calculate its height.
Student answers to Question 1 .
ee Figure .
revealed calculation errors due to procedural misunderstanding, particularly in operations involving fractions.
Of 28 students, 19 students .
%) made similar errors, mostly caused by incorrect order of operations.
Interviews showed that although they considered the question easy, they admitted to Auforgetting to complete the division step.
Ay These findings reflect epistemological obstacles related to procedural fluency (Ramli & Sufyani, 2.
Figure 2.
StudentAos written response showing error in fraction operation .
pistemological For Question 2 .
ee Figure .
, 11 students .
%) were confused about the correct mathematical operation and unsure whether to multiply or divide.
Their limited conceptual understanding indicated overlapping ontogenic, epistemological, and didactic obstacles.
Figure 3.
Misinterpretation of the phrase Autwo-thirds fullAy illustrating combined didactic and ontogenic obstacles.
Overcoming learning obstacles in cylinder and cone volume: A didactic .
Based on these findings, a Hypothetical Learning Trajectory (HLT) was designed (Figure .
as the foundation for the Hypothetical Didactic Design (DDH).
The HLT mapped specific tasks to identified learning obstacles, with contextual problems to strengthen representation and reasoning skills.
Figure 4.
Hypothetical learning trajectory (HLT) mapping tasks to specific learning-obstacle The design included four didactic situations (Brousseau, 1.
: action, formulation, validation, and institutionalization.
In the action and formulation phases, students worked on contextual tasks to address prior misconceptions such as writing the incorrect formula V = A y r t instead of V = ArAt.
Metapedadidactic analysis During the implementation of DDH, the metapedadidactic analysis focused on didactic relationships (HD), pedagogical relationships (HP), and anticipatory didactical phenomena (ADP).
Students were presented with the following problems:
Cylinder Problem I: A cylindrical water pipe is 2 m long and has an inner diameter of 20 How much water can flow through it? Cone Problem I: A cone-shaped container has a base radius of 14 cm.
Two-thirds of the container is filled with boiled peanuts.
If the height is 27 cm, determine the volume of the Titin Suryani.
Jamilah.
Reni Astuti In the validation phase, group discussions occurred, but peer-to-peer dialogue was The teacher provided scaffolding through reflective questioning, such as.
AuWhy did your group choose this method?Ay Table 1.
Didactic triangle analysis on the volume of cylinders and cones material HP (TeacherStudent Relationshi.
HD (StudentMaterial Relationshi.
Volume of Teacher presents problem using mixed units .
and c.
Students confuse unit conversion and treat diameter as Volume of a cone Teacher gives problem about a cone container two-thirds filled with peanuts.
Students Autwo-thirdsAy and apply wrong Teacher assigns combining cone and cylinder.
Students identify both heights but confuse which applies to each Problem Context Composite Shape ADP (Teacher Anticipation and Scaffoldin.
The teacher emphasizes the uniformity of units through scaffolding in the form of conversion examples, such as 5 m = 500 cm, so that the units of length correspond to the The teacher explains the meaning of 'two-thirds of the volume' through simple examples and scaffolding that fractions, such as , demonstrate the operation of multiplication.
Teacher reinforces concept of corresponding height through questioning and diagram Student Response (Empirical Evidenc.
AuI forgot to change m to cm, thatAos why my result was too Ay AuI divided by 3 instead of multiplying by .
Ay AuI know the cone is smaller, but I used the cylinderAos height for both.
Ay In the institutionalization phase, students solved new contextual problems, such as calculating the remaining tank volume or estimating materials for decorative cones.
A post-test was then given to measure learning improvement.
Quantitative comparison showed a notable improvement.
Procedural accuracy increased from 32% .
re-tes.
to 79% .
ost-tes.
, and the number of students confusing the cone height decreased from 8 to 3.
However, spatial misconceptions remained among a small group of Figure 5.
Post-test response showing confusion between cone and cylinder height .
ntogenic Overcoming learning obstacles in cylinder and cone volume: A didactic .
Interviews revealed that students confused the cylinder and cone heights in composite Although they applied formulas correctly, the misunderstanding stemmed from inadequate conceptual grasp of geometric components.
One student said:
AuI just use the formula.
I didnAot think which height was for the cone.
Ay This reflects procedural tendencies and ontogenic obstacles due to internal readiness (Jamilah, 2.
Retrospective analysis The retrospective analysis compared the Hypothetical Learning Trajectory (HLT) with the Actual Learning Trajectory (ALT) observed during implementation.
Overall, the ALT closely aligned with the HLT, though several key deviations provided valuable insight.
Systematic Comparison between HLT and ALT Action Phase: All 28 students participated actively in model observation, following the planned trajectory.
Formulation Phase: 8 students .
%) incorrectly identified the coneAos height as equal to the cylinderAos height or slant height an error unanticipated in the HLT.
Validation Phase: Most groups .
verified calculations correctly, though 2 groups relied solely on formulas without understanding the base height relationship.
Institutionalization Phase: Despite reinforcement, 4 students .
%) still struggled with cone height, suggesting insufficient visual scaffolding.
Empirical Data Triangulation Three data sources strengthened interpretation:
Student Work: Errors .
ee Figure .
showed confusion between cylinder and cone height .
ntered 7 cm instead of 6 c.
Validation Discussion:
S-12: AuI thought the coneAos height was the same as the cylinderAos height.
MaAoam.
Ay .
Teacher: AuPlease observe carefully.
The coneAos height is always perpendicular to its Ay Teacher Reflection: The teacher observed persistent confusion in distinguishing height from slant, recommending increased use of 3D models and cross-sectional visuals.
Implications for Learning Obstacles Analysis Initially, this confusion was identified as an ontogenic obstacle, as it appeared to stem from studentsAo internal readiness.
However, triangulation of evidence .
tudent work, reflection, and task analysi.
indicated that the root cause was insufficient visual support within the instructional design.
Consequently, the obstacle was reclassified as a didactic obstacle.
This reclassification was based on teacher reflection and task analysis, showing that the design rather than individual student readiness caused the difficulty.
Titin Suryani.
Jamilah.
Reni Astuti Discussion The post-intervention analysis revealed an important theoretical insight: several difficulties initially identified as ontogenic were, in fact, didactic in nature, arising not from studentsAo internal readiness but from limitations in instructional design.
This reclassification underscores a key principle in learning obstacle theory, as described by Suryadi .
, who distinguishes ontogenic obstacles as stemming from cognitive or motivational readiness, while didactic obstacles emerge from mismatches between instructional approaches and learner needs.
recognizing that some student challenges were triggered by the learning design itself, this study highlights the dynamic nature of obstacle classification within Didactical Design Research (DDR), where understanding evolves through iterative implementation and reflection.
The findings demonstrate that the Hypothetical Didactic Design (DDH), grounded in learning obstacle analysis, effectively supported studentsAo construction of the cylinder and cone volume concepts.
The structured progression through the action, formulation, validation, and institutionalization phases enabled the students to systematically develop conceptual understanding and gradually overcome both epistemological and didactic barriers.
However, this facilitation was only partially successful.
conceptual confusion persisted, particularly in distinguishing between slant height and vertical height, a well-documented epistemological obstacle in three-dimensional geometry (Battista, 2.
These findings suggest that studentsAo spatial reasoning and embodied visualization of three-dimensional structures remain limited, requiring sustained pedagogical interventions that emphasize spatial relationships and This interpretation aligns with previous studies that emphasize the role of well-structured didactic designs in reducing learning barriers and enhancing mathematical reasoning (Gravemeijer & Cobb, 2006.
Pramuditya et al.
, 2.
Likewise.
Sulastri et al.
and Sidik et al.
observed that conventional classroom instruction often lacks non-routine and spatially demanding problem types, which may explain the persistence of procedural tendencies among students in the current study.
As emphasized by Boaler .
, students conceptual engagement increases significantly when instruction focuses on meaningful exploration rather than repetitive calculation.
In this study, despite the integration of visual and contextual learning aids, many students still relied on memorized procedures instead of conceptual reasoning.
Although the DDH incorporates visualizations of formula derivations and connects them to the idea of volume as an accumulation of space, reinforcement during the early learning stages remains essential for deeper internalization of these conceptual connections.
From an international perspective, the present findings contribute to the broader discourse on geometry learning and spatial reasoning.
Data from the PISA and TIMSS consistently reveal that students across various countries experience difficulties in tasks requiring threedimensional understanding.
In this regard, the DDH model developed in this study provides a contextually grounded yet potentially transferable framework for improving geometry instruction beyond the Indonesian context, particularly in fostering the shift from procedural recall to conceptual comprehension.
Overcoming learning obstacles in cylinder and cone volume: A didactic .
Furthermore, this study extends the DDR methodology by demonstrating that obstacle classification is not static but evolves through empirical implementation and reflective analysis.
The process of identifying and reclassifying obstacles from ontogenic to didactic forms a methodological contribution that enhances the adaptability of DDR in addressing complex learning phenomena.
Guided by BrousseauAos theory of didactical situations (Yunarti, 2.
and further supported by Jamilah and Winarji .
, the iterative enactment of the four learning situations was crucial for fostering robust mathematical understanding.
Nonetheless, the study acknowledges its limitations, such as being conducted in a single classroom and within a short implementation duration, which may restrict the generalizability of its findings.
Thus, future didactic designs should aim to incorporate non-routine contextual problems that promote reasoning flexibility and adaptive thinking.
The validation phase can be strengthened by embedding peer questioning, justification prompts, and collaborative reflection activities to deepen studentsAo metacognitive engagement.
Moreover, conceptual understanding should be reinforced through spatial visualization, dynamic representations, and narrative explanations of geometric volumes.
To support future DDR cycles, systematic documentation through student work samples, interview excerpts, and teacher observation journals is vital for tracing the evolution of studentsAo reasoning and refining subsequent design iterations.
Conclusion This study demonstrates that learning obstacles are not static student deficits but dynamic interactions among task design, instructional approaches, and studentsAo prior knowledge.
Through the Didactical Design Research (DDR) approach, the developed didactic design effectively supported studentsAo understanding of cylinder and cone volumes.
However, limitations in the institutional phase revealed that several difficulties previously assumed to be ontogenic were, in fact, didactic, arising from insufficient scaffolding and task sequencing rather than studentsAo internal readiness.
This insight emphasizes that what appears to be ontogenic obstacles may often originate from design gaps, highlighting the need for continuous reflection and refinement in the instructional design.
Accordingly, future iterations should integrate concrete and technologysupported interventions, such as dynamic geometry software, physical manipulatives, and cross-sectional modeling, to strengthen studentsAo spatial reasoning and conceptual coherence.
Aligned with the principles of IndonesiaAos Merdeka Curriculum, this study underscores the role of DDR in fostering teacher autonomy and evidence-based pedagogical decision By embedding adaptive and reflective elements, teachers can iteratively develop responsive didactic designs that evolve with classroom realities, thereby promoting a deeper mathematical understanding and sustained learner growth.
Acknowledgment The authors would like to thank the mathematics teacher and seventh-grade students of SMP Al-Mumtaz Pontianak who participated as research subjects.
Appreciation is also extended to Titin Suryani.
Jamilah.
Reni Astuti colleagues who assisted in the development of instruments, data collection, and provided valuable input during the writing of this article.
Conflicts of Interest The authors declare no conflict of interest regarding the publication of this manuscript.
addition, the authors have completed the ethical issues, including plagiarism, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies Funding Statement This work received no specific grant from any public, commercial, or not-for-profit funding If there was no funding, the following wording should be used: This work received no specific grant from any public, commercial, or not-for-profit funding agency.
Author Contributions Titin Suryani: Conceptualization, methodology, investigation, writing original draft, and Jamilah: Validation, supervision and formal analysis.
Reni Astuti: Supervision, visualization, and project administration.
References