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Delectus - Scientific Journal, Inicc-Perú - [ISSN: 2663-1148]

URL: https://revista.inicc-peru.edu.pe/index.php/delectus

DOI: https://doi.org/10.36996/delectus

Email: publicaciones.iniccperu@gmail.com

Vol. 7 No. 1 (2024): July-December [Edit closure: 31/12/2024]


RECEIVED: 20/07/2024 | ACCEPTED: 29/11/2024 | PUBLISHED: 15/12/2024

Suggested quote (APA, seventh edition)

Guerra-Calixto, M. del R. (2024). Transforming Plane Geometry Learning with “Drawing and Construction”. Delectus, 7(2), 8-18. https://doi.org/10.36996/delectus.v7i2.289


Transforming Plane Geometry Learning with “Drawing and Construction”

Marianela del RocÍo Guerra-Calixto

d40405066m@aprendoencasa.pe

Doctorate in Educational Sciences, Graduate School, Universidad Nacional de Trujillo, Peru

https://orcid.org/0009-0002-6746-8786

*Corresponding author: D40405066m@aprendoencasa.pe

The pandemic has exacerbated educational gaps in mathematics, particularly in plane geometry, underscoring the need for effective pedagogical strategies. This study evaluated the impact of the didactic program “Drawing and Construction” on plane geometry learning among fourth-grade high school students, focusing on its influence on the dimensions of analysis, construction, demonstration, and investigation. A pre-experimental design with pretest and posttest was used on a sample of 33 students selected through cluster sampling. The intervention included 20 sessions based on the program's four phases, combining traditional and technological tools. Data were analyzed using Student’s t-test and the Wilcoxon test. Results showed significant improvements (p < 0.001) across all dimensions, with 54.5% of students reaching a high level in overall learning. The analysis dimension particularly strengthened logical reasoning, while the investigation dimension fostered creative and practical skills. The program proved to be an effective pedagogical strategy capable of transforming geometry teaching in diverse contexts. National implementation is recommended, with adaptations to various educational settings to reduce mathematics gaps.

Keywords: Geometry; Educational Strategies; Drawing; Competences; Mathematics; Educational Innovation.

Teaching geometry at the secondary level presents significant challenges due to the abstract nature of its concepts and the lack of effective teaching strategies. These factors limit students' understanding and affect their development in fundamental skills such as critical thinking, problem-solving, and creativity (Jablonski & Ludwig, 2023; Jagom et al., 2020; Muzaini et al., 2023).
Globally, the pandemic worsened educational disparities, particularly affecting underprivileged areas such as Latin America. Recent figures indicate that 88% of the most disadvantaged students in this region exhibit poor performance compared to 55% of their wealthier peers (BBC News Mundo, 2023; United Nations, 2022). In Peru, this situation is particularly critical, with mathematics performance dropping from 17.7% in 2019 to 11.3% in 2023, highlighting the urgent need to implement innovative teaching strategies to reduce these gaps and strengthen inclusive learning (UNESCO, 2023). This underscores the importance of inclusive educational policies that mitigate inequalities and enhance education system resilience to ensure equitable, high-quality learning.

Low performance in geometry stems from inadequate teaching methods, a lack of technological resources, and low motivation (Kwame et al., 2024; Maqoqa, 2024; Mukuka & Jogymol, 2024). These factors hinder the connection between geometric concepts and practical uses, emphasizing the need for pedagogical methods that promote active participation and meaningful learning (Mukuka et al., 2023; Prasad, 2024).

In this context, the program "Drawing and Construction" emerges as an innovative strategy integrating practical activities and technological tools, fostering meaningful learning tailored to students' needs. This approach combines individual exploration, collaboration, and problem-solving, aligning with Piaget and Vygotsky's constructivist theories to encourage understanding and application of geometric concepts in real-world contexts (Siegler et al., 2009; Wolf, 2023). Moreover, it strengthens understanding of geometric concepts through technological tools such as GeoGebra. This strategy promotes critical skills such as logical reasoning and problem-solving while enhancing motivation and collaboration among students (Abiola et al., 2024; Fauzi et al., 2023; Kumar, 2023). Its adaptability and ability to link theory with practice ensure a meaningful and relevant educational experience (Abdikerova, 2024; Abiola et al., 2024).

The research aligns with SDG 4 by promoting inclusive and quality education, aiming to reduce educational inequalities and develop essential skills through the program "Drawing and Construction." This method, rooted in Piaget and Vygotsky's theories, combines the active creation of knowledge with social cooperation, promoting contextual and relevant learning that meets the demands of students in disadvantaged environments (Siegler et al., 2009; Wolf, 2023).

The study's relevance in Latin America lies in its proposal of an innovative strategy that, through practical and accessible activities, promotes meaningful learning in a region marked by demotivation and low performance. Its flexibility allows adaptation to varied cultural and socio-economic contexts, promoting inclusion and essential skills. Furthermore, its replicability across institutions contributes to improving educational quality in the region (Racero, 2018; Ulloa et al., 2023).

In this context, the didactic program based on "Drawing and Construction" was developed to address deficiencies in geometry learning among fourth-grade secondary education students. The study's main objective was to analyze the program's influence on geometric learning, focusing on four fundamental stages: analysis, construction, demonstration, and investigation. Specific aspects evaluated included:

  • Analysis: Effectiveness in developing initial understanding of geometric concepts.
  • Construction: Contribution to practical skill-building through modeling and manipulation of figures.
  • Demonstration: Influence on students' ability to justify and explain geometric reasoning.
  • Investigation: Encouragement of exploration and problem-solving, such as understanding the circumference and its properties.

Plane geometry learning through the "Drawing and Construction" program is based on the principles of Piaget's constructivism and Vygotsky's socio-constructivism. According to Piaget, learning occurs through specific experiences that allow students to progressively build and organize their knowledge, facilitating the understanding of basic and advanced geometric concepts. In contrast, Vygotsky highlights the role of social interaction and teacher mediation in cognitive development, emphasizing that dialogue and collaboration in problem-solving strengthen both individual and collective learning. This integrative framework underlines the importance of combining practical and technological strategies for dynamic and contextualized learning.

Active strategies used in geometry teaching, such as those implemented in this program, focus on three key aspects: conceptualization, investigation, and demonstration. The conceptualization phase employs visual and manipulative representations to enable students to explore geometric properties and independently discover relationships, fostering autonomous learning. Regarding investigation, this phase stimulates the development of critical thinking and creativity by connecting geometric concepts to real-world problems present in the students’ environment. Finally, the demonstration phase prioritizes validating geometric properties and theorems through logical argumentation, enhancing meaningful learning and mathematical reasoning skills (Gasco-Txabarri, 2017).

    • “Drawing and Construction” Program”

The program combines traditional tools, such as the compass and ruler, with advanced technologies like GeoGebra to promote dynamic, active, and participatory learning. This approach facilitates the understanding of abstract concepts and promotes the application and consolidation of knowledge through practical activities such as analysis, construction, demonstration, and geometric investigation (Cosquillo & Matamoros, 2024). The integration of these methods ensures an educational process that drives the development of critical and contextualized skills.

Regarding geometric analysis, it focuses on strengthening critical skills through the combination of traditional tools, such as the compass and ruler, with innovative technologies like GeoGebra. These tools provide students with the opportunity to visualize abstract concepts and address complex geometric problems effectively, improving both their logical reasoning and critical analysis abilities (Cardenas et al., 2016; Diaz-Nunja et al., 2018).

In this sense, the Van Hiele geometric reasoning model, according to Cedeño and Cedeño (2024), facilitates a systematic analysis of basic concepts, such as polygons and circumferences, while dynamic geometry software fosters spatial thinking and understanding of complex geometric relationships (Adelabu et al., 2019; Flores et al., 2021). These approaches highlight the importance of integrating technological tools into teaching, promoting the construction of meaningful knowledge in students.

Geometric construction integrates traditional methods with advanced technologies, promoting practical learning that strengthens critical skills such as logical and spatial reasoning. Activities focused on creating geometric figures not only develop technical competencies but also increase students’ confidence and self-efficacy (Mántica & Freyre, 2019; Sánchez & Castillo, 2019). According to Tortop and Bahadır (2023), carefully planned construction activities enhance both practical performance and technical precision and foster creativity in geometric exploration. Likewise, these educational strategies promote the development of spatial and constructive skills, as highlighted by Tursynkulova and Praliyeva (2022), consolidating their relevance in the effective teaching of geometry in various settings. Altogether, this evidence supports the incorporation of tools and integrative approaches as essential elements in innovative educational programs.

Geometric demonstration through drawing stands out as a fundamental strategy to facilitate the visualization and validation of geometric theorems and properties, promoting key skills such as logical reasoning and mathematical argumentation. Pedagogical methods such as Project-Based Learning (PBL) strengthen this strategy by linking geometric concepts with practical applications, fostering both collaboration and joint problem-solving (Gómez-Tone, 2019; Velázquez & Rivas, 2019).

Previous studies have confirmed that the "Drawing and Construction" program stimulates critical thinking and enhances problem-solving in geometry, essential aspects for effectively validating mathematical relationships and properties (Rondan et al., 2020). Complementary methods, such as origami, have significantly improved the understanding of complex geometric relationships (Quispe, 2022), while the Van Hiele model has facilitated the acquisition of advanced concepts, including triangles and polygons (Pozo, 2023). Furthermore, innovative approaches like recreational mathematics have enhanced argumentative and demonstration skills, consolidating key geometric competencies in students (Tardio, 2023).

Geometric research focuses on exploring practical applications of geometric concepts in real-world contexts, stimulating both creativity and critical thinking. This approach enables students to develop innovative solutions to complex problems, establishing a solid connection between theory and practice. For example, Conde-Carmona et al. (2021) evidenced that the use of dynamic geometry software facilitates detailed investigations into geometric properties, strengthening students’ analytical skills. Additionally, strategies integrating drawing and construction have proven effective in teaching by increasing the relevance of learning in real educational scenarios, fostering meaningful relationships between theoretical concepts and their practical applications (Crisólogo, 2024; Rondan et al., 2020). Similarly, from a socio-constructivist perspective, the formulation of questions and the pursuit of applied answers are facilitated, reinforcing both logical reasoning and students’ scientific curiosity (Almeida et al., 2024).

The "Drawing and Construction" program combines tradition and innovation by integrating technological tools, such as GeoGebra, with practical methodologies that redefine the teaching of geometry in contemporary educational contexts. These tools strengthen geometric research and foster collaborative learning, promoting active interaction between students and geometric concepts (Zapata et al., 2023). By connecting theory and practice, this approach stimulates analytical skills, creativity, and problem-solving, key elements for meaningful and contextualized learning (Ruesta & Gejaño, 2022). Additionally, the integration of Information and Communication Technologies (ICT) and tangible materials fosters inclusive, dynamic, and adaptable learning for various contexts. This approach not only strengthens critical competencies such as logical reasoning and applied research but also drives students' academic and personal development, providing a solid foundation for addressing current educational challenges (Yazidi, 2023).

    • Developed Skills

The "Drawing and Construction" program stands out for enhancing key skills in geometry, promoting active and contextualized learning. In the analysis phase, students strengthen their critical thinking through tools like GeoGebra, which facilitates both the visualization and understanding of abstract concepts. During the construction phase, students apply theoretical knowledge to practical problems, developing essential technical competencies and spatial skills. In the demonstration phase, they refine their argumentative abilities and validate geometric properties, consolidating a solid logical reasoning foundation. Finally, in the research phase, they adopt a creative and exploratory approach that fosters the autonomous resolution of problems, effectively integrating theory and practice.

This strategy connects theory and practice, developing spatial reasoning, self-assessment, and collaborative skills. Additionally, it increases motivation and interest by making learning more dynamic and engaging, promoting critical competencies essential for the modern educational context. However, gaps in the literature are identified, particularly in Latin America, where its effectiveness in contexts with high cultural diversity and educational inequalities needs to be evaluated to support inclusive and contextualized strategies

    • Research Design

The study adopted a pre-experimental design with a quantitative approach, aimed primarily at evaluating the influence of the "Drawing and Construction" didactic program on plane geometry learning. Pretest and posttest assessments were used to measure changes in student performance after the intervention. While the absence of a control group prevents direct comparisons, this design provides significant initial evidence on the program's effectiveness in real educational contexts, laying a foundation for more robust future research (Gallardo, 2017).

    • Participants

The study population consisted of 162 high school students from an educational institution in Trujillo, La Libertad. Using cluster sampling, a sample of 33 students was selected, representing the typical diversity of a secondary school classroom. Inclusion criteria ensured the participation of students with regular class attendance and varying academic levels, making the obtained results representative of usual school dynamics and applicable to similar educational contexts.

    • Intervention and Program Phases

The intervention was conducted over 20 sessions structured according to the four phases of the "Drawing and Construction" program, designed to foster meaningful learning:

Analysis Phase: Students identified essential properties of geometric figures through freehand sketches. Activities such as analyzing a square (equal sides and right angles) prepared participants to construct figures using parallels and perpendiculars. Creating perpendicular bisectors and angle bisectors strengthened their understanding of basic concepts.

A Construction Phase: They applied strategies using traditional tools like a compass and ruler to construct geometric figures (triangles, circles, etc.). They solved practical problems, such as finding the center of a triangular table, developing technical precision and spatial reasoning.

Demonstration Phase: Students validated their constructions, ensuring they met the required properties by explaining and arguing their procedures. Comparing alternative approaches strengthened their logical reasoning and encouraged collaborative learning.

Research Phase: Students connected geometric concepts to real-world problems, exploring creative solutions. For example, reconstructing a broken wheel mold, they used strings and perpendicular bisectors to determine the center of the circle, fostering creativity and autonomy.

The integration of technological tools and traditional practices allowed for the development of critical skills such as logical reasoning, technical precision, and geometric argumentation. This methodological approach, applied in all sessions, ensured meaningful and contextualized learning.

    • Evaluation Instruments

Pretest and posttest assessments validated by a panel of five experts in mathematics education were employed. These tests measured the program's key dimensions: analysis, construction, demonstration, and research. Performance levels (low, medium, and high) were defined with standardized criteria to ensure the objectivity and reliability of the results. Statistical analysis was conducted using the paired-sample T-test and Wilcoxon test, suitable for identifying significant differences between pretest and posttest results. This methodology strengthened the validity of the findings and the program's effectiveness.

    • Ethical Aspects
The study complied with international and local ethical standards, obtaining informed consent from participants and their legal representatives. The purpose of the study was explained, ensuring voluntary participation and anonymity. Data collected were used exclusively for academic and scientific purposes, respecting participants' rights and ensuring ethics throughout the research process..
Table 1.
Distribution of Performance Levels and T-Student Test for Geometry Learning in Pretest and Posttest Phases
Pretest Postest t Sig.
  fi % fi %
Low 33 100,0 1 3,0 -26,508 .000
Medium 0 0 15 45,5
High 0 0 18 54,5
Total 33 100,0 33 100,0

El The overall analysis of the results of the "Drawing and Construction" program demonstrates a significant improvement in plane geometry learning.
Before the intervention, all students (100%) were at a low performance level. After implementation, this percentage drastically decreased to 3.0%, while 45.5% reached the medium level and 54.5% achieved the high level. The Student’s T-test (t = -26.508, p = 0.000) confirms that these differences are not due to chance, consolidating the effectiveness of the strategy.

Figure 1.
Box-and-whisker plot for overall plane geometry learning (pretest and posttest)
S

The visual analysis of the graph complements the quantitative results, showing an increase in the median posttest scores and greater data dispersion, indicating that the program successfully benefited students with various initial levels of learning.

This reinforces the approach's capacity to bridge gaps in geometric learning. However, these findings also highlight the need to explore the sustainability of the results and their replicability in educational contexts with limited resources or larger populations. Addressing these challenges is crucial to maximizing the program's educational impact and solidifying its value as an innovative pedagogical tool.

Table 2.
Distribution of Performance Levels and Wilcoxon Test for the Dimensions of Analysis and Construction (Pretest and Posttest)
Dimensions Levels Pretest Postest z Sig.
  fi % fi %
Analysis Low 22 66,7 0 0 -5,052b .000
Medium 11 33,3 14 42,4
High 0 0 19 57,6
Total 33 100,0 33 100,0
Construction Low 33 100,0 0 0
Medium 0 0 15 45,5 -5,131b .000
High 0 0 18 54,5
Total 33 100,0 33 100,0
Demonstration Low 33 100,0 6 18,2
Medium 0 0 23 69,7 -5,068 b .000
High 0 0 4 12,1
Total 33 100,0 33 100,0
Investigation Low 33 100,0 1 3,0 -5,060 b .000
Medium 0 0 19 57,6
High 0 0 13 39,4
Total 33 100,0 33 100,0

The results obtained in the four evaluated dimensions (Analysis, Construction, Demonstration, and Research) confirm the effectiveness of the "Drawing and Construction" program in plane geometry learning, showing significant improvements after the intervention. The Wilcoxon tests (p < 0.001 for all dimensions) statistically supports these changes.

En In the Analysis dimension, students initially concentrated predominantly at low performance levels, with 66.7% in this category and no records in the high level. After the intervention, the low level was completely eliminated, with 42.4% of students reaching the medium level and 57.6% achieving the high level. These results reflect a significant strengthening of logical reasoning and critical analysis skills, essential for geometric understanding.

In the Construction dimension, an equally significant advancement was observed. Before the intervention, all students (100%) were at the low level. Subsequently, this level was eliminated, with 45.5% reaching the medium level and 54.5% achieving the high level. These findings highlight the development of practical skills, such as constructing and manipulating geometric concepts, achieved through traditional and technological tools.

En In the Demonstration dimension, the results reveal an increase in medium and high-performance levels after the intervention. Although 100% of students started at the low level, 69.7% reached the medium level, and 12.1% achieved the high level in the posttest. While significant progress in argumentation and geometric validation skills is evident, the lower percentage in the high level suggests the need for additional support to consolidate these competencies.

Finally, the Research dimension experienced a remarkable transformation. Initially, all students were at the low level. After the intervention, this percentage dropped to 3.0%, while 57.6% reached the medium level, and 39.4% achieved the high level. This underscores the program's impact on developing research competencies, such as exploration and problem-solving in applied geometric contexts.

Figure 2.
Box-and-Whisker Plots for the Dimensions of Analysis, Construction, Demonstration, and Research in Pretest and Posttest Phases

Figure 2 complements these results with box-and-whisker plots illustrating the improvements in each dimension. A considerable increase in the median posttest scores compared to the pretest is observed, along with greater data dispersion. This pattern reflects a positive impact of the program on a wide range of students, regardless of their initial performance levels.

Overall, the improvements in dispersion and the rise in the median posttest scores highlight the program's success in fostering meaningful geometric learning. However, the differences in posttest dispersion suggest that some students were more receptive to the methodological approach than others. This underscores the importance of exploring complementary strategies to maximize the impact across all student profiles.

These findings consolidate the applied program as an effective pedagogical tool, while also emphasizing the need for future studies to evaluate its sustainability and applicability in more diverse educational contexts.

    • Evidence of the Program’s Positive Impact

The results obtained in the study demonstrate a significant positive impact of the "Drawing and Construction" program on geometry learning. Across the four dimensions evaluated—Analysis, Construction, Demonstration, and Research—a significant change was observed in students' performance levels, shifting from an absolute predominance at the low level in the pretest to more balanced distributions with a considerable increase in medium and high levels in the posttest.

The Wilcoxon test applied to individual dimensions and the Student’s T-test for overall geometry learning yielded statistically significant values (p = .000), indicating that the improvements were not due to chance. This impact is reflected in the development of critical skills such as logical reasoning, problem-solving, and the ability to apply geometric concepts in practical contexts, confirming the program's effectiveness as an innovative didactic tool.

The primary objective of the study, focused on evaluating the impact of the "Drawing and Construction" program on plane geometry learning, is grounded in Piaget’s constructivist and Vygotsky’s socio-constructivist theories. These propose that students construct their knowledge through active manipulation and social interaction, principles reflected in the program’s design. Statistical results, validated by the paired-sample Student’s T-test, show a significant improvement in posttest scores compared to pretest scores (p < 0.001), demonstrating the program's positive impact on the learning of geometric concepts.

Previous studies, such as those by Cedeño and Cedeño (2024) in Ecuador and Crisólogo (2024) in Peru, corroborate these findings, emphasizing how active and visual strategies, such as the Van Hiele model and socio-constructivist approaches, significantly improve mathematical learning. These precedents reinforce the validity of interactive methods for addressing educational challenges in geometry.

Thus, the results suggest that programs like "Drawing and Construction" not only facilitate the understanding of geometric concepts but also promote critical and practical skills. However, their implementation may face limitations in resource-constrained contexts, highlighting the need to adapt these strategies to diverse educational realities. This study provides relevant evidence to strengthen the mathematics curriculum and promote innovative methodologies in education.

Regarding the specific objectives, the applied program demonstrated a significant improvement in students' logical reasoning and analytical capacity, evidenced by the elimination of the low level and the 57.6% increase in the high level after the intervention. This result aligns with the Van Hiele model, which highlights the importance of systematic analysis in geometric understanding (Cedeño and Cedeño, 2024). Additionally, the integration of technological tools like GeoGebra allowed students to visualize and explore abstract concepts, strengthening critical skills as supported by previous research (Flores et al., 2021). This progress reinforces the effectiveness of the practical and visual approach to addressing initial deficiencies in geometry teaching.

Geometric construction demonstrated a transformative impact, with 100% of the students initially at the low level and 54.5% reaching the high level in the posttest. These results confirm the program's ability to develop practical and spatial skills through the combined use of traditional and technological tools. Previous research, such as that by Tortop and Bahadır (2023), supports that these strategies increase students’ confidence and self-efficacy, essential factors for meaningful learning. Constant practice and the focus on applied problems contributed to consolidating these skills.

Although significant improvement was observed in demonstration, with 69.7% of the students reaching the medium level, the percentage at the high level (12.1%) reflects the need for additional support to consolidate argumentative and geometric validation skills. This result aligns with constructivist theories, which highlight the importance of social interaction and collaborative learning for the development of advanced competencies. Tools such as Project-Based Learning (PBL) and the use of origami proved effective in reinforcing geometric argumentation, as indicated by studies by Quispe Masco (2022) and Rondan Zamata et al. (2020).

The research dimension stood out for its significant progress, with 39.4% of students reaching the high level after the intervention. This progress highlights the program's potential to foster exploratory and creative skills in real-world contexts, aligning with research such as Conde-Carmona et al. (2021), which underscores the relevance of technological tools for geometric research. Additionally, the connection between theory and practice, characteristic of the socio-constructivist approach, facilitated the development of meaningful and applied learning (Crisólogo, 2024).

The implementation of the "Drawing and Construction" program in teaching plane geometry has demonstrated significant improvements in student performance, evidencing the effectiveness of active methodologies and the use of technological tools like GeoGebra. These strategies not only facilitate the understanding of abstract concepts but also develop critical skills such as logical reasoning and problem-solving.

For teachers, adopting this program entails updating their use of educational technologies and applying student-centered pedagogical approaches. This requires continuous training and adaptation of teaching practices to effectively integrate these tools into the classroom. Educational policymakers should consider including similar programs in the curriculum, promoting investment in technological resources and teacher training to ensure successful implementation.

However, the application of this program faces challenges, especially in contexts with limited resources. The lack of access to technologies and the need for specialized training may hinder its adoption. It is essential to develop strategies that allow the program's adaptation to diverse educational realities, ensuring its viability and sustainability in different environments.

One of the main limitations of this study lies in its pre-experimental design, characterized by the absence of a control group. While this approach allowed the evaluation of the "Drawing and Construction" program's impact on a single group, the lack of direct comparison with a non-intervened group limits the ability to attribute the results exclusively to the program. This could have influenced the interpretation of the findings, as other uncontrolled contextual factors might also have affected the results.

For future studies, it is recommended to use more robust experimental designs, such as randomized controlled trials, including a control group. This would enable more precise comparisons and strengthen the validity of the conclusions. Additionally, it would be beneficial to expand the sample to include students from different institutions and educational levels, ensuring greater representativeness and generalization of the results. These methodological improvements would not only enrich the analysis of the program’s impact but also provide a more comprehensive view of its applicability in diverse educational contexts.

Contribution to Knowledge
This research presents a significant pedagogical innovation through the implementation of the "Drawing and Construction" program, which combines traditional and technological tools to improve the learning of plane geometry. The results highlight notable improvements in skills such as logical reasoning and problem-solving, demonstrating the potential of this strategy to transform geometry teaching.

Limitations
The findings, although encouraging and extraordinary, should be interpreted with caution due to the pre-experimental design and the absence of a control group. Additional studies with more robust designs and in different educational contexts are recommended to validate its impact.

The "Drawing and Construction" program has proven to be an effective pedagogical tool for improving plane geometry learning among secondary school students. The implementation of this program has resulted in significant increases in the dimensions of analysis, construction, demonstration, and research, evidencing its capacity to address previous deficiencies in geometric understanding.

The combination of practical methodologies with advanced technologies such as GeoGebra and constructivist approaches has promoted meaningful learning, developing critical skills such as logical reasoning, geometric argumentation, and problem-solving. These results underline the importance of integrating interactive and visual strategies into the school curriculum, especially in areas where students face greater challenges.

It is recommended to consider the implementation of the program at a national level as part of an educational policy that prioritizes active methodologies in mathematics teaching. To adapt the program to various school contexts, including rural and urban-marginal areas, it is essential to:

  • Train teachers in the use of technological tools and constructivist approaches, ensuring effective program application;
  • Adapt educational resources to local realities, considering the technological and cultural limitations of each region; and
  • Encourage the participation of the educational community, involving parents and local authorities to ensure the initiative's support and sustainability.

The careful adaptation of the "Drawing and Construction" program to different contexts will contribute to reducing learning gaps and improving educational quality across the country.

Conflicts of Interest: The author declares no conflict of interest.

Author Contributions:
Guerra-Calixto, M.: Conceptualization, Formal Analysis, Methodology, Research, Supervision, Validation, Writing - Original Draft, Writing - Review & Editing.

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