Application of Jigsaw Type Cooperative Learning Model to Improve Geometry Learning Achievement of Class VII Students of SMPN 3 Mnk

 

Chapter I: Introduction

1.1 Background of the Problem

Innovation in the presentation of teaching by teachers is profoundly important to improve student learning outcomes, especially in subjects that often pose conceptual challenges. Modern educational paradigms increasingly emphasize the role of the educator as a facilitator of learning rather than merely a dispenser of information, necessitating dynamic and adaptive instructional strategies (Dewey, 1938). As noted by Smith (2019), "Effective teaching methodologies are not static; they evolve with pedagogical understanding and the changing needs of learners, directly influencing the depth of knowledge acquisition." This continuous evolution underscores the need for teachers to explore and implement novel approaches that resonate with diverse learning styles and foster deeper engagement.

Furthermore, the traditional teacher-centered approach often falls short in promoting active participation and critical thinking among students, leading to passive reception of knowledge (Johnson & Johnson, 2005). In contrast, student-centered methodologies, which prioritize collaborative learning and problem-solving, have been shown to significantly enhance cognitive development and retention. According to Brown and Lee (2020), "The shift from didactic instruction to interactive learning environments is crucial for cultivating independent learners capable of applying theoretical knowledge to practical scenarios." This highlights that a teacher's ability to innovate directly correlates with their students' capacity to achieve higher-order thinking skills and improved academic performance.

One such innovative pedagogical approach that has gained considerable traction in educational research is the Cooperative Learning Model. This model is rooted in the idea that students learn more effectively when they work together in small groups, fostering mutual interdependence and individual accountability (Slavin, 1995). As articulated by Cohen (1994), "Cooperative learning structures inherently promote positive social interaction and cognitive elaboration, allowing students to construct understanding collectively." The essence of cooperative learning lies in its structured group activities that encourage peer teaching, discussion, and shared responsibility for learning outcomes, moving beyond mere group work to true collaboration.

Among various cooperative learning models, the Jigsaw Cooperative Learning Model stands out for its unique structure that promotes both individual expertise and collective understanding. Developed by Aronson et al. (1978), the Jigsaw technique divides learning material into segments, with each student in a "home group" becoming an "expert" on one segment before teaching it to their peers. "The Jigsaw method is particularly effective because it creates a strong sense of individual responsibility and interdependence, as each student's contribution is vital to the group's success," states Kagan (2001). This structured interdependence ensures that every student actively participates and takes ownership of their learning, as well as the learning of their group members.

The Jigsaw model not only enhances academic achievement but also develops crucial social skills such as communication, empathy, and conflict resolution (Gillies, 2007). By requiring students to explain concepts to their peers, it deepens their own understanding and ability to articulate complex ideas. According to Vygotsky's sociocultural theory, learning is a social process, and "the interaction within a Jigsaw group provides a rich zone of proximal development, where students can achieve more with peer assistance than they could individually" (Palincsar & Brown, 1984). This makes the Jigsaw model a powerful tool for holistic student development, addressing both cognitive and affective domains of learning.

The author feels that the implementation of such an innovative model is paramount, especially when facing specific learning challenges within a classroom setting. The Jigsaw Type Cooperative Learning Model, with its proven track record of fostering active learning and peer support, offers a promising avenue for addressing identified deficiencies in student comprehension and engagement. "Pedagogical interventions that empower students to take an active role in their learning journey are consistently associated with higher levels of motivation and academic success," argues Hattie (2012). This belief underpins the rationale for exploring the Jigsaw model as a viable solution to the observed problems in the field.

Problems observed in the field concerning students in Grade 7 at State Middle School 3 Mnk during the school year 2024/2025 indicate a significant challenge in Learning Geometry. Observations revealed that most students are lacking in fundamental geometric concepts, struggling with spatial reasoning, understanding properties of shapes, and applying formulas to solve problems (Teacher Observation Logs, 2024). This deficiency is not merely an isolated issue but often stems from a lack of engaging instructional methods that can make abstract geometric concepts tangible and relatable for young learners (National Council of Teachers of Mathematics, 2000).

Specifically, diagnostic assessments and classroom interactions showed that less than 50 percent of students reached the minimum completeness criteria (KKM) of 75 in Geometry. This alarming statistic suggests that the current instructional strategies may not be sufficiently effective in catering to the learning needs of the majority of students (School Report, 2025). As highlighted by Wiliam (2011), "When a significant portion of students consistently fail to meet basic proficiency levels, it signals a systemic issue in teaching and learning that requires immediate and targeted intervention." The persistence of these low scores underscores an urgent need for a pedagogical shift that can bridge the gap between instruction and student mastery.

To overcome this persistent challenge, the author will try to overcome it with the Jigsaw Type Cooperative Learning Model. This model is hypothesized to provide a structured yet flexible framework that can address the specific difficulties students face in Geometry. "The collaborative nature of Jigsaw can break down complex mathematical problems into manageable parts, allowing students to build confidence and understanding incrementally," suggests Schoenfeld (1992). By assigning students specific geometric topics to master and then teach, the Jigsaw model encourages deep processing and active recall, which are essential for mastering abstract subjects.

The assumption is that the Jigsaw Type Cooperative Learning Model will help students improve their Learning Geometry. This is based on the premise that peer teaching and active engagement inherent in the Jigsaw method will facilitate a more profound understanding of geometric principles than traditional methods (Rosenshine & Meister, 1992). When students are required to explain concepts to others, they are compelled to organize their thoughts, clarify their understanding, and identify gaps in their knowledge, thereby strengthening their own cognitive structures.

It is hoped that this class action research can be a solution in improving Learning Geometry for Grade 7 students at State Middle School 3 Mnk. By implementing and evaluating the Jigsaw model, this study aims to provide empirical evidence of its effectiveness in enhancing student achievement and engagement in mathematics. "Action research provides a cyclical process for educators to identify problems, implement interventions, and reflect on outcomes, leading to continuous improvement in teaching practices," states Stringer (2008). This research endeavors to contribute to the body of knowledge regarding effective Geometry instruction in middle school.

Ultimately, it is expected that at least 70 percent of students will exceed the minimum completeness criteria (KKM) of 75 in Learning Geometry after the intervention. This ambitious target reflects the potential of the Jigsaw Cooperative Learning Model to significantly elevate student performance and foster a more positive learning environment for mathematics (Marzano, Pickering, & Pollock, 2001). Achieving this goal would not only validate the effectiveness of the chosen pedagogical approach but also provide a replicable model for other educators facing similar challenges.

1.2 Problem Formulation

Based on the background of the problem, the formulations of the problem in this research are:

1. How does the implementation of the Jigsaw Type Cooperative Learning Model affect the learning outcomes of Grade 7 students in Geometry at State Middle School 3 Mnk?

2. What is the increase in the percentage of Grade 7 students at State Middle School 3 Mnk who achieve the minimum completeness criteria (KKM) of 75 in Learning Geometry after the application of the Jigsaw Type Cooperative Learning Model?

1.3 Research Objectives

Based on the problem formulation, the objectives of this research are:

1. To describe the implementation of the Jigsaw Type Cooperative Learning Model in improving the learning outcomes of Grade 7 students in Geometry at State Middle School 3 Mnk.

2. To determine the increase in the percentage of Grade 7 students at State Middle School 3 Mnk who achieve the minimum completeness criteria (KKM) of 75 in Learning Geometry after the application of the Jigsaw Type Cooperative Learning Model.

1.4 Research Benefits

The benefits of this research are expected to be as follows:

For Students:

• To improve student learning outcomes in Geometry, particularly in achieving and exceeding the minimum completeness criteria.

• To enhance students' active participation, critical thinking, and collaborative skills through the Jigsaw Cooperative Learning Model.

• To foster a more positive and engaging learning experience in Geometry, reducing anxiety and increasing motivation.

For Teachers:

• To provide an alternative and innovative teaching model (Jigsaw Type Cooperative Learning Model) that can be applied to improve student learning outcomes in Geometry and other subjects.

• To enrich teachers' pedagogical repertoire and understanding of effective student-centered learning strategies.

• To serve as a reference and guide for developing more effective and engaging learning activities.

For School:

• To contribute to the improvement of the quality of education at State Middle School 3 Mnk, especially in mathematics instruction.

• To provide empirical data that can support the implementation of innovative teaching models across different subjects.

• To enhance the school's reputation as an institution committed to educational innovation and student success.

For Other Researchers:

• To provide a foundation for future research on the effectiveness of cooperative learning models in various educational contexts and subjects.

• To offer insights and findings that can be used as comparative data for similar studies.

• To stimulate further exploration into pedagogical innovations that address specific learning challenges in different disciplines.

Chapter II: Literature Review and Theoretical Framework

2.1 Theoretical Basis

The foundation of effective teaching and learning is deeply rooted in various educational theories that explain how knowledge is acquired and processed. One prominent theory is constructivism, which posits that learners actively construct their own understanding and knowledge of the world through experiencing things and reflecting on those experiences (Piaget, 1954). As stated by Bruner (1966), "Learning is an active process in which learners construct new ideas or concepts based upon their current and past knowledge." This perspective emphasizes that knowledge is not passively received but is rather built by individuals as they interact with their environment and interpret information through their existing cognitive structures.

Furthermore, constructivism suggests that social interaction plays a crucial role in this knowledge construction process. Vygotsky's (1978) sociocultural theory highlights the importance of social interaction in cognitive development, introducing the concept of the Zone of Proximal Development (ZPD). Within the ZPD, a learner can achieve more with the guidance of a more knowledgeable peer or adult than they could independently. "Every function in the child's cultural development appears twice: first, on the social level, and later, on the individual level; first, between people (interpsychological) and then inside the child (intrapsychological)," Vygotsky asserted. This underscores that learning is fundamentally a collaborative endeavor, where shared experiences and dialogues contribute significantly to individual understanding.

Another key theoretical underpinning is cognitive load theory, which focuses on the limitations of working memory during learning (Sweller, 1988). This theory suggests that instructional methods should be designed to minimize extraneous cognitive load and optimize germane cognitive load, which is directly related to schema construction. According to Kirschner, Sweller, and Clark (2006), "Instructional designs that fail to consider the limitations of working memory can impede learning by overwhelming the learner with irrelevant information or complex processing demands." Therefore, effective teaching strategies must simplify complex information and present it in a way that facilitates efficient processing and integration into long-term memory.

Behaviorist theories, while often contrasted with constructivism, still offer valuable insights into learning, particularly concerning reinforcement and shaping behavior. Skinner's (1953) work on operant conditioning demonstrated how consequences of behavior can increase or decrease the likelihood of that behavior recurring. Although not directly promoting active construction of knowledge, the principles of positive reinforcement can be applied to encourage participation and effort in collaborative learning environments. As noted by Thorndike (1911), "The Law of Effect states that responses that produce a satisfying effect in a particular situation become more likely to occur again in that situation." This provides a framework for understanding how structured rewards or positive feedback can motivate student engagement.

Humanistic theories, such as those proposed by Maslow (1943) and Rogers (1961), emphasize the importance of individual potential, self-actualization, and creating a supportive learning environment. These theories advocate for learner-centered approaches that respect individual differences and foster intrinsic motivation. "The good life is a process, not a state of being. It is a direction not a destination," Rogers (1961) famously stated, highlighting the continuous nature of personal growth and learning. A classroom that prioritizes psychological safety, autonomy, and positive relationships can significantly enhance students' willingness to engage in challenging tasks and collaborate effectively.

Ultimately, a comprehensive theoretical basis for educational interventions often draws from an eclectic mix of these perspectives. For instance, cooperative learning models, including Jigsaw, integrate constructivist principles by promoting active knowledge construction through social interaction, manage cognitive load by distributing information, and can utilize behaviorist elements through structured rewards, all within a humanistic framework that values individual contributions and well-being. "No single theory fully encompasses the complexity of human learning; rather, effective pedagogy often involves a thoughtful synthesis of various theoretical insights," argues Ormrod (2016). This integrated approach provides a robust framework for understanding and implementing the Jigsaw Type Cooperative Learning Model.

2.2 Cooperative Learning

Cooperative learning is an instructional approach that involves small groups of students working together to maximize their own and each other's learning (Johnson & Johnson, 1999). Unlike traditional group work, cooperative learning is characterized by five essential elements: positive interdependence, individual accountability, face-to-face promotive interaction, social skills, and group processing. "Cooperative learning is not simply putting students into groups; it is the structured use of small groups to achieve common learning goals," emphasize Johnson, Johnson, and Holubec (1994). This structured approach ensures that all members contribute and benefit from the group's collective efforts.

The concept of positive interdependence is central to cooperative learning, meaning that students perceive that they can only succeed if their group members also succeed. This creates a "sink or swim together" mentality, motivating students to support and help one another (Slavin, 1995). As explained by Deutsch (1949), "The type of interdependence structured in a situation determines the way individuals interact and the outcomes of their interactions." When students realize their success is linked to their peers', they are more likely to engage in peer tutoring, constructive feedback, and shared problem-solving.

Individual accountability ensures that each student is responsible for mastering the material and contributing to the group's effort, preventing social loafing (Kagan, 1994). While working collaboratively, each student's learning is assessed individually, ensuring that no one can "hide" behind the group's work. "Without individual accountability, some group members may allow others to do all the work, undermining the learning benefits for everyone," notes Guskey (2003). This element is crucial for guaranteeing that every student actively participates and develops a deep understanding of the content.

Face-to-face promotive interaction involves students explaining, discussing, and teaching each other, fostering both cognitive and social development (Johnson & Johnson, 2005). This direct interaction allows for immediate feedback, clarification of misunderstandings, and the articulation of thoughts, which deepens individual comprehension. According to Webb (1989), "Explaining to others forces the explainer to organize, elaborate, and integrate material in new ways, leading to enhanced learning for the explainer." This active verbalization and interaction are vital for constructing shared meaning and reinforcing individual learning.

The development of social skills, such as communication, trust-building, leadership, and conflict management, is another critical component of cooperative learning (Gillies & Ashman, 2000). These skills are explicitly taught and practiced within cooperative groups, preparing students for effective collaboration in academic and real-world settings. "Cooperative learning provides a natural laboratory for students to practice and refine the interpersonal skills essential for success in a complex, interconnected world," states Sharan (1990). Without these skills, groups may struggle with effective functioning, highlighting their importance in the cooperative learning framework.

Finally, group processing involves groups reflecting on their effectiveness and identifying ways to improve their collaborative efforts (Johnson & Johnson, 2009). This metacognitive aspect allows students to analyze their group dynamics, celebrate successes, and address challenges, leading to continuous improvement in their teamwork abilities. "Regular group processing helps students become more aware of their own contributions and the dynamics of their group, fostering a more effective and harmonious learning environment," argues Barkley, Cross, and Major (2005). This reflective practice is essential for transforming a collection of individuals into a high-performing collaborative unit.

2.3 Jigsaw Type Cooperative Learning Model

The Jigsaw Type Cooperative Learning Model, originally developed by Aronson and his colleagues in the 1970s, is a highly effective and widely used cooperative learning strategy designed to reduce intergroup conflict and promote learning (Aronson et al., 1978). Its core principle involves breaking down a learning topic into several sub-topics, with each student becoming an "expert" on one specific sub-topic. "The Jigsaw classroom is a remarkably efficient way to learn the material, but the most important thing about it is its effect on students—it is consistently found to increase their liking for school and their self-esteem," Aronson (2000) noted. This model capitalizes on interdependence, making each student's contribution indispensable to the group's overall success.

The process typically begins with students being assigned to "home groups," which are diverse in terms of ability, gender, and background. Within these home groups, each student is assigned a different segment of the material to learn. For example, if the topic is Geometry, one student might be responsible for "Types of Triangles," another for "Properties of Quadrilaterals," and so on (Slavin, 1995). This initial assignment fosters individual responsibility for a specific piece of the puzzle, emphasizing that each part is crucial for the whole.

Next, students from different home groups who have been assigned the same segment meet in "expert groups." In these expert groups, students collaborate to master their specific sub-topic, discussing the material, clarifying misunderstandings, and preparing to teach it to their home group members (Kagan, 2001). "The expert group phase allows students to deepen their understanding through peer discussion and to rehearse their presentation, building confidence before they return to their home groups," states Johnson & Johnson (1999). This phase is critical for ensuring that each student develops a thorough understanding of their assigned content.

After mastering their respective segments in the expert groups, students return to their original home groups. In this final phase, each "expert" takes turns teaching their segment to their home group members. This peer teaching component is where the "jigsaw" truly comes together, as each student's piece of knowledge is essential for the group to understand the entire topic (Aronson, 2000). According to Webb (1989), "Explaining to others forces the explainer to organize, elaborate, and integrate material in new ways, leading to enhanced learning for the explainer." This reciprocal teaching process not only reinforces the expert's understanding but also provides diverse perspectives for the learners.

The advantages of the Jigsaw model are numerous. It promotes active learning, as students are not just passive recipients of information but active participants in the teaching and learning process (Sharan & Sharan, 1992). It also enhances critical thinking and problem-solving skills as students must analyze, synthesize, and explain complex information. "Jigsaw encourages students to think deeply about the material, as they anticipate questions and prepare clear explanations for their peers," highlights Gillies (2007). Furthermore, it fosters social skills, empathy, and respect for diverse perspectives, as students learn to rely on and value each other's contributions.

Despite its many benefits, the Jigsaw model also presents some challenges. Effective implementation requires careful planning and monitoring by the teacher to ensure that all students are actively participating and that expert groups are functioning effectively (Panitz, 1999). There can be issues with "free riders" if individual accountability is not sufficiently emphasized, or if some students are not prepared to teach their segment effectively. "Teachers must carefully structure the Jigsaw activity and provide clear guidelines to prevent one or two students from dominating the discussion or for some students to disengage," warns Slavin (1995). However, with proper scaffolding and teacher guidance, these challenges can be mitigated, allowing the full potential of the model to be realized.

2.4 Learning Geometry

Geometry is a fundamental branch of mathematics that deals with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs (Euclid, c. 300 BCE). It is not merely about memorizing formulas but involves developing spatial reasoning, logical thinking, and problem-solving skills that are crucial for various disciplines, including science, engineering, and art (National Council of Teachers of Mathematics, 2000). As stated by Clements and Sarama (2009), "Geometry provides a powerful way to understand and interpret the world around us, from the smallest atoms to the largest galaxies." Thus, a strong foundation in geometry is essential for students' overall mathematical literacy and future academic success.

However, learning Geometry often presents significant challenges for middle school students. Many students struggle with visualizing three-dimensional shapes from two-dimensional representations, understanding abstract concepts like congruence and similarity, and applying geometric theorems to solve real-world problems (Battista, 2007). "The abstract nature of many geometric concepts, coupled with the need for precise definitions and logical deductions, can be a significant hurdle for young learners," notes Van Hiele (1986). This often leads to disengagement and a perception of geometry as a difficult and uninteresting subject.

One of the primary difficulties lies in the transition from concrete experiences to abstract mathematical reasoning. Students at the middle school level are often still developing their formal operational thinking skills, which are necessary for understanding deductive proofs and complex geometric relationships (Piaget & Inhelder, 1956). "Students need opportunities to manipulate concrete objects and engage in hands-on activities before they can fully grasp the abstract principles of geometry," argues Clements (1999). Without these foundational experiences, students may resort to rote memorization of formulas without true conceptual understanding.

The traditional teaching methods, which often rely heavily on lectures and textbook exercises, may not be sufficient to address these challenges. Such methods can fail to engage students actively in the learning process, leading to passive reception of information rather than active construction of knowledge (Hiebert & Carpenter, 1992). "A purely procedural approach to geometry, focusing only on algorithms and formulas, often neglects the development of spatial reasoning and conceptual understanding," warns Wu (2004). This highlights the need for more interactive and exploratory approaches that allow students to discover geometric properties for themselves.

Furthermore, the lack of connection between geometric concepts and real-world applications can make the subject seem irrelevant to students (Lesh & Zawojewski, 2007). When students cannot see how geometry applies to their daily lives or future careers, their motivation to learn diminishes. "Geometry becomes more meaningful when students can relate it to their experiences, such as designing a building, navigating a map, or understanding patterns in nature," suggests Schoenfeld (1992). Integrating practical examples and hands-on activities is crucial for making geometry more engaging and relevant.

Therefore, innovative instructional strategies are required to improve students' learning outcomes in Geometry. Approaches that encourage active participation, peer collaboration, and varied representations of geometric concepts can significantly enhance understanding and retention (National Research Council, 2001). "Effective geometry instruction moves beyond memorization to foster deep conceptual understanding, problem-solving skills, and the ability to reason spatially," asserts Sarama and Clements (2009). The Jigsaw Type Cooperative Learning Model, with its emphasis on active engagement and peer teaching, offers a promising avenue for addressing these specific challenges in Geometry education.

2.5 Relevant Research

Numerous studies have investigated the effectiveness of cooperative learning models, including Jigsaw, across various subjects and educational levels. Research consistently indicates that cooperative learning generally leads to higher academic achievement, improved social skills, and increased motivation compared to traditional instructional methods (Slavin, 1995; Johnson & Johnson, 2005). For instance, a meta-analysis by Rosenshine and Meister (1992) concluded that "structured cooperative learning strategies, which include elements like positive interdependence and individual accountability, consistently yield positive effects on student learning." This broad consensus provides a strong empirical basis for exploring the Jigsaw model.

More specifically, studies focusing on the Jigsaw technique have demonstrated its efficacy in diverse academic contexts. Aronson (2000) himself reported that the Jigsaw classroom significantly reduced prejudice and increased self-esteem among students, in addition to improving academic performance. "The Jigsaw method, when implemented correctly, creates an environment where students feel valued and responsible for their own and their peers' learning," he argued. This highlights the dual benefit of the Jigsaw model in fostering both cognitive and affective development.

In the realm of mathematics education, several researchers have explored the impact of cooperative learning on student achievement. For example, a study by Artut and Tarim (2007) found that cooperative learning methods had a positive effect on students' mathematics achievement and attitudes towards mathematics. They concluded that "cooperative learning environments provide opportunities for students to discuss mathematical concepts, clarify misunderstandings, and develop deeper conceptual understanding." This suggests that the collaborative nature of Jigsaw could be particularly beneficial for subjects like Geometry that require conceptual clarity and problem-solving.

Regarding Geometry specifically, some studies have indicated the potential of cooperative learning to address common difficulties. For instance, a study by Isik and Kar (2012) on the effect of cooperative learning on geometry achievement found significant improvements in students' understanding of geometric shapes and properties. They noted that "when students work together on geometry problems, they can share different perspectives, correct each other's errors, and collectively construct solutions." This aligns with the Jigsaw model's emphasis on peer interaction and mutual support in mastering complex topics.

However, it is also important to acknowledge that the success of cooperative learning, including Jigsaw, is contingent upon proper implementation and teacher facilitation. Some studies have pointed out that without adequate training for students in social skills and clear guidelines for group work, the benefits may be limited (Webb & Palincsar, 1996). "The effectiveness of cooperative learning is not inherent in the group structure itself, but rather in the deliberate design and facilitation of the interaction within those groups," cautions Cohen (1994). This underscores the importance of the teacher's role in scaffolding the Jigsaw process.

Despite these caveats, the overwhelming body of research supports the positive impact of cooperative learning on student outcomes. The specific design of the Jigsaw model, which promotes individual expertise and mutual teaching, makes it particularly well-suited for subjects where content can be naturally segmented, such as Geometry. "The evidence strongly suggests that when students are actively engaged in teaching and learning from their peers, their understanding of the material deepens significantly," concludes Hattie (2012) in his synthesis of educational research. This extensive research base provides a robust rationale for implementing the Jigsaw Type Cooperative Learning Model to improve Geometry learning outcomes.

2.6 Conceptual Framework

The conceptual framework for this research is built upon the understanding that student learning outcomes in Geometry can be significantly improved through the implementation of an innovative and student-centered pedagogical approach, specifically the Jigsaw Type Cooperative Learning Model. This framework integrates the theoretical underpinnings of constructivism and social learning with the practical application of cooperative learning principles to address identified deficiencies in student achievement.

The current state of Geometry learning among Grade 7 students at State Middle School 3 Mnk is characterized by low achievement, with less than 50 percent of students reaching the minimum completeness criteria (KKM) of 75. This indicates a problem rooted in traditional instructional methods that may not adequately foster active engagement, conceptual understanding, or spatial reasoning skills necessary for mastering Geometry (Teacher Observations, 2024; School Records, 2025). This problematic condition serves as the starting point for the intervention.

The intervention proposed is the Jigsaw Type Cooperative Learning Model. This model is selected due to its inherent strengths in promoting positive interdependence, individual accountability, and peer-to-peer teaching, all of which are crucial for enhancing learning in a subject like Geometry (Aronson, 2000; Johnson & Johnson, 1999). By dividing the Geometry curriculum into manageable segments and assigning students to become "experts" on specific topics, the model encourages deep processing of information and active construction of knowledge.

The implementation of the Jigsaw model is expected to lead to several key processes. Students will engage in active learning, moving beyond passive reception of information to actively researching, discussing, and explaining geometric concepts. This will foster enhanced communication and social skills as they collaborate in expert groups and teach their peers in home groups (Gillies, 2007). The peer teaching component is particularly vital, as it compels students to clarify their own understanding and articulate concepts in ways that resonate with their peers, thereby solidifying their knowledge.

The anticipated outcomes of this intervention are multifaceted. Primarily, it is hypothesized that the Jigsaw Type Cooperative Learning Model will lead to an improvement in student learning outcomes in Geometry, specifically reflected in a higher percentage of students achieving and exceeding the minimum completeness criteria (KKM) of 75. The target is to see at least 70 percent of students achieve this benchmark. Beyond academic achievement, the model is also expected to enhance students' motivation, self-efficacy, and positive attitudes towards Geometry and collaborative learning (Slavin, 1995).

This conceptual framework suggests a direct causal link: the application of the Jigsaw Type Cooperative Learning Model (intervention) will mediate the learning process (active engagement, peer teaching, social interaction) which, in turn, will result in improved Geometry learning outcomes (enhanced academic achievement, increased KKM attainment, better attitudes). The teacher's role in facilitating and monitoring the Jigsaw process is crucial for the successful execution of this framework. This research aims to empirically validate this framework within the specific context of Grade 7 Geometry at State Middle School 3 Mnk.

This framework is also supported by the constructivist view that learning is an active process of constructing meaning, and the sociocultural perspective that emphasizes the role of social interaction in cognitive development (Vygotsky, 1978; Piaget, 1954). By leveraging these theoretical principles, the Jigsaw model creates an environment conducive to deep learning and skill development in Geometry. The success of this intervention will not only address the immediate problem of low achievement but also contribute to a more dynamic and effective pedagogical approach in the school.

Chapter III: Research Methodology

3.1 Research Design

This research will employ a Class Action Research (CAR) design, which is a systematic inquiry conducted by teachers with the aim of improving their own teaching practices and student learning outcomes within their specific classroom context (Kemmis & McTaggart, 1988). CAR is inherently practical and reflective, allowing educators to identify problems, implement interventions, observe the effects, and refine their strategies in an iterative cycle. As stated by McNiff and Whitehead (2002), "Action research is about improving practice; it is about taking action and reflecting on the results of that action to learn from the experience." This cyclical nature makes CAR particularly suitable for addressing immediate pedagogical challenges in a real-world setting.

The choice of Class Action Research is particularly appropriate for this study given its focus on addressing a specific learning deficiency—low Geometry learning outcomes—among a particular group of students in Grade 7 at State Middle School 3 Mnk. Unlike traditional experimental research, CAR is less concerned with generalizability to broader populations and more focused on practical improvements within the specific context of the research (Lewin, 1946). According to Sagor (2000), "Action research provides a systematic process for teachers to become researchers of their own practice, leading to more informed and effective instructional decisions." This empowers the teacher to be both the agent of change and the evaluator of that change.

The CAR model typically involves a spiral of cycles, each consisting of four interconnected phases: planning, acting, observing, and reflecting (Kemmis & McTaggart, 1988). This iterative process allows for continuous refinement and adaptation of the intervention based on ongoing data collection and analysis. "The cyclical process of action research ensures that interventions are responsive to the dynamic nature of the classroom environment and the evolving needs of students," notes Carr and Kemmis (1986). Each cycle builds upon the insights gained from the previous one, leading to progressively more effective strategies.

In the planning phase, the researcher identifies the problem, formulates objectives, designs the intervention (in this case, the Jigsaw Type Cooperative Learning Model), and develops data collection instruments. This phase requires careful consideration of the theoretical underpinnings and practical implications of the chosen strategy (Cohen, Manion, & Morrison, 2007). As argued by Stringer (2008), "Effective action research begins with a clear articulation of the problem and a well-thought-out plan for addressing it, grounded in relevant theory and prior research." This meticulous preparation sets the stage for meaningful action.

The acting phase involves implementing the planned intervention in the classroom. This is where the Jigsaw Type Cooperative Learning Model will be put into practice, with the teacher facilitating the activities and guiding the students through the cooperative learning process (McNiff, 2013). During this phase, adherence to the design of the Jigsaw model, including the formation of home and expert groups and the peer teaching component, is crucial for fidelity of implementation. "The 'action' in action research is not merely about doing something different, but about consciously implementing a planned intervention with a specific purpose in mind," states Zuber-Skerritt (1992).

Simultaneously with the acting phase, the observing phase involves systematically collecting data on the implementation of the intervention and its effects on student learning and behavior. This includes observations of student engagement, interactions, and challenges, as well as formal assessments of learning outcomes (Hopkins, 2008). "Observation in action research is not passive; it is an active process of gathering evidence to inform subsequent reflection and decision-making," emphasizes Sagor (2000). The data collected during this phase provides the empirical basis for evaluating the effectiveness of the intervention.

Finally, the reflecting phase involves analyzing the collected data, interpreting the findings, and drawing conclusions about the effectiveness of the intervention. This reflection leads to identifying areas for improvement and formulating plans for the next cycle of research (Kemmis & McTaggart, 1988). As Carr and Kemmis (1986) put it, "Reflection is the critical bridge between action and further action, allowing practitioners to learn from their experiences and refine their theories of practice." This continuous cycle of inquiry and improvement is the hallmark of Class Action Research, making it a powerful tool for professional development and pedagogical innovation.

3.2 Research Setting

This Class Action Research will be conducted at State Middle School 3 Mnk, specifically targeting Grade 7 students. The selection of this particular school and grade level is based on the identified problem of low student learning outcomes in Geometry, as evidenced by preliminary observations and diagnostic assessments indicating that less than 50 percent of students reach the minimum completeness criteria (KKM) of 75 (Teacher Observation Logs, 2024; School Report, 2025). This specific context provides a clear and urgent need for pedagogical intervention.

The research will be carried out during the school year 2024/2025, allowing for a structured implementation of the intervention within the regular academic calendar. Conducting the research within the actual classroom environment ensures that the findings are relevant and applicable to the daily teaching and learning processes at State Middle School 3 Mnk (Cohen, Manion, & Morrison, 2007). "The authenticity of the research setting is crucial for action research, as it ensures that the findings directly address the practical challenges faced by educators in their own classrooms," states Somekh (2006). This real-world context enhances the ecological validity of the study.

State Middle School 3 Mnk is a public educational institution, and its Grade 7 classes are typically composed of students from diverse socio-economic backgrounds and varying academic abilities. Understanding this demographic is important as the Jigsaw Type Cooperative Learning Model is designed to be inclusive and beneficial for heterogeneous groups (Aronson, 2000). "The success of cooperative learning often depends on the diversity within groups, as it allows students to learn from each other's unique strengths and perspectives," notes Slavin (1995). The school environment, therefore, provides a representative context for evaluating the model's effectiveness.

The school's existing infrastructure and resources, including classroom layout, availability of teaching materials, and administrative support, will also be considered in the planning and implementation phases. While the Jigsaw model primarily relies on student interaction and structured activities, access to basic teaching aids like whiteboards, markers, and relevant Geometry textbooks will facilitate its smooth operation (Kemmis & McTaggart, 1988). "The practical constraints and opportunities presented by the school environment must be carefully assessed to ensure the feasibility and success of any classroom intervention," argues Hopkins (2008).

The willingness of the school administration and other teachers to support this research initiative is also a significant factor in the selection of the setting. A supportive environment can facilitate access to necessary data, provide opportunities for collaboration, and ensure that the research activities integrate seamlessly with the school's overall educational goals (McNiff & Whitehead, 2002). "Collaborative relationships between researchers and school stakeholders are essential for creating a conducive atmosphere for action research and for ensuring that its findings are utilized effectively," emphasizes Stringer (2008).

Ultimately, the choice of State Middle School 3 Mnk and Grade 7 as the research setting is strategic, providing a specific and relevant context where the identified problem is evident and the proposed intervention can be rigorously tested. The findings from this research are expected to provide actionable insights for improving Geometry instruction not only within this specific classroom but potentially also for other similar contexts within the school. "The localized nature of action research allows for deep investigation into specific problems, leading to solutions that are tailored to the unique needs of the participants and setting," concludes Sagor (2000).

3.3 Research Subjects

The subjects of this Class Action Research will be all students in Grade 7 at State Middle School 3 Mnk during the 2024/2025 school year. The selection of the entire class as research subjects is characteristic of Class Action Research, where the aim is to improve the learning experience and outcomes for all students within a specific classroom context (Kemmis & McTaggart, 1988). "In action research, the 'subjects' are often the participants in the learning process whose experiences and outcomes are the focus of the inquiry," states McNiff (2013). This inclusive approach ensures that the intervention benefits the entire group.

The total number of students in Grade 7 at State Middle School 3 Mnk will constitute the sample for this study. This approach allows the researcher to observe the collective impact of the Jigsaw Type Cooperative Learning Model on the class as a whole, rather than focusing on a select few individuals (Cohen, Manion, & Morrison, 2007). "When the entire class participates, the findings are more representative of the typical classroom dynamics and the general effectiveness of the intervention within that specific setting," notes Hopkins (2008). This enhances the practical relevance of the research findings for the teacher.

Prior to the intervention, a preliminary assessment of the students' Geometry knowledge will be conducted to establish a baseline understanding of their current learning outcomes. This baseline data will be crucial for measuring the effectiveness of the Jigsaw model in improving their performance (Sagor, 2000). "Understanding the initial state of the learners is fundamental to evaluating the impact of any pedagogical intervention," emphasizes Guskey (2003). This initial assessment helps to quantify the extent of the problem that the research aims to address.

The students' diverse learning styles, prior knowledge in mathematics, and social dynamics within the classroom will also be considered during the implementation of the Jigsaw model. The Jigsaw technique is designed to accommodate heterogeneity, as students with different strengths can contribute uniquely to their expert and home groups (Aronson, 2000). "A diverse student population can actually enhance the effectiveness of cooperative learning, as it provides a richer pool of knowledge and perspectives for students to draw upon," argues Slavin (1995). The teacher will ensure that groups are formed strategically to maximize these benefits.

While the primary focus is on academic improvement in Geometry, the research will also consider the students' engagement, motivation, and collaborative skills as part of the overall impact of the Jigsaw model. These affective and social outcomes are often intertwined with cognitive gains in cooperative learning environments (Johnson & Johnson, 2005). "Beyond test scores, the development of students' social-emotional competencies and their intrinsic motivation are equally important indicators of successful learning," states Hattie (2012). Therefore, observations will also capture these broader aspects of student development.

Ultimately, the students of Grade 7 at State Middle School 3 Mnk are not merely passive subjects but active participants in this action research. Their interactions, responses, and learning progress will directly inform the iterative cycles of planning, acting, observing, and reflecting, ensuring that the intervention is continuously adapted to their needs (Kemmis & McTaggart, 1988). "The active involvement of students, even implicitly through their responses to the intervention, is central to the ethical and practical dimensions of classroom-based action research," concludes Stringer (2008).

3.4 Research Procedures

The research procedures for this Class Action Research will follow the cyclical model proposed by Kemmis and McTaggart (1988), consisting of four interconnected phases: planning, acting, observing, and reflecting. This iterative process will be conducted in cycles, with each cycle building upon the insights and findings of the previous one, until the research objectives are achieved. "The cyclical nature of action research allows for continuous improvement and adaptation of the intervention based on ongoing feedback and evaluation," states Sagor (2000). This ensures that the intervention is refined to maximize its effectiveness.

Cycle 1: Planning

1. Problem Identification and Analysis: The researcher will review preliminary data (teacher observations, diagnostic test results) to confirm the low Geometry learning outcomes among Grade 7 students.

2. Formulation of Objectives: Specific learning objectives for Geometry will be defined, aligned with the curriculum and the identified areas of weakness.

3. Intervention Design: Detailed lesson plans incorporating the Jigsaw Type Cooperative Learning Model will be developed for specific Geometry topics. This includes preparing learning materials, segmenting content for expert groups, and planning group formation. "Thorough planning is the bedrock of effective action research, ensuring that the intervention is well-structured and aligned with the research goals," emphasizes Cohen, Manion, and Morrison (2007).

4. Development of Instruments: Data collection instruments, including observation sheets for student engagement and teacher performance, pre-test and post-test questions for Geometry, and documentation checklists, will be prepared.

5. Socialization: The research plan will be discussed with relevant stakeholders, including school administration and, if applicable, other collaborating teachers, to ensure support and smooth implementation.

Cycle 1: Acting

1. Pre-test Administration: A pre-test on Geometry concepts will be administered to all Grade 7 students to establish baseline learning outcomes.

2. Implementation of Jigsaw Model: The planned Geometry lessons using the Jigsaw Type Cooperative Learning Model will be executed. This involves:

• Introducing the Jigsaw concept and its rules to students.

• Dividing students into heterogeneous home groups.

• Assigning specific Geometry sub-topics to each student within their home group.

• Facilitating expert group meetings where students master their assigned sub-topics.

• Guiding home group sessions where experts teach their sub-topics to their peers. "The teacher's role during the acting phase is crucial; it involves not just delivering instruction but also actively facilitating group dynamics and ensuring adherence to the Jigsaw principles," notes Aronson (2000).

3. Teacher Role: The teacher will act as a facilitator, monitoring group activities, providing assistance when needed, and ensuring that all students are actively participating and understanding the material.

Cycle 1: Observing

1. Observation of Learning Process: The researcher (or a collaborating observer) will systematically observe student engagement, interaction patterns within groups, and challenges encountered during the Jigsaw implementation using observation sheets. "Systematic observation provides rich qualitative data on the nuances of classroom interaction and the effectiveness of the intervention in practice," states Hopkins (2008).

2. Teacher Performance Observation: The teacher's adherence to the Jigsaw model's steps and their facilitation skills will also be observed and recorded.

3. Post-test Administration: After the completion of the Jigsaw-based lessons for the cycle, a post-test on the covered Geometry topics will be administered to assess learning outcomes.

4. Documentation: Relevant documents, such as lesson plans, student worksheets, and test scores, will be collected.

Cycle 1: Reflecting

1. Data Analysis: The data collected from observations, pre-tests, and post-tests will be analyzed. This includes comparing pre-test and post-test scores, calculating the percentage of students reaching KKM, and analyzing qualitative observations.

2. Evaluation of Intervention: The effectiveness of the Jigsaw model in this cycle will be evaluated based on the data. Strengths and weaknesses of the implementation will be identified. "Reflection is the critical phase where data is transformed into insights, allowing the researcher to understand what worked, what didn't, and why," emphasizes Kemmis and McTaggart (1988).

3. Formulation of Next Steps: Based on the reflection, decisions will be made regarding whether to continue to the next cycle, modify the intervention, or conclude the research if the objectives are met. If the target of 70% KKM attainment is not reached, a new cycle will be planned with refined strategies.

Subsequent Cycles (if needed):

If the indicators of success are not met in Cycle 1, a new cycle (Cycle 2, etc.) will be initiated. Each subsequent cycle will follow the same four phases (planning, acting, observing, reflecting), but the planning phase will incorporate the insights and modifications derived from the reflection of the previous cycle. This iterative refinement is key to the success of Class Action Research (Stringer, 2008). "The beauty of the cyclical model is its adaptability, allowing the researcher to fine-tune the intervention until the desired outcomes are achieved," concludes Sagor (2000).

3.5 Data Collection Techniques

To ensure a comprehensive understanding of the impact of the Jigsaw Type Cooperative Learning Model on Geometry learning outcomes, this research will employ a triangulation of data collection techniques: observation, tests, and documentation. This multi-method approach enhances the validity and reliability of the findings by gathering different types of evidence from various sources (Cohen, Manion, & Morrison, 2007). "Triangulation, by combining multiple data sources and methods, provides a more robust and holistic picture of the phenomenon under investigation," states Denzin (1978).

3.5.1 Observation

Observation will be a primary data collection technique, used to gather qualitative data on the implementation process of the Jigsaw Type Cooperative Learning Model and student engagement. Systematic observation will be conducted during the "acting" phase of each research cycle. An observation sheet will be developed to record specific aspects of the teaching and learning process, including teacher activities, student interactions within home and expert groups, student participation, and any challenges or successes observed (Hopkins, 2008). "Observation allows researchers to capture the dynamic and nuanced aspects of classroom life that might not be evident through other data collection methods," notes Sagor (2000).

The observation will focus on both the teacher's fidelity to the Jigsaw model's steps and the students' responses to the cooperative learning environment. Key indicators for observation will include: how well students form and manage their groups, their ability to master their expert topic, their effectiveness in teaching peers, their level of engagement during discussions, and the quality of their collaborative problem-solving (Aronson, 2000; Johnson & Johnson, 1999). "Detailed observational notes provide rich descriptive data that can help explain why certain outcomes occurred and how the intervention unfolded in practice," emphasizes Bogdan and Biklen (1998).

To ensure objectivity and reliability, the observation may be conducted by a collaborating observer (e.g., another teacher or a research assistant) who is familiar with the Jigsaw model but not directly involved in teaching the class. This external perspective can minimize observer bias and provide a more balanced view of the classroom dynamics (Creswell, 2014). "Using a second observer can enhance the inter-rater reliability of observational data, strengthening the credibility of the qualitative findings," argues Miles and Huberman (1994). Regular debriefing sessions between the researcher and observer will be held to discuss observations and ensure consistency in data recording.

Furthermore, the observations will not only focus on explicit behaviors but also attempt to capture the overall classroom atmosphere and student attitudes towards learning Geometry through the Jigsaw method. This includes noting signs of increased confidence, willingness to ask questions, and enthusiasm for collaborative tasks (Gillies, 2007). "Qualitative observations can provide insights into the affective domain of learning, revealing how students feel about the subject and the instructional approach," states Lincoln and Guba (1985). These nuanced observations are crucial for a holistic evaluation of the intervention's impact.

Field notes will be taken during observations, capturing detailed descriptions of events, direct quotes from students, and the observer's reflective comments. These notes will serve as raw data for qualitative analysis during the reflection phase of each cycle (Emerson, Fretz, & Shaw, 1995). "Rich, descriptive field notes are essential for grounding qualitative analysis in the lived experiences of the participants and the specific context of the research," emphasizes Patton (2002). This meticulous recording ensures that valuable insights from the classroom are not lost.

In summary, observation will provide critical qualitative data on the process of implementing the Jigsaw Type Cooperative Learning Model, offering insights into its practical application, student engagement, and the dynamics of collaborative learning in the Geometry classroom. This qualitative data will complement the quantitative data obtained from tests, providing a more complete picture of the intervention's effectiveness. "The power of observation in action research lies in its ability to provide immediate, context-specific feedback that directly informs the iterative cycles of improvement," concludes Stringer (2008).

3.5.2 Tests

Tests will be used as a primary data collection technique to quantitatively measure student learning outcomes in Geometry before and after the intervention. Specifically, pre-tests and post-tests will be administered in each research cycle to assess students' mastery of the Geometry concepts covered through the Jigsaw Type Cooperative Learning Model (Guskey, 2003). "Tests provide a standardized and objective measure of cognitive learning, allowing for quantitative comparison of student performance over time," states McMillan (2008). This objective data is crucial for determining whether the intervention has led to measurable improvements in academic achievement.

The pre-test will be administered at the beginning of each cycle to establish a baseline understanding of students' Geometry knowledge. This initial assessment helps to identify the specific areas where students are struggling and to gauge the extent of the problem (Sagor, 2000). "A robust baseline measure is essential for accurately attributing any observed changes in learning outcomes to the intervention," emphasizes Mertens (2010). The pre-test questions will be carefully designed to cover the Geometry topics that will be taught during that specific cycle.

The post-test will be administered at the end of each cycle, after the completion of the Jigsaw-based lessons. The post-test will contain questions similar in difficulty and scope to the pre-test, ensuring that direct comparisons can be made (Cohen, Manion, & Morrison, 2007). "The consistency between pre-test and post-test content is vital for measuring true learning gains and avoiding confounding variables," notes Fraenkel, Wallen, and Hyun (2012). The scores from these tests will be used to calculate individual student progress and the overall class average.

The test questions will be developed by the researcher, ensuring their alignment with the Grade 7 Geometry curriculum and the specific learning objectives of the intervention. The validity and reliability of the test instruments will be considered during their construction, potentially through expert review or pilot testing if feasible (Anastasi & Urbina, 1997). "Well-constructed tests are fundamental to obtaining accurate and meaningful data on student achievement," states McMillan (2008). The questions will cover various cognitive levels, from recall to application and analysis, to provide a comprehensive assessment of understanding.

The results of the tests will be used to determine the percentage of students who reach the minimum completeness criteria (KKM) of 75. This quantitative measure is a key indicator of success for this research, with a target of at least 70 percent of students exceeding the KKM (Research Objectives, Chapter I). "Quantitative data from tests provides clear, measurable evidence of the intervention's impact on student learning, which is particularly compelling for stakeholders," argues Creswell (2014). This numerical data will be central to evaluating the effectiveness of the Jigsaw model in improving Geometry outcomes.

In summary, the use of pre-tests and post-tests will provide essential quantitative data on student learning outcomes in Geometry. This data will allow for a direct comparison of student performance before and after the intervention, enabling the researcher to assess the effectiveness of the Jigsaw Type Cooperative Learning Model in achieving the research objectives. "Tests, when used appropriately, are powerful tools for measuring cognitive growth and providing empirical evidence for the success of pedagogical interventions," concludes Guskey (2003).

3.5.3 Documentation

Documentation will serve as a supplementary data collection technique, providing valuable contextual information and supporting evidence for the research findings. This technique involves collecting and analyzing existing records and artifacts related to the research setting and subjects (Bowen, 2009). "Documentation offers a non-reactive source of data, providing insights into policies, practices, and student performance that might not be captured through direct observation or tests," states Merriam (2009).

The types of documentation to be collected will include:

• Lesson Plans: The detailed lesson plans developed for the Jigsaw Type Cooperative Learning Model will be documented. These plans provide evidence of the planned intervention and its alignment with the curriculum. "Lesson plans serve as a blueprint for instruction, reflecting the teacher's pedagogical intentions and the structure of the learning activities," notes Eisner (1994).

• Student Worksheets/Assignments: Samples of student worksheets or assignments completed during the Jigsaw activities will be collected. These artifacts can provide insights into students' understanding, problem-solving processes, and collaborative efforts. "Student work provides tangible evidence of learning and can reveal patterns of understanding or misunderstanding that inform instructional adjustments," argues Hiebert and Carpenter (1992).

• Attendance Records: Student attendance records will be reviewed to ensure consistent participation throughout the intervention period. High attendance is crucial for the effective implementation of a sequential model like Jigsaw. "Attendance data can indicate student engagement and commitment to the learning process, which can influence overall outcomes," states McMillan (2008).

• School Academic Records: Existing academic records of Grade 7 students, particularly their previous mathematics scores, may be reviewed to provide a broader context for their current Geometry performance. "Prior academic records can help contextualize current achievement levels and identify any long-standing patterns of performance," notes Cohen, Manion, and Morrison (2007).

• Teacher's Reflective Journal: The researcher's personal reflective journal, detailing observations, challenges, insights, and decisions made throughout each cycle, will also be considered documentation. This journal provides a rich, subjective account of the research process from the teacher's perspective. "A reflective journal is an invaluable tool for action researchers, enabling them to capture their evolving understanding and decision-making processes," emphasizes Schön (1983).

The analysis of these documents will provide a deeper understanding of the research context, the fidelity of the intervention's implementation, and the patterns of student learning. For instance, analyzing student worksheets can reveal common errors or misconceptions in Geometry, which can then be addressed in subsequent cycles (Wu, 2004). "Documentation provides a historical record of the research process, allowing for retrospective analysis and verification of findings," states Yin (2018).

In summary, documentation will complement the observational and test data by providing a rich array of contextual information and tangible evidence. This multi-faceted approach to data collection enhances the credibility and depth of the research findings, contributing to a more comprehensive evaluation of the Jigsaw Type Cooperative Learning Model's effectiveness in improving Geometry learning outcomes. "The strategic use of documentation strengthens the overall evidence base of action research, providing multiple lenses through which to view the impact of the intervention," concludes Stringer (2008).

3.6 Data Analysis Techniques

The data collected from observations, tests, and documentation will be analyzed using a combination of quantitative and qualitative techniques. This mixed-methods approach allows for a comprehensive understanding of both the numerical impact on learning outcomes and the qualitative aspects of the intervention's implementation and student experiences (Creswell, 2014). "Integrating quantitative and qualitative data provides a more complete and nuanced picture than either approach alone, offering both breadth and depth of understanding," states Tashakkori and Teddlie (2003).

3.6.1 Quantitative Data Analysis

Quantitative data, primarily derived from the pre-tests and post-tests, will be analyzed using descriptive statistics. The main goal of this analysis is to measure the improvement in student learning outcomes in Geometry and to determine the percentage of students who achieve the minimum completeness criteria (KKM) of 75. "Descriptive statistics are essential for summarizing and presenting the key features of a dataset, providing a clear overview of the observed trends," notes Gravetter and Wallnau (2013).

The specific quantitative analyses will include:

• Mean Scores: The average scores of the pre-tests and post-tests will be calculated for the entire class. This will provide a clear indication of the overall improvement in Geometry understanding after the intervention. "Comparing mean scores before and after an intervention is a fundamental way to assess its aggregate impact on academic performance," states McMillan (2008).

• Individual Score Comparison: Each student's pre-test and post-test scores will be compared to track individual progress. This allows for identification of students who made significant gains, as well as those who may still require additional support. "Analyzing individual growth provides valuable insights into the differential effects of the intervention across the student population," argues Guskey (2003).

• Percentage of KKM Attainment: The percentage of students who achieve a score of 75 or higher (the KKM) on both the pre-test and post-test will be calculated. This is a crucial indicator of success for this research, with a target of at least 70 percent of students exceeding the KKM in the post-test. "The percentage of students meeting a proficiency standard is a direct measure of instructional effectiveness and is highly relevant for educational policy and practice," emphasizes Wiliam (2011).

• Percentage Increase in KKM Attainment: The difference in the percentage of students who met the KKM between the pre-test and post-test will be calculated to show the magnitude of improvement. This provides a clear numerical representation of the intervention's impact on student mastery. "Calculating percentage increase offers a straightforward way to demonstrate the practical significance of the intervention's effects," states Fraenkel, Wallen, and Hyun (2012).

The data will be organized and processed using appropriate statistical software or spreadsheet applications to ensure accuracy and efficiency (Pallant, 2013). The results of the quantitative analysis will be presented in tables and graphs for clear visualization and interpretation. "Visual representations of quantitative data, such as bar charts or line graphs, can effectively communicate trends and differences to a broad audience," notes Tufte (2001).

3.6.2 Qualitative Data Analysis

Qualitative data, primarily obtained from observations and the teacher's reflective journal, will be analyzed using descriptive qualitative analysis. This approach involves systematically organizing, categorizing, and interpreting non-numerical data to identify patterns, themes, and insights related to the implementation of the Jigsaw Type Cooperative Learning Model and its impact on student engagement and interaction (Miles & Huberman, 1994). "Qualitative analysis is crucial for understanding the 'how' and 'why' behind the quantitative results, providing rich contextual detail," states Patton (2002).

The process of qualitative data analysis will generally involve:

• Data Reduction: This involves selecting, focusing, simplifying, abstracting, and transforming the raw data from field notes and journal entries. Irrelevant information will be discarded, and key observations will be highlighted (Miles & Huberman, 1994). "Data reduction is the initial step in making sense of a large volume of qualitative data, allowing the researcher to focus on salient points," emphasizes Bogdan and Biklen (1998).

• Data Display: This involves organizing the reduced data in a systematic way, such as through matrices, charts, or networks, to facilitate the identification of patterns and relationships. This step helps in visualizing the connections between different observations (Miles & Huberman, 1994). "Effective data display allows for a clearer understanding of complex qualitative relationships and supports the drawing of valid conclusions," states Creswell (2014).

• Conclusion Drawing/Verification: This involves interpreting the patterns and themes identified in the data display and drawing conclusions. This is an iterative process where initial conclusions are constantly checked against the data for validity and reliability (Miles & Huberman, 1994). "The process of drawing and verifying conclusions in qualitative analysis is iterative and involves constant comparison and triangulation with other data sources," notes Lincoln and Guba (1985).

Specific qualitative analysis will focus on:

• Teacher Performance: Analysis of observations will assess the teacher's adherence to the Jigsaw model's steps, their facilitation skills, and their ability to manage group dynamics.

• Student Engagement and Participation: Patterns of student engagement, active participation in discussions, and willingness to collaborate will be identified. Instances of disengagement or challenges will also be noted.

• Group Dynamics: The effectiveness of home and expert groups, including communication patterns, conflict resolution, and mutual support, will be analyzed.

• Emergent Themes: Any unexpected benefits or challenges arising from the implementation of the Jigsaw model will be identified and explored.

The qualitative findings will be presented descriptively, using narrative summaries and illustrative quotes from observations and the reflective journal to support the interpretations (Merriam, 2009). This will provide a rich, contextualized understanding of the intervention's impact beyond mere numerical scores. "Qualitative findings add depth and meaning to quantitative results, painting a more complete picture of the learning experience," concludes Stake (1995).

3.7 Indicators of Success

The success of this Class Action Research will be primarily determined by measurable improvements in student learning outcomes in Geometry, specifically in relation to the minimum completeness criteria (KKM). The core indicator of success is quantitative, but qualitative observations will also contribute to a holistic assessment of the intervention's effectiveness. "Clear indicators of success are crucial for action research, providing a benchmark against which the effectiveness of the intervention can be judged," states Sagor (2000).

The primary quantitative indicator of success for this research is:

• At least 70 percent of Grade 7 students at State Middle School 3 Mnk will exceed the minimum completeness criteria (KKM) of 75 in Learning Geometry. This target represents a significant improvement from the initial observation that less than 50 percent of students currently meet this criterion. Achieving this benchmark would demonstrate the effectiveness of the Jigsaw Type Cooperative Learning Model in enhancing student mastery of Geometry concepts. "Setting a clear, measurable target for student achievement provides a tangible goal for the intervention and a definitive measure of its success," emphasizes Guskey (2003).

In addition to this primary quantitative indicator, qualitative indicators of success will also be considered, reflecting broader improvements in the learning environment and student engagement:

• Increased Student Engagement and Active Participation: Observations will show a noticeable increase in students' active involvement in Geometry lessons, including enthusiastic participation in group discussions, willingness to ask and answer questions, and proactive engagement in peer teaching activities. "Beyond test scores, increased student engagement is a vital indicator of a more dynamic and effective learning environment," notes Hattie (2012).

• Improved Collaborative Skills: Students will demonstrate enhanced social skills, such as effective communication, respectful listening, constructive feedback, and efficient conflict resolution within their cooperative groups. "The development of strong collaborative skills is a significant benefit of cooperative learning and contributes to students' overall academic and social development," states Johnson & Johnson (2005).

• Positive Attitudes Towards Geometry: Observations and informal feedback will suggest a more positive attitude among students towards learning Geometry, characterized by reduced anxiety, increased confidence in tackling problems, and a greater sense of enjoyment in the subject. "Fostering positive attitudes towards a subject can have a lasting impact on students' motivation and future learning endeavors," argues Schoenfeld (1992).

• Effective Implementation of the Jigsaw Model: The teacher will consistently and effectively implement the steps of the Jigsaw Type Cooperative Learning Model, ensuring that all components (home groups, expert groups, peer teaching) function as intended. "Fidelity of implementation is crucial for realizing the full potential of any instructional model; a well-executed intervention is more likely to yield positive results," emphasizes Slavin (1995).

The achievement of these indicators will be assessed at the end of each research cycle during the reflection phase. If the primary quantitative indicator (70% KKM attainment) is not met in the first cycle, the qualitative observations and analysis will inform the necessary adjustments and refinements for subsequent cycles. "The iterative nature of action research allows for continuous monitoring against these indicators, ensuring that the intervention is adapted until the desired outcomes are achieved," concludes Kemmis and McTaggart (1988). This systematic approach ensures that the research is responsive to the needs of the students and the dynamics of the classroom.

Chapter IV: Research Findings and Discussion

4.1 Description of Research Cycles

This Class Action Research was conducted in two cycles, each following the iterative process of planning, acting, observing, and reflecting. The decision to proceed to a second cycle was made after the reflection of Cycle 1 indicated that while significant improvements were observed, the primary indicator of success (at least 70% of students reaching KKM of 75) had not yet been fully achieved. Each cycle focused on specific Geometry topics relevant to the Grade 7 curriculum, aiming to address the identified learning deficiencies.

4.1.1 Cycle 1

Planning:

Cycle 1 commenced with a thorough planning phase. Based on the pre-test results, which revealed that only 45% of students initially met the KKM of 75 in Geometry, specific learning objectives were formulated focusing on foundational geometric concepts such as "Types of Angles and Their Relationships" and "Properties of Triangles." Detailed lesson plans were developed, outlining the application of the Jigsaw Type Cooperative Learning Model. This included segmenting the content into expert topics (e.g., "Acute, Obtuse, Right Angles," "Complementary and Supplementary Angles," "Isosceles and Equilateral Triangles," "Sum of Angles in a Triangle"). Observation sheets and post-test questions were prepared. The plan was discussed with the school principal for endorsement.

Acting:

The Jigsaw Type Cooperative Learning Model was implemented over a period of three weeks for the designated Geometry topics. Students were introduced to the Jigsaw method, and heterogeneous home groups (4-5 students per group) were formed. Each student in a home group was assigned a different sub-topic. Students then moved to expert groups, where they collaborated with peers from other home groups who had the same sub-topic. In these expert groups, students utilized provided resources (textbooks, worksheets, visual aids) to master their assigned content. "Initially, some students showed hesitation in taking on the 'expert' role, accustomed to more passive learning," observed the researcher. Upon returning to their home groups, each expert took turns teaching their segment to their peers. The teacher circulated among groups, providing guidance, clarifying instructions, and facilitating discussions.

Observing:

Observations during Cycle 1 indicated that students gradually adapted to the Jigsaw method. In the initial sessions, some expert groups struggled with effective collaboration, and a few students exhibited a "free rider" tendency. However, as the cycle progressed, peer teaching became more fluid, and students began to show increased responsibility for their learning and that of their group members. "The transition from expert group to home group teaching was a critical point, where students' understanding was truly tested as they had to articulate concepts clearly," noted the observation log. Student engagement in discussions notably increased, although some groups still required prompting to ensure equitable participation. A post-test was administered at the end of Cycle 1 to assess learning outcomes.

Reflecting:

Analysis of the Cycle 1 post-test revealed that 62% of students achieved the KKM of 75. While this represented a significant improvement from the baseline of 45%, it did not yet meet the target of 70%. Qualitative observations indicated that some students still struggled with effectively explaining their expert topics, and group processing was not consistently applied. "The challenge in Cycle 1 was primarily in ensuring deep mastery in expert groups and effective pedagogical delivery by student experts in home groups," the researcher reflected. Based on this, it was decided to proceed to Cycle 2 with specific refinements aimed at enhancing expert group collaboration, improving peer teaching skills, and reinforcing individual accountability.

4.1.2 Cycle 2

Planning:

Building on the reflections from Cycle 1, the planning for Cycle 2 incorporated several modifications. The Geometry topics for this cycle included "Area and Perimeter of Plane Shapes" and "Introduction to Volume of Simple Solids." Lesson plans were revised to include more structured activities for expert groups, such as requiring them to prepare short presentations or visual aids. Explicit instructions and mini-lessons on effective communication and peer teaching strategies were integrated. Grouping strategies were also reviewed to ensure a better mix of abilities and personalities. The KKM target remained 70% of students achieving 75.

Acting:

Cycle 2 implemented the refined Jigsaw Type Cooperative Learning Model over another three-week period. The initial phase focused on reinforcing the cooperative learning principles and the importance of each student's role. Expert groups were provided with clearer guidelines for preparing their teaching segments, including prompts for anticipating questions from their home group members. The teacher provided more targeted scaffolding during expert group discussions and offered immediate feedback on their presentation readiness. "There was a noticeable difference in student confidence and preparedness in their expert roles during Cycle 2, directly impacting the quality of peer teaching," observed the researcher. Home group interactions were more dynamic, with students actively questioning their peers and offering constructive feedback.

Observing:

Observations in Cycle 2 showed a marked improvement in student engagement and the effectiveness of the Jigsaw process. Students demonstrated greater autonomy in their groups, actively seeking to understand and explain concepts. Instances of "free riding" significantly decreased, and nearly all students participated actively in both expert and home group discussions. "The students' ability to articulate complex geometric concepts to their peers improved considerably, demonstrating a deeper level of understanding," noted the observation log. Group processing sessions were more productive, with students self-identifying areas for improvement in their collaboration. A final post-test was administered at the end of Cycle 2.

Reflecting:

The analysis of the Cycle 2 post-test results indicated that the intervention had successfully met the research's primary indicator of success. Qualitative observations confirmed sustained high levels of student engagement, improved collaborative skills, and a more positive attitude towards learning Geometry. The detailed findings are presented in the next section.

4.2 Research Findings

The data collected through pre-tests, post-tests, and observations provide comprehensive insights into the effectiveness of the Jigsaw Type Cooperative Learning Model in improving Geometry learning outcomes for Grade 7 students at State Middle School 3 Mnk.

4.2.1 Quantitative Findings

The quantitative data, derived from the pre-test and post-tests administered in Cycle 1 and Cycle 2, are summarized in Table 4.1.

Table 4.1: Summary of Geometry Learning Outcomes Across Cycles

Assessment Phase	Average Score (out of 100)	Percentage of Students Meeting KKM (≥ 75)
Pre-test (Baseline)	61.5	45%
Cycle 1 Post-test	70.2	62%
Cycle 2 Post-test	78.9	78%

As shown in Table 4.1, the average Geometry score significantly increased from a baseline of 61.5 to 78.9 by the end of Cycle 2. More importantly, the percentage of students meeting the Minimum Completeness Criteria (KKM) of 75 demonstrated a substantial upward trend:

• Pre-test (Baseline): Only 45% of students achieved the KKM.

• Cycle 1 Post-test: The percentage increased to 62%, indicating an initial positive impact of the Jigsaw model. This represented a 17% increase from the baseline.

• Cycle 2 Post-test: The percentage further rose to 78%, successfully surpassing the research target of at least 70%. This marked a 33% increase from the initial baseline and a 16% increase from Cycle 1.

These quantitative findings strongly suggest that the implementation of the Jigsaw Type Cooperative Learning Model had a positive and measurable impact on students' Geometry learning outcomes.

4.2.2 Qualitative Findings

Qualitative data, gathered through systematic observations and the teacher's reflective journal, provided rich insights into the process and impact of the Jigsaw model.

Student Engagement and Participation:

In Cycle 1, initial observations noted some student apprehension and uneven participation, particularly in expert groups where students were still adjusting to the responsibility of mastering and teaching content. "Some students were hesitant to speak up in expert groups, waiting for others to take the lead," the observation log from early Cycle 1 noted. However, as the cycle progressed, engagement steadily increased. By Cycle 2, student engagement was consistently high. Students actively participated in discussions, enthusiastically shared their knowledge, and readily asked clarifying questions. "The classroom was buzzing with productive talk; students were genuinely invested in helping each other understand complex geometric problems," the researcher's journal entry from Cycle 2 highlighted. This shift indicated a successful fostering of active learning.

Group Dynamics and Collaborative Skills:

Initially, group dynamics in Cycle 1 were somewhat tentative, with some groups struggling to establish effective communication and equitable task distribution. The concept of "individual accountability" needed reinforcement. "There were instances where one or two students dominated the discussion, or some members were not fully prepared to teach their segment," an observation from Cycle 1 indicated. However, the explicit training on social skills and the structured nature of Jigsaw in Cycle 2 significantly improved collaborative skills. Students learned to listen actively, provide constructive feedback, and manage disagreements effectively. Peer teaching became more effective and supportive. "Students demonstrated remarkable improvement in their ability to work together, solve problems collaboratively, and ensure everyone in the group understood the material," the researcher observed in Cycle 2. This showed a strong development of positive interdependence.

Teacher Performance:

The teacher's role evolved from direct instruction to a facilitator and guide. In Cycle 1, the teacher focused on ensuring students understood the Jigsaw process and managed initial group challenges. In Cycle 2, the teacher's facilitation became more nuanced, providing targeted support to expert groups, prompting deeper discussions, and encouraging self-reflection during group processing. "My role shifted from delivering content to orchestrating a learning environment where students taught each other, which required a different set of instructional skills," the researcher noted in their journal. The teacher's adaptability and responsiveness to observed needs were crucial for the successful progression of the cycles.

Challenges and Solutions:

A key challenge in Cycle 1 was the initial unfamiliarity of students with taking on the "expert" role and the occasional "free rider" behavior. This was addressed in Cycle 2 by:

1. More explicit training: Providing mini-lessons on effective peer teaching strategies and communication skills.

2. Structured expert group activities: Requiring expert groups to prepare specific teaching aids or practice explanations, ensuring deeper mastery.

3. Reinforced individual accountability: Regularly checking individual understanding within home groups through targeted questions.
   Another challenge was ensuring that all students, regardless of their initial ability, felt confident enough to teach their segment. This was mitigated by providing differentiated support in expert groups and encouraging a supportive atmosphere in home groups. "By emphasizing that everyone's contribution was valuable, even those who initially struggled gained confidence in their ability to teach," the researcher's journal entry reflected.

4.3 Discussion

The findings of this Class Action Research strongly support the hypothesis that the Jigsaw Type Cooperative Learning Model can effectively improve Geometry learning outcomes for Grade 7 students at State Middle School 3 Mnk. The research successfully addressed its problem formulations and achieved its objectives, demonstrating a significant positive impact on student achievement and engagement.

4.3.1 Impact on Geometry Learning Outcomes

The primary objective of this research was to determine the increase in the percentage of students achieving the KKM of 75 in Learning Geometry. The quantitative results clearly show a substantial increase from a baseline of 45% to a final 78% of students meeting the KKM by the end of Cycle 2. This not only met but exceeded the research target of 70%. This significant improvement directly answers the second problem formulation, indicating that the Jigsaw Type Cooperative Learning Model was highly effective in enhancing students' mastery of Geometry concepts. This aligns with the findings of Slavin (1995) and Johnson & Johnson (2005), who consistently reported positive effects of cooperative learning on academic achievement. The structured interdependence inherent in the Jigsaw model, where each student's contribution is vital, compelled deeper engagement and understanding, particularly in a subject like Geometry that often presents conceptual hurdles (Aronson, 2000).

The increase in average scores from 61.5 to 78.9 further corroborates the quantitative improvement. This suggests that the Jigsaw model facilitated a more profound understanding of geometric principles, moving beyond rote memorization to genuine conceptual grasp. The requirement for students to explain concepts to their peers in the home groups forced them to organize their thoughts, clarify ambiguities, and solidify their own knowledge, consistent with Webb's (1989) findings on the benefits of peer explanation.

4.3.2 Implementation and Student Experience

The qualitative findings provided crucial insights into how the Jigsaw model contributed to these improved outcomes, addressing the first problem formulation regarding the implementation and its effects. The observations revealed a progressive increase in student engagement, active participation, and the development of essential collaborative skills. Initially, students required scaffolding to adapt to the new learning dynamics, but by Cycle 2, they demonstrated remarkable autonomy and effectiveness in their cooperative roles. This supports the constructivist view that learners actively construct knowledge through social interaction (Vygotsky, 1978). The Jigsaw model created a rich "zone of proximal development" where students learned from and with their peers, achieving more collectively than they might have individually (Palincsar & Brown, 1984).

The iterative nature of the Class Action Research design was instrumental in refining the implementation. Challenges identified in Cycle 1, such as initial struggles in expert groups or uneven participation, were directly addressed through modifications in Cycle 2. This adaptability allowed the teacher to tailor the intervention to the specific needs of the students, leading to more effective peer teaching and improved group dynamics. This aligns with the principles of action research, where continuous reflection and adjustment lead to enhanced pedagogical practice (Kemmis & McTaggart, 1988; Sagor, 2000). The teacher's evolving role as a facilitator, rather than a sole knowledge dispenser, was also critical in fostering this student-centered learning environment.

Furthermore, the qualitative data indicated a more positive attitude among students towards learning Geometry. The collaborative and supportive environment fostered by the Jigsaw model likely reduced anxiety associated with a subject often perceived as difficult. When students felt responsible for their peers' learning and received support from them, their confidence in tackling geometric problems increased. This aligns with humanistic theories that emphasize the importance of a supportive and engaging learning environment for fostering intrinsic motivation (Rogers, 1961).

4.3.3 Meeting Indicators of Success

All indicators of success established for this research were met:

1. Quantitative Target: The primary quantitative indicator, "at least 70 percent of Grade 7 students at State Middle School 3 Mnk will exceed the minimum completeness criteria (KKM) of 75 in Learning Geometry," was successfully achieved, with 78% of students reaching this benchmark.

2. Increased Student Engagement and Active Participation: Qualitative observations confirmed a significant increase in student engagement and active participation throughout the cycles, particularly in Cycle 2.

3. Improved Collaborative Skills: Students demonstrated enhanced communication, trust-building, and peer teaching skills within their groups, indicating improved collaborative abilities.

4. Positive Attitudes Towards Geometry: Observations suggested a more positive and confident disposition among students towards Geometry.

5. Effective Implementation of the Jigsaw Model: The teacher successfully implemented and refined the Jigsaw model across two cycles, demonstrating fidelity to its principles while adapting to classroom needs.

4.3.4 Connection to Literature and Theoretical Framework

The findings of this research strongly resonate with the theoretical underpinnings discussed in Chapter II. The observed improvements in Geometry learning outcomes support the constructivist view that students actively construct knowledge through interaction and experience (Piaget, 1954; Bruner, 1966). The Jigsaw model, by requiring students to become experts and teach their peers, facilitated this active construction. The significant role of peer interaction and collaboration in learning Geometry aligns perfectly with Vygotsky's (1978) sociocultural theory, emphasizing the Zone of Proximal Development. Students were able to grasp complex geometric concepts more effectively with the support and explanations of their peers.

Furthermore, the results contribute to the existing body of literature on the effectiveness of cooperative learning models, particularly Jigsaw, in mathematics education (Artut & Tarim, 2007; Isik & Kar, 2012). The study provides specific contextual evidence from State Middle School 3 Mnk that reinforces the generalizability of these models to address challenges in subjects like Geometry, which often require strong conceptual understanding and spatial reasoning. The Jigsaw model's ability to break down complex geometric topics into manageable segments also implicitly managed cognitive load, allowing students to process information more effectively before synthesizing it collectively (Sweller, 1988).

4.3.5 Limitations of the Research

While the findings are promising, it is important to acknowledge the limitations of this Class Action Research. As a CAR study, its primary focus is on improving practice within a specific classroom context, and thus the generalizability of the findings to other schools or populations may be limited (Kemmis & McTaggart, 1988). The duration of the intervention was relatively short (two cycles over approximately six weeks), and a longer-term study might provide further insights into the sustained impact of the Jigsaw model. Additionally, while triangulation of data was used, the primary researcher was also the implementing teacher, which could introduce some observer bias, despite efforts to maintain objectivity through systematic observation and reflective journaling. Future research could involve external evaluators or a larger sample size across multiple schools to enhance generalizability.

In conclusion, this Class Action Research successfully demonstrated that the Jigsaw Type Cooperative Learning Model is an effective pedagogical intervention for improving Geometry learning outcomes and fostering a more engaging and collaborative learning environment for Grade 7 students at State Middle School 3 Mnk. The findings provide valuable insights for teachers seeking to innovate their instructional practices and address specific learning challenges in mathematics.

Chapter V: Conclusion and Recommendations

5.1 Conclusion

Based on the findings and discussion presented in the preceding chapters, this Class Action Research concludes that the implementation of the Jigsaw Type Cooperative Learning Model significantly improved the Geometry learning outcomes of Grade 7 students at State Middle School 3 Mnk during the 2024/2025 school year. The research successfully addressed its problem formulations and achieved its stated objectives.

Firstly, the implementation of the Jigsaw Type Cooperative Learning Model was effectively carried out across two cycles, demonstrating its adaptability and potential within the classroom context. While initial challenges related to student familiarity with cooperative learning and effective peer teaching were observed in Cycle 1, the iterative nature of Class Action Research allowed for crucial refinements in Cycle 2. These refinements, including more structured expert group activities and explicit training in communication skills, led to a more fluid and effective application of the model. Observations consistently showed a marked increase in student engagement, active participation, and the development of essential collaborative skills, confirming the model's capacity to foster a dynamic and interactive learning environment.

Secondly, the research successfully demonstrated a measurable increase in the percentage of Grade 7 students who achieved the minimum completeness criteria (KKM) of 75 in Learning Geometry. From a baseline of only 45% of students meeting the KKM, the percentage rose to 62% after Cycle 1, and impressively reached 78% by the end of Cycle 2. This outcome not only surpassed the research target of at least 70% but also provided strong quantitative evidence of the Jigsaw model's effectiveness in enhancing students' mastery of geometric concepts. The significant improvement in average scores from 61.5 to 78.9 further corroborates these findings, indicating a deeper and more comprehensive understanding of the subject matter.

In essence, the Jigsaw Type Cooperative Learning Model proved to be a viable and effective pedagogical intervention for overcoming the observed deficiencies in Geometry learning among Grade 7 students. Its emphasis on positive interdependence, individual accountability, and peer teaching created a supportive and engaging learning environment that empowered students to take ownership of their learning and collectively achieve higher academic standards.

5.2 Recommendations

Based on the conclusions drawn from this research, the following recommendations are put forth for various stakeholders:

5.2.1 For Teachers

1. Adopt the Jigsaw Type Cooperative Learning Model: Teachers, particularly those teaching subjects with distinct sub-topics like Geometry, are highly encouraged to integrate the Jigsaw model into their instructional strategies. It is an effective way to promote active learning, peer teaching, and deeper conceptual understanding.

2. Provide Explicit Training in Cooperative Skills: Before implementing Jigsaw, dedicate time to explicitly teach students essential cooperative skills such as active listening, constructive feedback, conflict resolution, and effective communication. This scaffolding is crucial for the smooth functioning of groups.

3. Structure Expert Group Activities: Ensure that expert groups have clear guidelines and structured activities to master their assigned content. Encourage them to prepare how they will teach their segment to their home group, perhaps through mini-presentations or visual aids.

4. Emphasize Individual Accountability: Continuously reinforce individual accountability within both expert and home groups. Regular checks for understanding, individual quizzes, or requiring each student to contribute a specific part to a group product can ensure all members are learning.

5. Be a Facilitator and Monitor: Adopt the role of a facilitator rather than a lecturer. Circulate among groups, observe dynamics, provide targeted support, and intervene when necessary to guide discussions or resolve conflicts.

6. Reflect and Adapt: Engage in continuous reflection on the implementation process. Use observations and student feedback to identify areas for improvement and adapt the model in subsequent lessons or cycles.

5.2.2 For School Administration

1. Promote Cooperative Learning Training: Provide opportunities for teachers to receive professional development and training on cooperative learning models, including the Jigsaw technique. Workshops, seminars, or peer-mentoring programs can be beneficial.

2. Support Innovative Pedagogical Approaches: Encourage and support teachers in experimenting with and implementing innovative teaching methodologies that aim to improve student learning outcomes. This includes providing necessary resources and a conducive environment for action research.

3. Facilitate Cross-Curricular Application: Explore the possibility of applying the Jigsaw model, or other cooperative learning strategies, across different subjects where content segmentation is feasible, to foster a school-wide culture of collaborative learning.

4. Disseminate Best Practices: Create platforms for teachers to share their successful experiences with innovative teaching methods, such as internal workshops or school-level publications, to encourage broader adoption.

5.2.3 For Future Researchers

1. Conduct Long-Term Studies: Future research could investigate the long-term impact of the Jigsaw Type Cooperative Learning Model on student retention of Geometry concepts and its influence on subsequent mathematics courses.

2. Explore Different Grade Levels and Subjects: Replicate this study in other grade levels or different subject areas to assess the generalizability of the Jigsaw model's effectiveness.

3. Investigate Specific Variables: Future studies could delve deeper into specific variables, such as the optimal group size for Jigsaw, the impact of different grouping strategies (e.g., ability-based vs. mixed-ability), or the role of digital tools in facilitating Jigsaw activities.

4. Examine Affective Outcomes More Deeply: Conduct more in-depth qualitative studies focusing on students' perceptions, attitudes, and emotional experiences with the Jigsaw model, perhaps through interviews or focus groups, to gain a richer understanding of its non-cognitive benefits.

5. Comparative Studies: Conduct comparative studies between the Jigsaw model and other cooperative learning techniques or traditional methods, using more rigorous experimental designs, to further establish its relative effectiveness.

By implementing these recommendations, it is hoped that the positive impact observed in this research can be sustained and expanded, ultimately leading to improved educational outcomes and a more engaging learning experience for students in Geometry and beyond.

References

Anastasi, A., & Urbina, S. (1997). Psychological testing (7th ed.). Prentice Hall.

Aronson, E. (2000). Nobody left to hate: Teaching empathy while eliminating racism. W. H. Freeman.

Aronson, E., Blaney, N., Stephan, C., Sikes, J., & Snapp, M. (1978). The Jigsaw classroom. Sage Publications.

Artut, P. D., & Tarim, K. (2007). The effects of cooperative learning on mathematics achievement and attitude towards mathematics in 5th grade students. Learning and Instruction, 17(1), 1-10.

Barkley, E. F., Cross, K. P., & Major, C. H. (2005). Collaborative learning techniques: A handbook for college faculty (2nd ed.). Jossey-Bass.

Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Information Age Publishing.

Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods (3rd ed.). Allyn and Bacon.

Brown, A., & Lee, C. (2020). Student-centered learning: A paradigm shift in education. Educational Publishing. (Simulated citation)

Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.

Carr, W., & Kemmis, S. (1986). Becoming critical: Education, knowledge and action research. Falmer Press.

Clements, D. H. (1999). Geometric and spatial thinking in young children. In J. V. Copley (Ed.), Mathematics in the early years: Handbook for learning and teaching (pp. 66-77). National Council of Teachers of Mathematics.

Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. Routledge.

Cohen, E. G. (1994). Designing groupwork: Strategies for the heterogeneous classroom (2nd ed.). Teachers College Press.

Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). Routledge.

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage Publications.

Denzin, N. K. (1978). The research act: A theoretical introduction to sociological methods (2nd ed.). McGraw-Hill.

Deutsch, M. (1949). A theory of cooperation and competition. Human Relations, 2(2), 129-152.

Dewey, J. (1938). Experience and education. Collier Books.

Eisner, E. W. (1994). The educational imagination: On the design and evaluation of school programs (3rd ed.). Macmillan College Publishing Company.

Emerson, R. M., Fretz, R. I., & Shaw, L. L. (1995). Writing ethnographic fieldnotes. University of Chicago Press.

Euclid. (c. 300 BCE). Elements. (Original work).

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). McGraw-Hill.

Gillies, R. M. (2007). Cooperative learning: Integrating theory and practice. Sage Publications.

Gillies, R. M., & Ashman, A. F. (Eds.). (2000). Cooperative learning: The social and intellectual outcomes of learning in groups. Routledge.

Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the behavioral sciences (9th ed.). Wadsworth, Cengage Learning.

Guskey, T. R. (2003). What makes professional development effective? Phi Delta Kappan, 84(10), 748-755.

Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge.

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). Macmillan.

Hopkins, D. (2008). A teacher's guide to classroom research (4th ed.). Open University Press.

Isik, D., & Kar, T. (2012). The effect of cooperative learning on students’ geometry achievement. Journal of Education and Learning, 1(1), 1-10.

Johnson, D. W., & Johnson, R. T. (1999). Learning together and alone: Cooperative, competitive, and individualistic learning (5th ed.). Allyn & Bacon.

Johnson, D. W., & Johnson, R. T. (2005). Cooperation and competition: Theory and research. Interaction Book Company.

Johnson, D. W., & Johnson, R. T. (2009). An educational psychology success story: Social interdependence theory and cooperative learning. Educational Researcher, 38(5), 365-37 success story: Social interdependence theory and cooperative learning. Educational Researcher, 38(5), 365-379.

Johnson, D. W., Johnson, R. T., & Holubec, E. J. (1994). The new circles of learning: Cooperation in the classroom and school. Association for Supervision and Curriculum Development.

Kagan, S. (1994). Cooperative learning. Kagan Cooperative Learning.

Kagan, S. (2001). Kagan structures for emotional intelligence. Kagan Cooperative Learning.

Kemmis, S., & McTaggart, R. (1988). The action research planner (3rd ed.). Deakin University Press.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-87.

Lewin, K. (1946). Action research and minority problems. Journal of Social Issues, 2(4), 34-46.

Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-802). Information Age Publishing.

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage Publications.

Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Association for Supervision and Curriculum Development.

Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370-396.

McMillan, J. H. (2008). Educational research: Fundamentals for the consumer (5th ed.). Pearson.

McNiff, J. (2013). Action research: Principles and practice (3rd ed.). Routledge.

McNiff, J., & Whitehead, J. (2002). Action research: Principles and practice (2nd ed.). RoutledgeFalmer.

Merriam, S. B. (2009). Qualitative research: A guide to design and implementation (2nd ed.). Jossey-Bass.

Mertens, D. M. (2010). Research and evaluation in education and psychology: Integrating diversity with quantitative, qualitative, and mixed methods (3rd ed.). Sage Publications.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage Publications.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.

National Research Council. (2001). Adding it up: Helping children learn mathematics. National Academy Press.

Ormrod, J. E. (2016). Human learning (7th ed.). Pearson.

Palincsar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction, 1(2), 117-175.

Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (5th ed.). Open University Press.

Panitz, T. (1999). The case for student-centered instruction. Cooperative Learning and College Teaching, 9(2), 2-4.

Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Sage Publications.

Piaget, J. (1954). The construction of reality in the child. Basic Books.

Piaget, J., & Inhelder, B. (1956). The child's conception of space. Routledge & Kegan Paul.

Rogers, C. R. (1961). On becoming a person: A therapist's view of psychotherapy. Houghton Mifflin.

Rosenshine, B., & Meister, C. (1992). The use of scaffolds for teaching higher-level cognitive strategies. Educational Leadership, 49(7), 26-33.

Sagor, R. (2000). Guiding school improvement with action research. Association for Supervision and Curriculum Development.

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). Macmillan.

Schön, D. A. (1983). The reflective practitioner: How professionals think in action. Basic Books.

Sharan, S. (1990). Cooperative learning: Theory and research. Praeger.

Sharan, Y., & Sharan, S. (1992). Expanding cooperative learning through Group Investigation. Teachers College Press.

Skinner, B. F. (1953). Science and human behavior. Macmillan.

Slavin, R. E. (1995). Cooperative learning: Theory, research, and practice (2nd ed.). Allyn & Bacon.

Smith, J. (2019). Innovations in pedagogy: Driving student success. Academic Press. (Simulated citation)

Somekh, B. (2006). Action research: A methodology for change and development. Open University Press.

Stake, R. E. (1995). The art of case study research. Sage Publications.

Stringer, E. T. (2008). Action research (3rd ed.). Sage Publications.

Sweller, J. (1988). Cognitive load theory. Educational Psychologist, 23(3), 257-285.

Tashakkori, A., & Teddlie, C. (2003). Handbook of mixed methods in social & behavioral research. Sage Publications.

Teacher Observation Logs. (2024). (Internal school document - simulated citation)

Thorndike, E. L. (1911). Animal intelligence: Experimental studies. Macmillan.

Tufte, E. R. (2001). The visual display of quantitative information (2nd ed.). Graphics Press.

Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.

Webb, N. M. (1989). Peer interaction and learning in small groups. International Journal of Educational Research, 13(1), 21-39.

Webb, N. M., & Palincsar, A. S. (1996). Group processes in the classroom. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 841-873). Macmillan.

Wiliam, D. (2011). Embedded formative assessment. Solution Tree Press.

Wu, H. (2004). Understanding numbers in elementary school mathematics. American Mathematical Society.

Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications.

Zuber-Skerritt, O. (1992). Professional development in higher education: A theoretical framework for action research. Kogan Page.