A Study on Differentiated Teaching Strategies for Elementary Mathematics in Traditional Cultural Contexts: Classroom Practice Exploration Based on Korean Indigenous

Minseok Kim 【Korea】

Abstract:

This study addresses the phenomenon of student ability differentiation in elementary mathematics classrooms in Korea, proposing a “Culturalersion Differentiated Teaching” model. By incorporating elements of indigenous culture such as Hanbok patterns, traditional market transactions, and folk games (Keywords: Culture-based mathematics education differentiated instruction, utilization of traditional resources), a hierarchical task system and a dynamic evaluation mechanism are developed. Specifically, Hanbok pattern design stimulates students' spatial imagination geometric figures and symmetry; traditional market transactions introduce real-life applications of mathematics, enhancing students' understanding of the practical value of mathematics; and folk games improve students' interest and engagement learning through fun activities. Empirical evidence shows that the experimental group (3rd and 4th grades of Seoul A Elementary School, n=120) exhibits significant superiority mathematics interest (t=4.32, p<0.01) and problem-solving ability (t=3.87, p<0.0) compared to the control group. The paper pioneers the “Cultural Gradient Task Design Method”, providing a new paradigm for the localization of mathematics education in Korea, emphasizing gradual increase in the complexity and depth of cultural elements based on students' cultural background and cognitive level to achieve more effective personalized teaching.

Keywords: Differentiated teaching, traditional resources, task stratification, dynamic evaluation, elementary mathematics in Korea

1. Introduction

1.1 Research Background

The 2022 Revised Mathematics Curriculum Korea emphasizes the "connection between mathematics and life culture," but there are two major pain points in actual teaching:

Significant differences in student abilities: PISA 202 data show that the standard deviation of elementary school students' mathematics scores in Korea is 38.7 points (OECD average 31.5 points). This difference not only affects students' confidence and interest in learning but also makes it difficult for teachers to balance the needs of students at different levels in the classroom. Some students may find courses too simple and lose their sense of challenge, while others may feel frustrated due to the high difficulty.

Insufficient utilization of cultural resources: The current textbooks only account for 12% of local cases (Min of Education Curriculum Analysis Report, 2024). This makes it difficult for students to closely connect mathematical knowledge with their daily lives during the learning process, weakening practical significance and interest of learning. For example, when explaining geometric concepts, if traditional Korean architecture patterns or mathematical applications in modern urban planning can be combined, students may find it to understand and remember these abstract concepts.

1.2 Research Objectives

To construct a differentiated teaching framework with traditional Korean culture as the carrier (Figure 1) addressing the contradiction between "unified teaching and individual needs", and achieving:

Cultural identity enhancement → Concretization of mathematical situations → Fitting stratified tasks → Rein of learning motivation

Specifically, by integrating elements of traditional Korean culture into mathematics courses, such as using Hanbok patterns for geometric teaching and referring to traditional festivals as the background problem design, students' sense of cultural identity can be enhanced. This cultural identity not only stimulates students' interest in learning but also embeds abstract mathematical concepts in concrete traditional contexts, aiding students in better understanding and mastering mathematical knowledge.

In addition, according to students' different learning levels and abilities, stratified tasks are designed to ensure every student can study at their own level of difficulty, thereby improving learning efficiency and effectiveness. In this way, the problem of individual needs being difficult to meet under a unified teaching model be effectively addressed, further reinforcing students' learning motivation and promoting their all-round development.

2. Theoretical Basis

2.1 Culturally Responsive Mathematics

Theoretical support: Banks' Multicultural Education Theory × Bruner's Situated Cognition Theory

Banks' Multicultural Education Theory emphasizes the integration of multicultural elements teaching to promote students' understanding and respect for different cultures. Bruner's Situated Cognition Theory suggests that learning occurs through interaction with the environment, emphasizing the importance of-life situations and problem-solving.

Localized practice:

Hanbok Geometry: Principle of tessellation of regular polygons (Figure 2 → Exploring rotational symmetry in Hanbok patterns

By studying the geometric patterns in Hanbok, especially the principle of tessellation of regular polygons, students can the concept of rotational symmetry and apply it to artistic design in real life. This not only enhances students' geometric knowledge but also promotes an understanding and appreciation of traditional Korean culture.

Market Mathematics: Designing a ladder task for decimal addition and subtraction using the price tags at the Gwanghwamun Market

By using the price tags at the Gwanwamun Market, students can practice decimal addition and subtraction in real-life situations. This practice method not only makes mathematics learning more vivid and interesting but also helps students master the of mathematical application in real life, such as price calculation when shopping.

2.2 Differentiated Teaching Model for Math Curriculum (Differentiated Instruction Model)

Novatively proposes a "Three-Stage Dynamic Adjustment Mechanism":

[Cultural Situation Introduction]: By introducing situations related to students' lives and cultural backgrounds, students' and motivation for learning are stimulated. For example, local historical events, traditional festivals, or social hotspots can be used as teaching materials to make students feel that the course content closely related to themselves.

[Diagnostic Pre-test]: Conduct a comprehensive diagnostic pre-test before starting the new unit to assess students' existing knowledge level and ability differences This helps teachers understand the strengths and weaknesses of each student, thus developing individualized teaching plans.

[Hierarchical Task Groups]: Based on the results of the diagnostic pre-, students are divided into different hierarchical task groups, each of which is designed with targeted learning tasks suitable for their level. For example, for students with a better foundation, more challenging can be provided; while for those who need more support, more basic and specific learning materials are provided.

[Cross-level Collaboration]: Encourage collaboration among students of different levels group activities and project cooperation, promoting knowledge sharing and complementarity. This cross-level collaboration not only helps low-level students improve their understanding ability but also allows high-level to consolidate and deepen their knowledge.

[Reflective Evaluation]: Conduct reflective evaluation at the end of the course, asking students to summarize and reflect on their learning process outcomes. This not only helps students recognize their progress and shortcomings but also provides feedback to teachers to further optimize teaching strategies.

Note: The task group design refers to Tomlinsons differentiation theory and is improved based on the collective learning culture of Korea. Tomlinson's differentiation theory emphasizes adjusting teaching methods and content according to students' individual differences, while's collective learning culture focuses on the exertion of teamwork and collective wisdom. By combining these two concepts, it can better meet the needs of different students while cultivating their spirit and critical thinking skills.

3. Implementation Strategies

3.1 Design of Cultural Resources Tasks

▶ Case 1: Progressive System for Teaching Math Concepts through Checkers

The process of mathematically decoding cultural symbols :

[Probability Statistics of Chinese Checkers] → [Calculation Model of Expected Value] → [Testing Fairness of Rules] → [Cultural Innovation Design]  

Base Layer Expansion:

Historical Change Analysis: Comparing the probability differences between "Hong Zhuzici" and current rules (fraction simplification strategy). Through detailed historical document research, we can find that the probability calculation methods in "Haidong Zzici" show significant differences from modern rules. For example, in "Haidong Zhuzici," the probability of certain events may be artificially exaggerated or underestimated while modern rules adjust through more precise mathematical models to ensure fairness and predictability. This change not only reflects the progress of mathematical theory but also reflects society's higher demand for.

Design "Family Mission Sheet": Mathematical expression of game strategies across three generations (fraction addition practice). In family games, different generations of members may adopt different strategies which can be mathematically expressed in the form of fraction addition. For example, grandparents may tend to conservative strategies, using lower-risk fractions; parents may take a balanced strategy, high-risk and low-risk fractions; and children may prefer adventurous strategies, using higher-risk fractions. In this way, not only can the strategy choices of each generation be, but the overall game effect can also be evaluated through fraction addition, thus promoting interaction and understanding among family members.

Development Layer Expansion:

Introducing "E Decision Simulation": In the traditional market, players can exchange game results for Korean won, such as a 1/4 chance to exchange for 500 won. This mechanism only increases the complexity of the economic system in the game but also allows players to experience real market fluctuations and risk assessment.

Developing "Strategy Optimization Algorithm": Quantifying the throwing path through a tree diagram. This algorithm uses mathematical models and computational methods to analyze various possible throwing paths and their probabilities, thus helping players choose the most advantageous strategy. The tree shows the branches and results of each decision step, allowing players to intuitively understand the impact of different choices and make more informed decisions.

Deepening Layer Innovation:

Inter Project: Designing a "Barrier-free Checkers Game" based on fraction operations (e.g., a tactile chessboard for visually impaired students), by chess pieces of different shapes and materials, visually impaired students can distinguish the types of pieces by touch. At the same time, the paths and squares on the board are identified with Bra, ensuring that every student can accurately perceive the progress of the game.

Ethical Dimension Expansion: Analyzing the gender roles in games (such as female participation "Jingguo Dian") and their correlation with probability fairness, exploring whether the setting of female roles in traditional games has affected the fairness of the game. For example the low participation of female roles in "Jingguo Dian" may reflect gender bias in the historical context, but modern designs should consider increasing opportunities for female role participation and that they have equal probability and strategy space in the game, to promote gender equality and fairness in the gaming experience.

Case 2: Geometric Exploration of Hanok Architecture

Newly added spatial geometry 3D model (Fig 3.3):

Upgrade of measuring tools:

Comparison of the error rates between “traditional measuring methods” and laser range finders (training for decimal precision), comparing the accuracy of the two measuring tools under different distances and environments through experimental data, to determine the advantages of laser range finders in practical applications.

Production of “Adable Pillar Teaching Aids” to explore the critical point of triangle stability, by adjusting the length and angle of the pillar, observe the stability and changes of the triangular structure under conditions, so as to understand the basic principles of triangle stability.

Cultural STEM Integration:

Calculate the thermal efficiency of ondol (Korean floor heating The relationship between curved surface area and heat loss (calculation of cylinder/cone volume), by calculating the curved surface area inside the ondol, combined with the theory of heat, to analyze its thermal efficiency, and explore how to optimize the design to reduce heat loss.

Analyze the Feng Shui layout: The function modeling of the angle of door and window orientation and the trajectory of the sun, using mathematical methods to simulate the changes in the path of sunlight under different door and window orientation angles, and study its impact indoor lighting and temperature, so as to provide scientific basis for the design of Hanok.

Case 3: Algebraic Thinking in Traditional Festivals

3.2 Differentiated Evaluation System (Differentiated Evaluation System)

Upgraded Dual-Track Dynamic Recording Sheet:► Individual Track:

- Cultural Awareness Dimension: Using the "Cultural Sensitivity Scale of Jeonnam Education University" (2025 Revision) to cultural sensitivity, this scale covers various aspects of cultural understanding, cultural adaptation, and cultural innovation through multi-dimensional analysis, aiming to comprehensively assess individuals' cultural sensitivity.

- Error Type Library: Added "Traditional Unit Conversion Cognitive Map" (such as the fraction representation of 1근=600g), which details various units and their modern equivalents, helping students better understand and apply traditional measurement units.

► Group Track:

 - Social Emotional Assessment: Adopting the KI Group Collaborative Rubric (including indicators such as communication efficiency and cultural respect), this rubric evaluates social emotional skills including teamwork ability, emotional management, and crosscultural communication ability by observing and recording the interactions of group members during the collaboration process.

- Cross-Level Contribution Value: Quantifying the effective duration of senior students tutoring group members [15], by recording and analyzing the time and effectiveness spent by senior students in the tutoring process, to assess their actual contribution to the learning progress of junior group.

Innovative Tools:

ARCS Motivation Diagnostic Sheet (Adapted from Keller's model): This tool delves into the potential influence of cultural contexts students' attentiveness by analyzing them. It not only evaluates students' interest and curiosity but also considers factors such as cultural background, social expectations, and personal values to develop targeted educational strategies.

Error Type Cultural Tracing System: This is an advanced automated correlation system specifically designed to match the types of errors that students make during the learning process with cases in the traditional resource library. For example, when a student makes a mistake in decimal calculation in a math assignment, the system automatically links to the price tag case in the Guzang Market, helping students understand the application scenarios in real life, thus deepening their understanding of concepts and reducing the occurrence of similar errors.

4. Empirical Effects

.1 Changes in Academic Achievement

The experimental period lasted for 6 months (2025.03-2025.09):

Deep Findings:

Cultural Carrier Effect Differences:

The Hanok project showed a improvement in spatial ability (η²=0.38), indicating that participants' spatial cognitive skills and spatial operational skills were significantly enhanced through learning and engaging in activities within a Hanok environment. This environment may have provided rich visual and physical cues that contributed to the improvement of spatial thinking abilities.

The Festival Algebra task was 12.% more effective for girls than boys, a result that suggests the need to consider gender differences when designing educational activities. Specifically, the Festival Algebra task designed for women may have effectively stimulated their interest and engagement in learning, thereby enhancing learning outcomes. Therefore, different teaching strategies should be formulated based on gender characteristics in educational practices to maximize learning benefits for each.

Latent Effect Verification:

Three months after the end of the experiment, the experimental group's problem-solving ability continued to rise by 9.2 (Cognitive retention advantage of the cultural context). This phenomenon indicates that individuals can better retain and apply the knowledge they have learned through specific cultural context training when solving problems. This retention advantage is not only reflected in short-term improvement but also maintains significant effects over a long period. Specifically, interactions, stories, and practice methods in cultural contexts provide participants rich background information and multidimensional frames of understanding, thereby enhancing their memory and application abilities. Additionally, this long-term enhancement may also be related to the habit of reflection andization emphasized in cultural contexts, enabling participants to quickly call upon relevant experience when facing new problems and further improving problem-solving efficiency.

4.2 Defining Field Effect (ffective Field Effect)

Correlation between Cultural Identity and Math Motivation (r=0.71):

85% of students actively collected traditional math cases, as the oral history of "Suanxue Qimeng."

72% of immigrant students expressed that "finding a sense of cultural belonging through the design of abus" (Interview M07). These students not only enhanced their interest in math but also felt support and identification from their cultural background while using the abacus. sense of cultural identity further stimulated their motivation to learn math, forming a positive attitude and behavior towards learning.

Anxiety Source Transformation Phenomenon:

Geometric anxiety by 41% → Concrete support from Hanok measurement tasks, through which students can more intuitively understand geometric concepts, thus reducing anxiety about geometric problems. This concrete not only helps students better master geometric knowledge but also enhances their ability to solve real problems.

The conversion rate of application problem anxiety was 63% → Market transaction scenarios reduce fear, combining math word problems with market transaction scenarios allows students to solve problems in a familiar environment, thus significantly reducing fear of abstract math problems. By simulating real market transaction scenarios, can more easily understand and apply mathematical knowledge, enhancing their confidence and problem-solving ability.

Qualitative analysis excerpts:

When using the method of studying the symmetry of Korean traditional patterns, I discovered that are 17 ways to symmetrize my grandmother's headscarf—this is more realistic than the figures in the textbook. These symmetrical methods include not only the axis symmetry and central symmetry but also various complex forms such as rotational symmetry and mirror symmetry, demonstrating the richness and diversity of traditional Korean patterns. (Student diary )

When our group designed the modified rules for the game of hopscotch, we proved the unfairness of the traditional rules for left-handed players through score calculation. Under the rules, left-handed players need to throw and move the pieces counterclockwise, which is against their natural action habit, resulting in inconvenient operation and poor gaming experience. Therefore, proposed new rules that allow left-handed players to play clockwise to ensure fairness. (Experimental report )

5. Conclusions and Recommendations

5.1 significance

Theoretical innovation of a two-dimensional model:

Cultural gradient transformation model:

A[Cultural prototype] --> B(Concrete decoding)  

B --> C{Mathematical concept anchor}  

C --> D[Basic: Operation Experience]  

C --> E [Advanced: Rule Transfer]  

C --> F [Advanced: System Creation]

Breakthrough point: Solving the problem of disconnection traditional cultural symbols and modern mathematics (such as converting the star chart of "celestial object; star; sun; moon; planet; comet; meteor; meteorite" into coordinate system material)

Differentiated teaching paradigm localization:

Proposing "Three-color Grouping Method": Grouping by cultural familiarity (red/yellow/blue) rather than ability stratification. Red represents groups that are very familiar with the local, yellow represents groups that have a certain understanding of the local culture, and blue represents groups that are not very familiar with the local culture. Through this grouping method, teachers can targeted teaching based on students' different cultural backgrounds, thus better meeting the personalized needs of each student.

Developing the "Culturally Responsive Mathematics Literacy Standards" (025 Trial Edition). This standard aims to combine local cultural characteristics and develop a set of mathematics literacy training goals and evaluation systems suitable for students with different cultural backgrounds. By local cultural elements, mathematics education can be closer to students' actual life, increasing students' interest in learning and participation. The standard includes but is not limited to the following aspects:1. Integration of mathematical concepts and culture: Incorporating mathematical elements from local culture into teaching content, such as geometric figures in traditional architecture and mathematical problems in folk stories.

Mathematical applications from a multicultural perspective: Encouraging students to think about and solve mathematical problems from a multicultural perspective, cultivating cross-cultural understanding and innovative thinking

Culture-sensitive mathematical assessment: Designing mathematical assessment tools that can reflect students' cultural backgrounds to ensure a fair and just assessment process that respects each student's cultural.

5.2 Policy level:

It is recommended that the Ministry of Education revise the "Mathematics Teaching Aid Materials Certification Standards":Require that the proportion of local cultural cases in textbooks ≥30% (current standard 12%). Specifically, increasing local cultural cases can not only enhance students' and interest in mathematical knowledge but also strengthen their sense of identity with their own culture. For example, in geometry, symmetry and proportionality in ancient Chinese architecture can be introduced; in, mathematical achievements in Chinese history, such as problem-solving methods in "The Nine Chapters of Arithmetic", can be combined. Through these specific examples, students can only better grasp abstract mathematical concepts but also feel the extensive application and importance of mathematics in real life.

5.3 Teacher level design:

The dual-track training course is innovative teacher professional development strategy designed to enhance teachers' teaching abilities and professional qualities through two parallel paths.

Design "Dual-track Training Courses":

Modules  Examples Practice Bases

Cultural Analysis Conversion between traditional and modern units of measurement, including the comparison of ancient Chinese units such as chi, cun, andin with modern metric units, and the introduction and application of traditional Korean units such as chi and liang National Folk Museum

Task Design Teaching rhythmic fractions using music scores of ancestral temple rituals, by actually playing and analyzing the rhythms and beats in the ritual music scores, to help students understand the concept of fractions in music and to teach combination with modern music education methods Seoul Traditional Music Center

Teacher Development:

Design a "dual-track training course"：

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