A Practice Research on the Integration of Cross-Cultural Situations into Junior High School Mathematics Inquiry Teaching— Case Study of Teaching Practice in Chiang Mai, Thailand

Somsak Chinnawat【Thailand】

Abstract: In view of the cognitive characteristics of Southeast Asian, this paper proposes a two-way mapping teaching method of “indigenous culture-mathematical concept”. Through a three-year action research, it is found that: transformation of cultural elements such as Thai architectural proportions, traditional weaving geometry, and the solar term cycle of the Buddhist calendar into chains of mathematical problems can significantly improve students' model thinking and-disciplinary transfer ability (the average score of the experimental class increased by 22.3%, and the willingness to solve problems reached 91%). The research forms three-stage teaching mode of "cultural situation import-mathematical essence extraction-real application verification", and provides a new path for the localization of mathematics education in developing.

Keywords: Cultural situation; Mathematical modeling; Inquiry teaching; Differentiated teaching; Thailand's mathematics education

1. Problem Presentation

At present, there two major dilemmas facing junior high school mathematics teaching in Thailand:

Cognitive barrier: the conflict between the abstract symbolic system and the students' concrete thinking habits (such as the rate of the concept of function reaching 38.2%). In the classroom, teachers often use complex formulas and symbols, and these abstract concepts are difficult to understand and accept students who are accustomed to concrete image thinking. For example, when explaining the concept of function, many students lose interest in learning because they cannot connect the abstract function image with the phenomena real life, and even drop out.

Application disconnection: the textbook cases are separated from the Thai life scene, and the students find it difficult to establish a knowledge significance point. Many cases in the existing mathematics textbooks are based on the western life background, such as the basketball parabola, etc., which lack familiarity and relevance for Thai students making it difficult for them to find the actual application scenario of knowledge in the learning process, thus affecting their understanding and mastery of mathematical knowledge.

International research shows that: culturally relevant can reduce math anxiety. However, the existing models mostly rely on Western cases (such as basketball parabola), and there is an urgent need to develop Southeast Asian cultural carriers By introducing more teaching cases related to local Thai culture, such as using geometric patterns in Thai architecture, time calculation in traditional festivals, etc., it can better help students connect mathematical with daily life, thus reducing their math anxiety and improving learning outcomes.

2. Theoretical Basis and Innovative Design

2.1 Theoretical Framework of Cultural Response Pedagogy

Knowledge be constructed through the cultural background of the learner. This process emphasizes the central role of culture in education, enabling students to understand and master new knowledge within a familiar cultural context.This study innovatively proposes: "The Dual-Channel Situational Transformation" Model

This model aims to transform local cultural elements into mathematical knowledge through two main channels and apply to the solution of real-world problems.

a. Local Cultural Elements

Firstly, abundant local cultural elements are extracted from the students' daily life, such as traditional festivals folk stories, local architecture, etc. These elements not only capture students' interest but also help them establish an emotional connection with the learning content.

b. Mathematization of Abraction (Space/Quantity/Relationship)

Next, these cultural elements are mathematically abstracted to distill spatial concepts, quantitative relationships, and logical structures. For example by analyzing the geometric shapes of traditional architecture, students can understand symmetry and proportion; by calculating the number of people participating in festive celebrations, students can master basic arithmetic operations.

Real-World Problem Verification

Finally, the abstracted mathematical knowledge is applied to solve real-life practical problems. This not only verifies the application value of mathematical knowledge also enhances students' learning motivation and confidence. For instance, students can optimize the arrangement of community activities through mathematical modeling or use statistical methods to analyze local environmental data and propose improvement suggestions

This dual-channel situational transformation model not only improves students' understanding and application of mathematical knowledge but also promotes their sense of identity and pride in local culture.

2.2. Innovative Teaching Strategies

3. Teaching Practice Case (Grade 8 "Linear Functions")

3.1 Cultural Introduction

Problem chain design:

[Situation] Pricing Strategy at the Chiang Mai Sunday Night Market Juice Stands

At the Chiang Mai Sunday Market, the air is filled with the fragrance of tropical fruits, and various brightly colored juice stalls attract both tourists and locals. The night market is bustling with lights and sounds and vendors enthusiastically greet their customers.

→ Task 1: Collect price lists from 3 stalls (fixed stall fee   cost per cup)

Students move between the stalls, carefully observing the price tags on each stall. They note that the first stall has a fixed stall fee of 500 baht and a cost of 20ht per juice; the second stall has a fixed stall fee of 600 baht and a cost of 18 baht per juice; and the third stall has fixed stall fee of 700 baht and a cost of 15 baht per juice. Students photograph these price tags with their phones for later analysis.

→ 2: Establish cost functions y = kx   b

Based on the collected data, students begin to establish cost functions. For the first stall, y = 20x   500; for the second stall, y = 18x   600; for the third stall, y = 15x   00. These functions help them understand the cost structure of each stall.

→ Task 3: Compare profit differences between linear pricing and tiered pricing

Students further explore profit differences between linear pricing and tiered pricing. Linear pricing means that the price per juice remains constant, while tiered pricing involves gradually reducing the price per juice as sales volume increases By calculating profits under different pricing strategies, students find that tiered pricing can significantly increase profits at high sales volumes but may not be as stable as linear pricing at low sales volumes

Note: Students use their phones to photograph stall price tags to complete data collection.

3.2 Mathematical Essence Extraction

Through interviews with vendors, it was discovered

Variable x (number of cups) is affected by the rainy season's customer traffic, specifically during the rainy season, the number of cups sold daily decreases due to a significant in customer traffic caused by the weather. Vendors typically prepare in advance based on weather forecasts to deal with possible fluctuations in sales.

Parameter b includes a 20 ba/day sanitation management fee, which covers the daily cleaning of the stall, waste disposal, and necessary disinfection measures to ensure that the stall meets local health standards and provides with a clean and safe consumption environment.

Guide students to establish a piecewise function:

(x is the daily sales volume, and the coefficient change reflects the discount)

During the teaching process, teachers can guide students to analyze the trend of variable x under different seasons and weather conditions and help them understand how to incorporate these factors into models with actual data. For example, during the rainy season, a lower sales limit can be set; during the dry season or holidays, a higher sales limit can be set. this way, students not only master the basic concept of piecewise functions but also learn how to apply them to solve practical problems.

3.3 Teaching Effect Comparison

A controlled was conducted in six middle schools in Chiang Mai：      

4. Core Implementation Strategies

4.1 Four-step Method for the Mathematization of Cultural Materials

Featureraction (e.g., the arithmetic sequence of the steps of Wat Pho, where the height and width of each step remain consistent, forming a regular geometric pattern that provides visitors a visually harmonious aesthetic experience)

Quantitative Modeling (establishing a relationship between step height and angular velocity, calculating the optimal angular velocity for visitors to climb safely and by measuring the height and depth of each step)

Parameter Tuning (simulating the comfortable slope for visitors of different heights, adjusting the step height and slope based on the center gravity and stride length of visitors of different heights to achieve the best climbing experience)

Cultural Feedback (optimizing the design of barrier-free paths in temples, combining modern-free design concepts, preserving traditional architectural styles, and adding accessible ramps and handrails to facilitate the entry of elderly and disabled visitors into the temple for sightseeing)

4.2 Differentiated Task Design

A[Cultural Situation] --> B{Cognitive Stratification}  

B -->|Basic Layer|[Recognize Shapes/Quantity]  

B -->|Intermediate Layer| D[Establish Simple Functions]  

B -->Advanced Layer| E[Optimize Real-life Solutions]

Case: Designing the "Estimate the Weight of the Candlestick Buddha" task for students struggling with (Density × Volume), while the top students research the stability of the Buddha's center of gravity. Specifically, students struggling with mathematics can estimate the weight of the Candick Buddha by observing its appearance, measuring its approximate dimensions, and looking up the density data of related materials, thus calculating the approximate weight of the Candlestick Buddha. They can simple tools such as rulers, balances, and density tables to complete this task. Top students, on the other hand, need to analyze the structure of the Buddha more deeply, the position of the center of gravity of different parts, study the stability of the Buddha under different angles, and even use computer simulation software for more accurate analysis.

5.lection and Suggestions

5.1 Practice Bottlenecks

Lack of interdisciplinary literacy among teachers: 63% of teachers lack in-depth understanding of the geometric in traditional Thai crafts, resulting in difficulties in guiding students to explore and apply these complex geometric concepts effectively during teaching. This not only limits students' creativity but also hinders their understanding traditional culture.

Outdated assessment system: The existing standardized tests fail to cover the ability to solve contextualized problems, leaving students lacking effective strategies when facing complex problems in real life This assessment method ignores students' ability to apply knowledge in real situations and fails to reflect their comprehensive quality and practical skills。

5.2 Localization improvement suggestions

Develop a teacher's manual for "Mathematics in Thai Culture" (with teaching), including detailed case studies and interactive exercises to help teachers better understand and apply the practical use of Thai cultural elements in mathematics teaching. The manual should include abundant images, charts, multimedia resources, showcasing the mathematical principles in traditional Thai architecture, handicrafts, and festival celebrations.

Incorporate "cultural mathematical transformation ability" into teacher certification requirements mandating that teachers must complete relevant courses and pass assessments during their training to ensure they can effectively combine mathematical knowledge with Thai local culture, stimulating students' interest in learning and cultural identity

Establish an inter-school cultural mathematics resource library (such as a Lanna architecture database), gathering educational resources from around the country, including detailed measurement data, design drawings and historical background introductions of Lanna architecture. The resource library should provide an online access platform for teachers and students to conveniently consult and download, promoting inter-school cultural exchanges resource sharing.

6. Pedagogical insights

When students use functions to calculate the ingredient ratio of family recipes, mathematics is no longer an alien symbolic system but a code that preserves cultural genes. The learning motivation sparked by this cultural identity far surpasses any technical tool. In the classroom, students, through precise calculations, feel the inheritance of their ancestors wisdom, as if they can smell the familiar fragrance wafting from the kitchen and see the bustling figures of their elders. The stories and emotions behind each dish are vividly through mathematical formulas, making the learning process both interesting and meaningful.

References:

[1]  Ministry of Education Thailand. (2023). Basic Education Core Curriculum B.E. 2560. Bangkok: Kurusapa Press.

[2] Sriwongchai, A. (2021). Integrating Lanna Architecture into Geometry Teaching. Journal of Southeast Asian Mathematics Education, 15(2), 45-63.

[3] Li, Zhongqing. (2012). Mathematics teaching should focus on the group tendency of students' cognitive styles [J. Education Guide (06). 5

[4] Gay, G. (2018). Culturally Responsive Teaching: Theory, Research and Practice (3rd ed.). Teachers College Press.

[5] Boonsathorn, S. (2024). Mathematical Modeling in Thai Night Market Economy. ASEAN Journal of STEM Education, 8(1).