Innovative Research on Hierarchical Teaching Model in Mathematics for Thai Public Elementary Schools

Songw Thanan 【Thailand】

Abstract：

This research, conducted within the context of Thailand's basic education reform, addresses the issue of polarized academic performance in mathematics at Panikong Government Elementary School. It proposes a "Culturally Responsive Hierarchical Teaching Model." Through a diagnostic test, students from grades 4 to 6 (=240) are divided into three groups: Basic, Development, and Challenge. Differentiated tasks are designed, integrating cultural elements such as the Thai baht currency system, forms of the Loy Krathong Festival, and the symmetry of the Sukhothai Ruins. Specifically, students in the Basic group enhance their basic math skills through simple conversion exercises; those in the Development group engage in shape analysis and calculations using the geometric shapes of Loy Krathong; and students in the Challenge group explore symmetry and proportional relationships in Sukhothai Ruins to elevate their advanced mathematical thinking. Empirical results show that the experimental group's average math score improved by 23% (P<.01), learning interest index increased by 35%, and calculation error rate decreased by 41%. This research proposes a "Rainbow Points Card dynamic assessment mechanism for the first time, which encourages active student participation in classroom activities through a reward system and adjusts teaching strategies in real-time based on student performance, providing a practice path for mathematics education in Thai elementary schools.

Keywords: Hierarchical Teaching, Cultural Responsiveness, Differentiated Assessment, Mathematics Education in Thailand

1.Introduction

1.1 Research Background

Policy Mandate: The "2017 Basic Education Curriculum Outline" emphasizes a "learner-centered" approach, requiring mathematics instruction to address individual differences. This policy aims to enhance students' interest and effectiveness in learning through personalized teaching methods and to ensure that every student can master mathematical knowledge at their own pace

Realistic Dilemma: According to ONET 2023 data, the mathematics pass rate for fifth-grade students stands at only 61.3, with this figure dropping to 48.7% in rural areas. This indicates that despite clear policy mandates, there are still considerable challenges and gaps in practice, particularly in-constrained rural areas.

Cultural Conflict: There is a conversion barrier between Thailand's traditional counting system and the widely used Arabic numerals. This cultural difference only affects students' understanding of mathematical concepts but also increases the difficulty for teachers. How to effectively integrate traditional counting methods with modern mathematics education is a pressing issue that needs to be addressed

1.2 Research Innovativeness

Dual Adaptation Mechanism:

Knowledge Hierarchy: Based on Vygotsky's (197) theory of the Zone of Proximal Development, which emphasizes that individuals, through interaction with more experienced peers or instructors in a specific context, can achieve higher cognitive levels. This applies this theory to the design of educational content, creating a tiered knowledge structure that allows students to progress incrementally from their existing capabilities.

Cultural Hierarchy: Integrated Princess Sirindhorn's "Joyful Learning" principle, which advocates for stimulating students' interest and enthusiasm in learning through fun and interactive methods. Specific measures include the introduction gamification elements, role-playing simulations, and cross-cultural exchange activities to enhance the learning experience and promote cultural understanding.

Dynamic Assessment Tool:

Developing Thailand's first "Cultural Integration Scale". This tool aims to quantitatively measure evaluate an individual's level of cultural adaptation within Thai society through scientific methods. The Cultural Integration Scale covers multiple dimensions, including language proficiency, social networks, cultural understanding, and acceptance Through detailed questionnaire surveys and data analysis, it can provide specific feedback for individuals, helping them better understand and improve their cultural integration process. Additionally, the tool has a dynamic adjustment function allowing for personalized settings based on the needs of different groups, ensuring the accuracy and practicality of the assessment results.

2. Literature Review

2.1 Theoreticalis of Hierarchical Teaching

Cognitive Development Theory: Singapore's CPA Instructional Approach to Hierarchical Task Design (Ministry of Education Singapore, 219)

The cognitive development theory emphasizes that individuals have different learning abilities and needs at different developmental stages. Singapore's CPA (Concrete-Pictorial-Abstract instructional approach designs hierarchical tasks to concretize abstract concepts, helping students gradually understand complex knowledge. First, students establish intuitive feelings through the manipulation of real objects (Concrete); second they deepen their understanding through the use of images and models (Pictorial); and finally, they enter the stage of abstract symbols and formulas (Abstract), cultivating their thinking abilities. This hierarchical design not only adapts to the cognitive development laws of students but also improves learning effectiveness.

Affective-Driven Theory: Japanese "Lesson" Proves that Reducing Anxiety Can Improve Achievement (Stigler & Hiebert, 1999)

The affective-driven theory that students' emotional states have a significant impact on the learning process and outcomes. Japan's "Lesson Study" (Lesson Study), through actual case analysis, has that when students feel anxious, their learning efficiency and achievement both significantly decrease. Therefore, teachers should pay attention to students' emotional needs, create a supportive and encouraging learning environment, reduce students' anxiety. Research shows that strategies such as group work, positive feedback, and personalized guidance can effectively reduce students' psychological stress, thereby improving their academic performance.

2.2 Research on the Mathematization of Thai Culture

Mathematical Value of Traditional Craftsmanship:

The bamboo weaving technique in cultural heritage is not only a traditional craft but also contains rich mathematical concepts. For example, plane tiling technique commonly used in bamboo weaving involves arranging different shapes of bamboo strips closely together to form seamless patterns, which involves the theory of plane tiling in geometry. In addition the application of bamboo weaving in three-dimensional space, such as when weaving baskets or containers, also involves the concept of spatial topology, that is, how to organize and connect different strips in three-dimensional space to form a stable structure.

Buddhist temple architecture, as another important cultural heritage, also widely applies mathematical concepts in its design and construction process For example, the layout of pagodas and temples often follows the principle of the golden ratio, which is considered to have a sense of aesthetic harmony. The golden ratio is special mathematical proportion, approximately equal to 1:1.618, and it widely exists in nature and art works, and is considered to be one of the most beautiful. In addition, the calculation of the volume of three-dimensional bodies in Buddhist temple architecture is also indispensable. Architects need to accurately calculate the volume of each part to ensure rational use of materials and the stability of the structure. These calculations usually involve the knowledge of solid geometry in geometry, including the volume formula of cylinders, spheres and polyhedrons.Festival activity teaching conversion: Songkran Festival water gun range parabola model, Loy Krathong Festival buoyancy calculation

During the Songkran Festival, people often water at each other with water guns, and this activity can be taught through the parabolic model in physics. When the water gun shoots at a certain angle and speed, the trajectory of water droplets forms a parabola. By analyzing the initial velocity, angle and acceleration of gravity, the maximum range of the water gun can be calculated. This not only helps understand the basic principles of parabolic motion but also stimulates their interest in physics.

On the other hand, making and releasing water lanterns is an important traditional activity during the Krathong Festival. Water lanterns are usually made of banana leaves or paper, with candles or light bulbs placed inside. In order to ensure that the water lanterns float smoothly on the water surface, the concept of buoyancy needs to be considered. According to Archimedes' principle, the buoyancy that an object receives in a liquid equal to the weight of the liquid it displaces. Therefore, when designing a water lantern, it is necessary to ensure that its density is less than the density of water, the structure is light enough to maintain stable floating in the water. Through these practical applications, students can better master the knowledge related to buoyancy and density.

3. Research Methods

3.1 Hierarchical Model Optimization Design

Diagnostic Tool Development Process:

A[Four Main Domains Curriculum Standards] --> B(Compiling a Two-Way Checklist)

B --> C{Expert Validity Test}

C --> D[Cultural Questions Account for 30%]

D --> E[Predictive Reliability α=0.82

In the four main domains of curriculum standards, the first step is to compile a two-way checklist. A two-way checklist is a tool that combines curriculum content and assessment to ensure that the examination content covers all important knowledge points and skills. In the process of compiling a two-way checklist, it must undergo an expert validity test to ensure the effectiveness accuracy of its content.

Expert validity testing is conducted by inviting experts in the relevant field to review and provide feedback on the checklist to confirm whether it fully and accurately reflects the of the curriculum standards. In this process, experts pay special attention to the proportion of cultural questions, ensuring that cultural questions account for 30% of the total number of to reflect the emphasis on cultural literacy in the curriculum.

To further verify the quality of the two-way checklist, a predictive reliability test is also required. Predictive reliability to the consistency of a measurement tool when used repeatedly at different times or under different conditions. In this case, the predictive reliability α value is 0.82, indicating that checklist has a high degree of internal consistency and can stably measure students' learning outcomes.

3.2 Hierarchical Teaching Activity Rep

3.3 Dynamic Evaluation Mechanism

Rainbow Points Card Rules:

Total Score = Base .5   Culture 0.3   Creativity * 0.2

This function calculates a weighted score based on three components: Base, Culture, and Creativity

The Base part accounts for 50% of the final score, Culture for 30%, and Creativity for 20%.

Each parameter should be numerical value representing the weight or performance of the corresponding aspect.

Hierarchical Trigger Condition: Automatic promotion to the next group if the points increase by ≥15% 3 consecutive times

4. Research Results

4.1 Academic Achievement

Improved scores: The average post-test score of the experimental group reached 826 points (control group 64.2 points), with a significant difference of P<0.01. This indicates that through the implementation of stratified strategies, students have significantly improved their academic performance, especially in subjects that require logical thinking such as mathematics and science.

Error type analysis: Stratified teaching reduced the calculation error rate 41% (see Figure 1). Specifically, stratified teaching helped students better understand basic concepts, thus reducing calculation errors caused by shaky foundational knowledge., this teaching method also promoted students' personalized learning, allowing each student to practice at their own level of difficulty, further reducing the error rate.

4.2 Non-c Development

Reduction in learning anxiety:

The learning anxiety index decreased by 28% (using T-TEST), indicating a significant change in which students experienced a marked in psychological pressure after engaging in mathematical activities. A relaxed atmosphere prevailed in the classroom, with students no longer nervously biting their pencil or frequently checking the clock, but instead participating confidently in classroom discussions.

Cultural identity effect:

83% of students agreed that "mathematical activities made me more aware of Thai culture," through these activities students not only mastered mathematical knowledge but also gained in-depth insights into Thailand's traditional festivals, dietary habits, and historical background. For example, when solving mathematical problems related Thai market transactions, students experienced the use of Thai currency through simulated transactions and learned about the operation of local markets. In addition, they also learned about the geographical distribution and climate characteristics Thailand through mathematical games, making the learning process both enjoyable and educational.

"By calculating the load-bearing capacity of the water-lantern, I understood the wisdom of my. This traditional craft not only requires superb manual skills but also a profound understanding of the material properties and physical principles. Each step of the operation contains a wealth of historical and cultural background allowing me to feel the inheritance and innovation of culture in practice."

– Interview record of students in the experimental group

Teacher feedback:

"The bamboo weaving motivated underachieving students to actively research the angles of regular polygons. This course not only enhanced students' hands-on ability but also stimulated their interest in geometry. Students the angle distribution and structural stability of regular polygons through the weaving process, actual measurement, and calculation, thus deepening their understanding and application of mathematical concepts.

5. Discussion and Suggestions

5.1 Innovative Value

Cultural Responsive Teaching: Incorporating traditional bamboo weaving craftsmanship spatial thinking training, students can not only enhance their hands-on ability but also cultivate respect and understanding for traditional culture through practical operation and handicraft making. As an ancient manual skill the complex weaving techniques and unique aesthetic value of bamboo weaving can stimulate students' creativity and imagination, while also promoting their understanding of geometric shapes and spatial structures.

Differentiated: Developing a "Rainbow Points" dynamic adjustment stratification, this flexible evaluation method allows teachers to provide timely feedback and encouragement based on each student's learning progress and. Rainbow points cards not only motivate students to actively participate in classroom activities but also help teachers better understand individual differences among students, thus developing more personalized teaching plans. The different colors on points card represent different achievement levels, and students can earn points by completing specific tasks or showing progress, thereby upgrading to higher color levels. This mechanism helps to enhance students' confidence learning motivation.

5.2 Practical Suggestions

Teacher Training: It is recommended to carry out "Differentiated Teaching Design Workshop", through which teachers can learn to design personalized teaching plans according to the abilities and needs of different students. This not only helps to improve teaching effectiveness but also stimulates students' interest and potential. The workshop content include the theoretical basis of differentiated teaching, practical operation skills, and successful case sharing.

Teacher Training Program:

Resource Development: Compilation of "Thai Cultural Math Activity Case Collection", which will include a series of math activities based on Thai culture aiming to enhance students' interest and understanding in mathematics through cultural context. Activities in the case collection will cover different grades and difficulty levels, ensuring applicability in various teaching environments. Each case detail the activity objectives, required materials, implementation steps, and expected outcomes, allowing teachers to easily apply them to daily teaching.

References:

[1] Stigler J.W., & Hiebert, J. (1999). The Teaching Gap. Free Press.

[2] Phutthamonk Primary School (2023). Math Learning Outcomes Report.

[3] Vygotsky, L.S. (1978). Mind Society. Harvard University Press.

[4] Singapore Ministry of Education (2019). Primary School Mathematics Syllabus.

[5] Institute for Promotion Science and Technology Education. (2024). Learning Guide for Cultural Mathematics.

[6] Bangpong, Siravong. (202). Mathematics in Thai Handicrafts. Tsinghua University Press.

[7] UNESCO Bangkok Office. (2025). Cultural Elements in Education in Southeast Asia.