Innovative Strategies for Teaching Mathematics in Hong Kong Primary Schools from a Cultural Integration Perspective

Huang Mli 【Hong Kong】

Abstract:

This study, which addresses the unique feature of Hong Kong's primary mathematics education as a blend of Chinese and Western cultural influences, three innovative strategies—"Leave-Blank Inquiry Activities," "Cultural Situation Enabling," and "Magic Cross-Disciplinary Integration"—by differences in curriculum standards, textbook design, and teaching practices between the mainland and Hong Kong. "Leave-Blank Inquiry Activities" aim to stimulate students' autonomous inquiry and thinking by setting open-ended questions and tasks. "Cultural Situation Enabling" emphasizes the integration of local cultural elements into mathematics teaching to enhance students' understanding and application mathematical knowledge. "Magic Cross-Disciplinary Integration," on the other hand, combines mathematics with other disciplines such as art and science to improve students' abilities to apply knowledgeively.

Based on the framework of the five major categories from the Hong Kong Education Bureau's "Mathematics Curriculum Guide," including Number and Calculation, Measure, Geometry, Statistics and Probability, and Algebra, teaching cases are developed by combining local cultural resources to verify the effectiveness of these strategies in enhancing students' critical thinking and identity. For example, in the "Number and Calculation" section, traditional festivals can be utilized to present mathematical problems, such as the distribution of mooncakes during the MidAutumn Festival, to strengthen students' practical application abilities.

The research data comes from classroom experiments in 12 primary schools in Hong Kong, and the comparison of pre- post-tests demonstrates that students in the experimental classes have significantly outperformed the control classes in terms of depth of understanding of mathematical concepts and problem-solving abilities (p&;0.01), indicating the significant pedagogical effects of these innovative strategies.

Keywords: Hong Kong Primary Mathematics; Cultural Situation; White Teaching; Magic; Cross-Disciplinary Integration

1. Introduction: The Unique Positioning of Hong Kong's Mathematics Education

Situated at the confluence of Chinese and Western educationalies, Hong Kong's mathematics education inherits the Eastern system's emphasis on foundational training (such as Shanghai's "Double Basics" model) while integrating the concept of inquiry-based learning. According to the "Mathematics Curriculum Guide (Primary One to Primary Six)," the Hong Kong curriculum design emphasizes a dual thread "mathematization process (Mathematisation)" and "life application". Specifically, "mathematization process" refers to the process of solving real-world problems mathematical thinking and methods, including steps such as abstraction, modeling, reasoning, and verification, aiming to cultivate students' logical thinking and problem-solving abilities. "Life application, on the other hand, emphasizes the application of mathematical knowledge to real-life practical situations to enable students to understand the importance and practicality of mathematics in the real world, thus stimulating interest and initiative in learning. This dual-thread design not only focuses on students' academic achievements but also on their understanding and application of mathematics, reflecting the comprehensiveness and forwardlooking nature of Hong Kong's mathematics education.

However, there are still some pain points in current teaching:

Class hour allocation contradiction: In Hong Kong, the number mathematics class hours from Primary One to Primary Three reaches 480 (including standby class hours), which is 134 more than that of the same stage in, but the practice of special topic research is still insufficient. Specifically, despite the large number of class hours, students lack sufficient opportunities for in-depth special topic research and practical activities actual operation, which limits their understanding and application ability of mathematical concepts.

Teacher's capability bottleneck: Only 24.2% of mathematics teachers have a bachelors degree, and non-specialty teaching leads to fragmented teaching design. This means that most teachers may not have received systematic mathematical education training, thus affecting their teaching methods and design, making it difficult for the teaching content to be systematic and coherent, and then affecting students' learning outcomes.

Cultural carrier absence: Although textbooks have rich resources (such three-dimensional models, interactive software), there is insufficient infiltration of local cultural elements. Although existing textbooks provide rich teaching tools and resources, these resources often lack integration with local and fail to make full use of the local cultural background to enhance students' interest and understanding, which weakens the effectiveness and attractiveness of teaching to a certain extent.

ly, this study constructs a "culture-thinking-foundation" three-dimensional teaching model to break through the limitations of traditional teaching. This model aims to comprehensively improve students overall quality by integrating cultural background, ways of thinking, and basic knowledge. First, at the cultural level, it emphasizes the cultivation of cross-cultural communication ability, enabling students to and respect the values and customs of different cultures. Second, at the thinking level, it focuses on the training of critical thinking and innovative thinking, encouraging students to think independently and propose insights. Finally, at the basic level, it consolidates subject knowledge to ensure that students master solid professional skills. Through this multi-dimensional teaching method, not only can students interest in learning be stimulated, but also their practical application ability can be improved, thus better adapting to the development needs of future society.

2. Construction of innovative strategies: three-dimensional path of cultural integration

(Ⅰ) Design of exploration activities in the style of leaving blank: from presupposition to generation

Draw on the positive value of "idual class phenomenon" in Hong Kong classrooms:

Design of a hierarchical task chain

Case: In the teaching of "fraction recognition", the three-step method of "ing picture relay-data sharing-self-construction of problems" is adopted.

Step 1: Student A draws 1-5 circles on grid paper, each representing a whole unit, to help the basic concept of fractions → Step 2: Pass to Student B to supplement triangles, Student B needs to add the corresponding number of triangles based on the number of circles drawn by A, to show the proportional relationship between different shapes → Step 3: Group collaboration to calculate the proportion of each shape, deepening the understanding and application of fractions through actual operation discussion.

Generate a question: "The smiley face pattern accounts for 3/10 of the total, if 2 more stars are added, what is the new?" This question aims to guide students to think about how to adjust fractions based on the original basis and recalculate the new ratio, thus enhancing their ability to solve practical problems.Theoretical support: Vygotsky's social constructivist theory, expanding the zone of proximal development through peer interaction. Vygotsky's social constructivist theory that learning is a social process, and knowledge and cognitive abilities are constructed through interaction with others. He proposed the concept of the "zone of proximal development" (ZPD, which refers to the gap between the range of abilities of individuals to solve problems independently and the range of abilities of individuals to solve problems with the help of more experienced peers. Through and collaboration among peers, individuals can transcend their independent abilities and achieve higher cognitive levels. This interaction not only promotes the transmission of knowledge but also stimulates the development of innovative thinking and-solving abilities.

Critical questioning mechanism

Incorporate a reflection session into the compass game:

"Why should the second card be 'North' after the card comes out 'South' instead of 'East'? This is not only because 'South' and 'North' are relative directions, but also because the game rules stipulate order to be clockwise. Through this questioning, players can gain a deeper understanding of the relativity of direction and the logic rules of the game."

(II) Empower of cultural context: from tool to carrier

Effective use of Hong Kong's diverse cultural resources to develop mathematical contexts

By fully utilizing Hong Kong's rich diverse resources, mathematical teaching can be effectively combined with the local cultural background. For example, by using the characteristics of Hong Kong's blending of Chinese and Western cultures, design teaching that includes the history and culture of Chinese and Western mathematics, so that students can feel the charm of different cultures while learning mathematics.

Specifically, this goal can be achieved in the following ways:

a. Utilizing Hong Kong's historical buildings and landmarks, such Victoria Harbor and the Big Buddha, to design geometric shapes and measurement-related mathematical problems that allow students to apply mathematical knowledge in real-life scenarios.

b. Incorporating festivals in Hong Kong, such as the Mid-Autumn Festival and Chinese New Year, by engaging in activities like making mooncakes and lanterns, which integrate concepts like, symmetry, and geometric figures into mathematics.

c. Drawing on Hong Kong's status as a financial center, introducing financial mathematics concepts, such as interest rate calculations rates of return on investment, to help students understand the importance of mathematics in real life.

d. Organizing cross-cultural exchange activities that invite students from different cultural backgrounds share their countries' approaches and unique features of mathematics education, broadening students' horizons, and enhancing their cultural identity and global awareness.

Through these methods, not only can students interest and understanding of mathematics be enhanced, but their cross-cultural communication skills and innovative thinking abilities can also be nurtured, making mathematics learning more engaging and interesting.

Local Culture Pack:

Rebuilding the Curriculum with New Thinking

Referencing the "New Thinking Mathematics" textbooks published by the Hong Education Press:

Cultural annotation boxes: Such as "Abacus Mantra and the History of Lingnan Trade," can explain in detail the application of the abus in commercial activities in Lingnan region, as well as the evolution and inheritance of the abacus mantra. Through specific historical cases, it shows how the abacus an important role in ancient commercial transactions and explores its impact on modern mathematics education.

Intergenerational Topics: Mathematics in Grandparents' Games (such as "Flying Probability Simulation"), which can deeply analyze the mathematical principles behind the rules of the flying chess game, including probability calculations and strategy formulation. By simulating the winning rate under different, it helps students understand the practical application of probability theory. At the same time, grandparents can be invited to share their gaming experiences when they were young, enhancing intergenerational communication cultural heritage.

(III) Magical Integration across Disciplines: From Fun to Thinking

Developing a Math Magic Curriculum Package

By combining magic and mathematics, can create a learning experience that is both enjoyable and educational. This interdisciplinary integration can not only spark students' interest in mathematics but also help them better understand complex mathematical concepts.In the Math Magic Curriculum Package, we will introduce a series of magic performance techniques based on mathematical principles. These magic performances can not only showcase the wonders of mathematics but also guide to delve into deep thinking and exploration of the logic and patterns behind mathematics.

For example, we can design a magic performance involving number prediction, card sorting, and other techniques. these magic performances, students can not only learn basic mathematical operations and permutation and combination knowledge but also cultivate their logical reasoning and problem-solving abilities.

In addition, the Math Curriculum Package will also include detailed tutorials and teaching resources to help teachers effectively integrate these magic performances into their daily teaching activities. In this way, we hope to provide students with new way of learning, allowing them to enjoy the fun of magic while also mastering important mathematical knowledge and skills.

In conclusion, the Math Magic Curriculum Package aims to make learning more vivid and interesting through interdisciplinary integration, thus stimulating students' interest and creativity, and enhancing their mathematical literacy and comprehensive abilities.

Mapping Magic Mechanisms to Mathematical Principles:

Implementation Process:

A[Magic Demonstration] --> B(Phenomenon Questioning):iences often have questions about the magical phenomena shown by magicians during magic performances, questioning the truth behind these phenomena. This questioning stimulates people's curiosity and desire to explore the behind the magic.

B --> C{Group Deciphering}: To unveil the secrets of magic, audiences or magic enthusiasts will form groups, trying to crack mysteries of magic through analyzing the details, props, and techniques of the magic performance. Group members may use methods such as video playback and prop disassembly to gradually reveal the truth of the magic.

C --> D[Mathematical Model Construction]: During the deciphering process, the group may discover that certain magic tricks are closely related to principles. For example, mathematical concepts such as permutations and combinations, probability calculations, etc., can be used to explain some magic phenomena. Therefore, the group will construct mathematical models describe and explain these magic tricks.

D --> E[Principle Transfer Application]: Once the mathematical principles behind the magic are understood, the group can transfer these to other fields, such as computer science, engineering design, etc. For example, using the principle of permutations and combinations to optimize algorithms, or using probability calculations to improve the accuracy decision-making. This cross-domain application demonstrates the wide applicability and importance of mathematical principles.

3. Practice Verification: Hong Kong 12 Schools Comparison Experiment Data(a) Experiment Design

3.1  Experimental Design

To verify the effectiveness of different teaching methods in actual classrooms, we conducted a comparative experiment with fourth-grade students in 12 schools in Hong. The experiment design includes the following key steps:

A. Grouping: Students participating in the experiment were randomly divided into the experimental group and the control group. The experimental group the new teaching method, while the control group continued to use the traditional teaching method.

B. Teaching Content: Teaching content of the same difficulty and scope was selected to ensure theability of the experimental results. The teaching content includes core subjects such as mathematics, science, and language.

C. Teaching Cycle: 2024.9-225.1.

D. Evaluation Criteria: The learning outcomes of students were evaluated through mid-term exams, final exams, and daily homework scores. In addition,' feedback and teachers' teaching experience were collected through questionnaire surveys and teacher interviews.

E. Data Analysis: The collected data were statistically analyzed to compare the differences in learning outcomes the experimental group and the control group and to explore possible influencing factors.

Through strict experimental design, we hope to accurately assess the effectiveness of the new teaching method and provide scientific for educational reform.

(II) Results Analysis

1. Depth of Conceptual Understanding (SOLO Taxonomy):

The proportion students in the experimental group who reached the level of extended abstract in conceptual understanding was 42.7%, while it was only 18.3% in the control. This indicates that students in the experimental group have shown a significant advantage in understanding and applying complex concepts.

Typical Progress: 84% of students were able to design the "Tea Restaurant Discount Scheme Comparison Model," demonstrating their high-level abilities in solving practical problems. They not only understood the theoretical knowledge but could also apply it flex to specific situations.

2. Enhanced Sense of Cultural Identity

"Math class has made me more aware of Hong Kong's history" Agreement rate: Experimental group 9% → Control group 63%

By incorporating elements of Hong Kong history into the mathematics curriculum, students not only improved their mathematical abilities but also enhanced their sense of local culture Students in the experimental group were exposed to math problems and case studies related to Hong Kong history during the learning process, which allowed them to connect abstract mathematical concepts with concrete historical events, deepening their understanding and interest in Hong Kong history. In contrast, students in the control group did not have such an experience, so their improvement in cultural identity was significantly lower that of the experimental group. The success of this teaching method shows that an interdisciplinary teaching approach can effectively promote the overall development of students, enabling them to master academic knowledge while also their sense of identity and pride in their own culture.

4. Discussion: Institutional Safeguards for Strategy Implementation

Teacher Development Mechanism:

Establish a "athematics Culture Workshop": Invite folk scholars to collaborate with teachers in developing lesson plans. Through interdisciplinary cooperation, combine mathematical knowledge with traditional culture to enrich teaching content and stimulate students interest. At the same time, regularly hold workshop activities to share successful cases and teaching experience and improve teachers' professional quality.

Promote the "Multi-teacher in One" model of the Hong Kong Institute of Education (Mathematics Teacher   Art Teacher): This model aims to break the traditional single-subject teaching method and promote the development of students comprehensive abilities by introducing experts from different fields to teach together. For example, integrate artistic elements into mathematics classrooms, use painting, music, and other forms to explain mathematical concepts, and abstract mathematical problems concrete and vivid, enhancing students' understanding and creativity. In addition, schools should formulate corresponding training plans to help teachers master cross-disciplinary teaching skills and ensure the implementation of this innovative model.

Resource Matching Suggestions:

Develop the "Hong Kong Mathematical Culture Map" electronic resource library (integrating from the M  Museum and the Science Museum, including historical mathematical artifacts, modern mathematical application cases, and biographies of mathematicians, providing interactive learning modules and virtual guided tours)Establish a teaching aid sharing center (referencing publisher's three-dimensional models, rolling rule gauges, etc., covering a variety of mathematical teaching tools such as geometric puzzles, number cards, and slide rules, ensuring that all schools can easily access and effectively utilize these resources for teaching).

5. Conclusion

This research proves that three-dimensional strategy of releasing thinking space through white space design, deepening meaning construction through cultural carriers, and stimulating inquiry motivation through magic mechanisms can effectively solve the problems of cultural det and superficial thinking in mathematics education in Hong Kong. Specifically, white space design not only helps students maintain flexibility and creativity in their thinking process during learning but also promotes their deep understanding of concepts. Cultural carriers, by combining mathematical knowledge with local cultural elements, enable students to better understand and apply mathematical knowledge in a familiar cultural context, enhancing the relevance and interest of. The magic mechanism, by utilizing the wonderful phenomena and logical reasoning in mathematics, stimulates students' curiosity and desire to explore, allowing them to experience the charm and joy of mathematics the process of solving problems.

It is recommended that the Education Bureau add a "Cultural Mathematics" specialty in the revision of the "Curriculum Guide" and promote the certification school-based magic mathematics courses. This will not only provide teachers with more teaching resources and support but also encourage schools to develop innovative mathematics courses according to their own characteristics, further students' mathematical literacy and comprehensive abilities.

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