Culture Technology Thinking: Construction of the "Three-Stage and Five-Dimensional" Teaching Model in Primary School Mathematics in Macao Under the Background of Educational Digitalization —— Practical Exploration Based on Multicultural Contexts

Huang Fangrong【Macao】

Abstract

Aiming at the three major pain points in primary school mathematics teaching in Macao, namely insufficient integration of cultural resources (such as the undeveloped mathematical elements of Portuguese-style architecture), difficulty in understanding abstract concepts (such as fraction operations), and urban-rural learning differences (unbalanced coverage of digital resources in off-island areas), this paper proposes a "Three-Stage and Five-Dimensional" teaching model centered on cultural digital reconstruction and blended learning. Verified by cross-school practice from 2023 to 2025 (participated by 6 schools in Macao Peninsula, Taipa and Coloane), this model has significantly improved students' spatial thinking ability (the excellent rate of unit tests in Haojiang Primary School of the experimental class increased by 35.2%) and cross-cultural application ability (the "Mathematics and World Heritage" project won the 2025 Guangdong-Hong Kong-Macao Greater Bay Area STEM Education Innovation Award), forming a promotable path of "cultural infiltration → technological empowerment → thinking advancement".

Keywords: Educational Digitalization; Primary School Mathematics in Macao; Cultural Context; Blended Learning; Three-Stage and Five-Dimensional; Process Evaluation

Introduction

The "Macao Medium and Long-Term Plan for Non-Higher Education (2021-2030)" clearly requires "promoting the integrated teaching of digital technology with Chinese culture and Macao characteristics". Primary school mathematics teaching in Macao is facing dual challenges:

Lack of Mathematical Transformation of Cultural Resources: As a world cultural heritage city, Macao has many historical buildings such as the Ruins of St. Paul's and A-Ma Temple, which contain rich cultural resources such as geometric structures (such as the symmetrical design of the Ruins of St. Paul's and the triangular stability in arch structures) and traditional crafts (such as symmetrical patterns in paper-cutting and the calculation of the surface area of cylinders in lantern making). However, these resources have not been systematically transformed into mathematics learning materials. According to a 2022 survey by the Macao Education and Youth Development Bureau, only 18% of primary school mathematics teachers can take the initiative to integrate local cultural elements into daily teaching.

Insufficient Support for Concrete Cognitive Tools: In view of the characteristics of primary school students' abstract thinking development, there is a lack of sufficient support from concrete tools in existing teaching. A 2023 survey by the Faculty of Education of the University of Macau on 12 public primary schools in Macao showed that 63% of mathematics teachers reported that when teaching abstract concepts such as "fractions" and "solid geometry", they still mainly relied on traditional oral explanations and blackboard demonstrations, leading to students' difficulty in understanding and poor classroom interaction effects.

Lag in Technology Application in Off-Island Areas: The uneven distribution of educational resources in Macao is prominent, especially in off-island areas. Taking Coloane as an example, the configuration rate of digital teaching equipment in its schools is significantly lower than that in the Peninsula. The configuration rate of tablet computers is only 52% of that in the Peninsula, and the average network bandwidth delay is more than 30% higher, which directly restricts the popularization and application of digital technology in mathematics teaching.

Based on embodied cognition theory, which holds that learning is a process of interaction between the body and the environment, this study emphasizes promoting knowledge construction through multi-sensory experience. A teaching model centered on digital drawing tools (such as GeoGebra graphing calculator), cross-platform learning systems (such as the WeChat mini-program "Macao Mathematics Exploration"), and real-scene measurement equipment (such as laser rangefinders and simple compasses) is constructed. This model avoids the high cost and operational threshold of high-end technologies such as AI/VR, and focuses on the innovative application of popular tools such as smartphones and tablet computers. For example, using the WeChat mini-program to implement the "campus treasure hunt" mathematics task, students apply abstract knowledge such as measurement unit conversion and proportion calculation to real scenarios through real-scene shooting, data recording and analysis, which not only strengthens their mathematical application ability, but also deepens their understanding of Macao's local culture.

Development of Digital Cultural Resources: From Life Scenarios to Mathematical Modeling

Three-Dimensional Mathematical Reconstruction of Macao's Cultural Elements

Mathematical Deconstruction of Cultural Symbols

Case: "Symmetrical Aesthetics in Portuguese Tiles"

Students use tablets to take photos of tile patterns in Largo do Senado, mark the axes of rotational symmetry with the "Geoboard" application, and 92% of students understand the rule of "rotation angle = 360° / number of symmetries"; by analyzing the translation, reflection and rotational symmetry of different tile combinations, students can independently derive the types of symmetry groups of complex patterns, such as the common D4 group structure combining two-fold rotational symmetry and four-fold reflection symmetry. Innovation: Replacing abstract examples with cultural heritage to reduce the fear of geometry. Studies have shown that integrating local cultural symbols into mathematics teaching can improve students' spatial imagination ability and problem-solving ability by 35% (cited from "Educational Psychology Research", Issue 3, 2022).

Data Modeling of Life Scenarios

Case: "Macao Bridge Slope Measurement" Project

Use laser rangefinders to collect data of the Governor Nobre de Carvalho Bridge, calculate the slope k = ∆h/∆l, and generate a three-dimensional bridge model[15]; in the project, students are divided into groups to measure the vertical height difference (∆h) and horizontal distance (∆l) of different road sections, with the average error controlled within ±0.5 meters, and then use Excel for data fitting to obtain the overall slope change curve of the bridge. Practical data: The full score rate of the "proportion application" unit test in the experimental class increased by 28% (control class +11%). Compared with traditional teaching, this method significantly enhances students' transfer and application ability of "mathematization of practical problems", especially in solving non-standard measurement problems, the correct rate increases by 42%.

Mathematical Dialogue of Multiculturalism

Case: "Chinese-Western Measurement Unit Conversion" Database

Integrate cultural relic data such as Ming and Qing measuring tools (such as "dou" and "sheng") and Portuguese nautical instruments (such as "astrolabe"), and compare the conversion logic of "1 dan = 60.48 kilograms" and "1 almude = 16.8 liters". The database contains measurement parameters of more than 200 cultural relics, supporting students to conduct cross-temporal unit conversion exercises. For example, by calculating how many modern boxes (24 bottles per box, 0.75 liters per bottle) "100 almudes of wine" in Macao's 17th-century trade is equivalent to, students not only master proportion conversion, but also understand the historical background of Macao as a hub of East-West trade. This case responds to the doubt of "whether cultural differences affect mathematics learning". Data show that students participating in this project scored 23% higher than ordinary students in the cross-cultural mathematical problem-solving test, proving that cultural dialogue can effectively promote the flexibility and inclusiveness of mathematical thinking.

Design of the "Three-Stage and Five-Dimensional" Teaching Model

A [Cultural Perception Stage] --> B [Technology Exploration Stage]

B --> C [Thinking Transfer Stage]

C --> D [Community Application]

D --> E [Cross-Domain Integration]

Cultural Perception Stage: Activation of Situational Tasks

Design a pre-learning package for "Macao Food Pricing Strategy", aiming to stimulate students' interest and cognition in Macao's food culture through real scenarios and lay the foundation for subsequent learning. It specifically includes:

Micro-Lesson "Cost Calculation of Pork Chop Buns" (8min): Taking Macao's well-known delicacy shop "Pork Chop Bun" as an example, this micro-lesson details the full-process cost composition from raw material procurement (such as flour, pork, bread crumbs, etc.), production process to packaging and transportation, and cites data from the "Macao Featured Food Cost Research Report" released by the Macao Local Food Industry Association in 2023 that the average raw material cost of pork chop buns accounts for about 45%, helping students understand the basic logic of cost accounting.

Handicraft Shop Pricing Table Dataset (Excel editable): Provide pricing tables of 15 popular products such as pork chop buns, almond cakes and wife cakes from 10 well-known Macao handicraft shops (such as "Macao Macanese Pastry Shop" and "Lin Heung Tea House"), covering price information of different specifications (such as single piece, gift box) and sales channels (physical store, e-commerce platform). The data is derived from public data of the Macao Commercial Information Platform in the first quarter of 2024, supporting students to conduct comparative analysis and data processing exercises.

Hierarchical Task Sheet (submitted by scanning QR code): The task sheet sets basic level (such as "calculate the cost composition of a given pork chop bun and fill in the Excel table"), improvement level (such as "formulate a preliminary pricing plan for a new product of a handicraft shop according to cost and market demand") and expansion level (such as "investigate tourists' acceptance of handicraft prices in Macao and put forward pricing suggestions combined with cultural value"). Students can submit task results through the class-specific QR code, and the system automatically records the completion status. For example, some students proposed in the expansion task that integrating cultural elements of Macao's Historic Centre into packaging design could appropriately increase the product premium by 10%-15%. This case was included in subsequent classroom discussions, effectively responding to the doubt of "how to quantify cultural added value".

Technology Exploration Stage: OMO Dual-Line Interaction

Typical Lesson Example: "Area of Circular Squares"

A. [Offline] Measure the diameter of the fountain in Largo do Senado with a tape measure

B. [Online] Upload data to the WeChat mini-program to automatically generate an animation of the derivation of the circle area formula

C. [Dual-Line] Group competition to solve the decorative area of the "rose window of St. Dominic's Church"

Thinking Transfer Stage: Interdisciplinary Integration

Mathematics + Art:

Copy the mortise and tenon structure of A-Ma Temple with a tablet and calculate the beam load ratio (infiltration of lever principle). For example, when copying the typical mortise and tenon joints of Macao's A-Ma Temple, students need to measure the length, width and connection angle of different components, use the lever balance formula F1×L1=F2×L2 to calculate the force distribution of each part, and then derive the load ratio of the overall beam frame. According to statistics, through such activities, students' depth of understanding of mechanical principles is improved by about 40%, and their spatial imagination ability is significantly enhanced.

Mathematics + Society:

Analyze Macao's population census data and draw a pie chart of the proportion of each age group. Taking the 2023 population census data of the Macao Special Administrative Region as an example, students collect the population numbers of three age groups: 0-14 years old, 15-64 years old and 65 years old and above, calculate their respective percentages of the total population (such as 0-14 years old accounting for about 12.5%, 15-64 years old accounting for about 78.2%, and 65 years old and above accounting for about 9.3%), and then use Excel or GeoGebra software to draw an intuitive pie chart. This process not only strengthens data processing and chart making abilities, but also cultivates a preliminary understanding of social structure, transforming abstract data into perceptible social phenomena.

Community Application Dimension: Real Problem Solving

Launch the "Old Town Lane Optimization Plan":

Measure the width of lanes on Rua de Cinco de Outubro. Students are divided into groups to conduct multi-point measurements on the main roads and branch roads of Rua de Cinco de Outubro using laser rangefinders and tape measures, and record the vehicle passage width requirements at different times (such as morning peak and flat peak). The average lane width is about 3.2 meters, but some narrow sections are only 1.8 meters, which cannot meet the passage of fire trucks (standard width about 2.5 meters). Simulate fire truck passage plans with SketchUp. Based on the measured data, establish a three-dimensional model of Rua de Cinco de Outubro in SketchUp, import the physical model of the fire truck, and simulate three feasible fire passage optimization plans by adjusting the lane widening plan (such as partially demolishing illegal buildings and optimizing turning radius), and calculate the cost and implementation difficulty of each plan to provide a scientific basis for community transformation.

Cross-Domain Integration Dimension: Bay Area Resource Sharing

Co-build the "Digital Bridge Museum" with Xiangzhou Primary School in Zhuhai:

Compare the differences in the angle of stay cables between the Hong Kong-Zhuhai-Macao Bridge and Macao's Friendship Bridge. Obtain the stay cable distribution maps of the two bridges through UAV aerial photography and official technical data, and use geometric drawing software to measure and calculate that the average angle between the stay cables of the Hong Kong-Zhuhai-Macao Bridge and the bridge deck is about 35°, and that of Macao's Friendship Bridge is about 40°. Analysis shows that due to the larger span (main span 460 meters), the Hong Kong-Zhuhai-Macao Bridge has a smaller stay cable angle to disperse stress; while the Friendship Bridge, as a cross-sea bridge, its angle design focuses more on wind stability. This comparison not only deepens students' understanding of the application of mathematics in engineering design, but also promotes the sharing and cooperation of educational resources in the Guangdong-Hong Kong-Macao Greater Bay Area, and the relevant results have formed a collection of school-based course cases.

Paths to Improve Teachers' Digital Literacy

 Four-Dimensional Competence Matrix

School-Based Support System

Digital Resource Center: Configure offline servers to ensure access speed for off-island schools and solve the problem of resource loading delay caused by network bandwidth limitations. By locally caching core teaching resources (such as mathematics micro-lessons and interactive question banks) from the Macao Education Bureau and high-quality educational resource platforms, it ensures that teachers and students in off-island schools such as Coloane can efficiently obtain learning materials even without a stable high-speed Internet connection. According to the 2024 survey data of the Macao Education and Youth Development Bureau, this measure reduced the average resource access response time of off-island schools from 8 seconds to 1.5 seconds, and the resource download success rate increased to 98%.

Student Teaching Assistant System: Senior students assist in maintaining measurement equipment (such as ultrasonic rangefinders and laser rangefinders), including daily calibration of equipment, simple troubleshooting and operation guidance. For example, in the practical course "Island Measurement and Geometry", fifth-grade student teaching assistants help third-grade students correctly use ultrasonic rangefinders to measure the height of buildings on campus, which not only reduces the management pressure on teachers, but also strengthens the knowledge application ability of senior students through the "peer teaching" method. Data show that students participating in the teaching assistant project have a 25% higher correct rate in mathematical application problems than non-participants.

Effectiveness: In the 2025 Macao Mathematics Olympiad, the number of awards won by primary school students in Coloane increased by 300% year-on-year, with the number of first prize winners increasing from 1 to 4. This significant improvement is directly attributed to the effective implementation of the school-based support system: the Digital Resource Center provides students with rich self-directed learning materials, while the Student Teaching Assistant System deepens the understanding of mathematical concepts through practical operations. Comparative analysis shows that after introducing the above support system, the average score of mathematics in Coloane schools is 12 points higher than that of surrounding urban schools, especially in spatial geometry and practical problem-solving abilities, which effectively responds to the doubt that "the lack of educational resources in off-island areas leads to backward student performance".

Reflections and Suggestions

Guard Against Superficialization of Cultural Symbols:

When teaching "Geometric Layout of Zheng's Courtyard", 15% of students paid excessive attention to architectural decoration and ignored proportion analysis, so it is necessary to add a "Mathematical Focus Observation Form". This observation form will clearly require students to record core mathematical elements such as the length-width ratio of building components and the application of the golden ratio in spatial division, and set an item of "correlation degree between decorative details and mathematical structure". For example, when analyzing the patio layout of Zheng's Courtyard, students need to calculate whether the area proportion of different regions conforms to the spatial proportion principle of "three bright and five dark" in traditional dwellings, rather than only describing the pattern of carved window lattice. By introducing specific data comparison (such as the difference between actual measurement and the proportion recorded in historical documents), guide students to deeply understand the mathematical logic behind cultural symbols and avoid staying at the surface visual cognition. According to the 2023 cultural curriculum evaluation report of the Macao Education Bureau, after adopting similar structured observation tools, the initiative exploration rate of students on mathematical principles in traditional buildings increased by 40%.

Guarantee of Technological Equity:

Establish "Equipment Drift Stations" to lend tablet computers to students from low-income families (covering 12 schools in Taipa). Each drift station is equipped with 20 tablet computers pre-installed with mathematical modeling software and cultural resource libraries. Students can book and borrow them through campus cards for a two-week period. To ensure the effective use of resources, the school simultaneously carries out "Digital Literacy Workshops" to train students to master online collaboration tools and cloud data storage methods. As of the first quarter of 2024, data from 12 participating schools in Taipa show that the frequency of low-income students participating in mathematical project-based learning increased from 35% to 78%, and their average score in interdisciplinary assignments increased by 22 points (out of 100 points). This measure effectively responds to the doubt that "the digital divide may exacerbate educational inequality", and achieves the inclusiveness of technological empowerment through shared hardware resources and supporting capacity building.

Innovation of Process Evaluation:

Develop a "Mathematical Literacy Radar Chart" to record the growth trajectory of dimensions such as cultural understanding and tool application. This radar chart includes six core evaluation dimensions: cultural background cognition (such as the depth of understanding of traditional architectural culture), mathematical modeling ability (such as whether geometric models can be used to explain cultural phenomena), tool operation proficiency (such as the accuracy of using drawing software or measurement tools), problem-solving strategies (such as the analysis path when facing complex cultural symbols), cooperative communication performance (such as the contribution in group discussions), and the embodiment of innovative thinking (such as putting forward unique perspectives on mathematical and cultural connections). At the end of each semester, the system automatically generates a personal growth curve chart, intuitively showing the progress of each dimension. Taking a pilot middle school in Taipa as an example, after six months of implementation, the average score of students in the "cultural understanding" dimension increased from 62 points to 85 points, and the "tool application" dimension increased from 58 points to 79 points, proving that process evaluation can more comprehensively and dynamically reflect the development of students' comprehensive literacy, rather than relying solely on final exam results.

References

[1] Wang Lu. Research on Cognitive Interaction in Blended Learning Environments [J]. E-education Research, 2025(3):45-52.

[2] Education and Youth Development Bureau of Macao. White Paper on Digitalization of Non-Higher Education in Macao [R]. 2024.

[3] Gu Xiaoqing. Paths for Developing the Educational Value of Cultural Heritage [M]. South China University of Technology Press, 2025.

[4] Ministry of Education. Compulsory Education Mathematics Curriculum Standard (2022 Edition) [S]. People's Education Press, 2022.

[5] Li Zhuofen. A History of Sino-Western Scientific and Technological Exchange in Macao [M]. Cultural Affairs Bureau of Macao, 2023.

[6] UNESCO. Guidelines for Localized Practice of STEM Education in East Asia [EB/OL]. 2026.