Exploration of Digital Teaching Practice in Middle School Mathematics in Macao Driven by Cultural Context

Cao hen zhen  【Macao】

Abstract

This article is based on Macao's multilingual cultural background and the requirements of the "Non-higher Education Development Plan (023-2030)", and constructs a three-dimensional teaching model of "cultural context - basic digital tools - process evaluation". Through the development of 2 localized cases such as world heritage building geometric analysis and Portuguese tile probability experiment, action research has been carried out in 8 Macao middle schools. The data show that the math ability of students in the experimental class has increased by 37.2%, and the awareness of cultural relevance has increased by 44.5%, which provides aicable path for the digital transformation of Macao's mathematics education.

Keywords: cultural context; digital teaching; process evaluation; Macao middle school mathematics; localized practice

1. Introduction

As a place where Chinese and Western cultures meet, Macao's mathematics education needs to respond to the curriculum goal of "training local talents with international vision" However, there are two major contradictions in current digital teaching:

Superficial application of technology: 85% of teachers only use PPT instead of blackboard writing and fail to play the function of technology to promote deep cognition (Macao Education and Youth Bureau, 2024 Annual Teaching Research).

Lack of cultural relevance The proportion of Portuguese cultural mathematical cases in textbooks is less than 8%, which fails to inspire students' sense of identity.

This article takes the basic digital tools such as calculators and geometry software as the carrier, and explores the deep coupling mechanism of cultural context and mathematical thinking.

2. Current Situation and Challenges of Digital Teaching of in Macao

(i) Bottleneck of Localized Practice

Insufficient transformation of cultural resources

Status quo: As a place where Chinese and Western cultures blend, Mac has a wealth of world cultural heritage and unique architectural features, such as the complex geometric structure of the Ruins of St. Paul's, the symmetrical patterns of Portuguese colestone roads, and the traditional architectural structure of the A-Ma Temple. These highly distinctive cultural symbols have not yet been systematically excavated, collated and transformed into vivid materials mathematical exploration. In actual teaching, the combination of mathematics curriculum content and local cultural resources is low, and the unique value of local culture in stimulating students' interest in learning, cultiv cultural identity and improving mathematical application ability has not been fully played.

Case: In the teaching of the unfolding diagram of the cube, most teachers still follow the traditional standard to demonstrate and explain, limited to the abstract geometric figure cognition, and fail to guide students to observe and analyze the geometric structure of the dome of the local landmark building "St Rose Church" - its complex combination of polyhedrons, symmetrical design and spatial form, which is itself a perfect embodiment of cubes, cuboids and other solid figures in reality If it can be introduced into the classroom, through field investigation, picture analysis, model making and other means, it will greatly enhance the interest and effectiveness of teaching.

Limited evaluation methods

Issue: According to the research data of the Macao Education Department, 93% of schools in Mac still rely mainly on traditional paper-and-pencil tests for mathematics teaching evaluation. This evaluation method focuses on the examination of students' knowledge memory and problem-solving skills but it neglects the dynamic trajectory of students' thinking development, cooperative inquiry ability, innovative consciousness, and information literacy in the process of digital learning. Digital teaching emphasizes process- learning and personalized development, but a single paper-and-pencil test can hardly reflect the real learning status and ability improvement of students in a digital environment in an all- and objective way.

Data: The questionnaire survey of Macao middle school students showed that only 28% of students agreed that "math homework is related to real life" asked. This reflects that the current mathematics teaching content is not closely connected with students' life experience, and the application of digital teaching resources has not effectively broken the disciplinary barriers, integrating knowledge with real life and social hotspots, resulting in insufficient perception of the significance of mathematics learning by students and a certain impact on learning motivation.

(II) Application Dile of Basic Technical Tools

3. Construction of a Digital Teaching Model Driven by Cultural Context

(a) Mathematical Transformation Framework of Cultural Resources

A[Macao Cultural Symbols] --> B(Mathematical Concept Extraction)

B --> C{Digital Tool Adapt}

C --> D[Inquiry Task Design]

In Macao's unique cultural context, local cultural resources such as the architectural structure of the A- Temple, the geometric patterns of the Rua da Carioca, the symmetrical layout of the Old City of Macao, the mosaic art of the Portuguese cobblestone, and the quantitative relationships in traditional festivals (such as the permutation and combination of dragon dance queues and the symmetry of lantern making) all contain rich mathematical elements. By establishing transformation framework of "Local Cultural Symbols—Mathematical Concept Extraction—Digital Tool Adaptation—Inquiry Task Design", the deep integration of cultural resources and teaching can be achieved.

Firstly, in the "A[Macao Cultural Symbols]" stage, it is necessary to systematically sort out the representative cultural symbols of Macao such as the spatial geometric relations contained in the eave and arch structure of the A-Ma Temple, the curve equation embodied in the spiral rising form of the Macao Tower, application of pi in the track design of the Macao Jockey Club, and the symmetrical patterns on the packaging of Macao souvenirs, etc. These symbols are the carriers the integration of culture and mathematics.

Secondly, in the "B(Mathematical Concept Extraction)" link, it is necessary to accurately extract mathematical concepts from cultural symbols For example, extract the calculation of the volume of prisms and pyramids in solid geometry from the flying eaves and arch structure of the A-Ma Temple; extract the t principle and angle calculation in plane geometry from the hexagonal mosaic of the Portuguese cobblestone road; extract the concepts of axis symmetry and central symmetry from the symmetrical patterns ofao's traditional paper-cutting art; extract the knowledge of probability and statistics from the odds calculation in Macao's gaming industry; extract the coordinate system and distance formula from grid layout of Macao's urban planning, etc., to make abstract mathematical concepts concrete and contextualized.

Next, in the "C{Digital Tool Adaptation step, it is necessary to select appropriate digital tools for adaptation according to the extracted mathematical concepts. For example, use the GeoGebra software to dynamically demonstrate the geometric transformation of architectural structure of the A-Ma Temple; use the Scratch programming to simulate the tiling process of the Portuguese cobblestone road; use the 3D modeling (such as SketchUp) to construct the three-dimensional model of the Macao Tower and calculate its surface area and volume; use Excel or Python to conduct probability simulation of Mac gaming odds; and experience the spatial symmetry of the Old City of Macao through virtual reality (VR) technology, so that learners can perceive the application scenarios of mathematical concepts in interaction.

Finally, in the "D[Inquiry Task Design]" phase, based on the results of the digital tool, inquiry-based teaching tasks are designed. For example, Task One: "Measure and calculate the volume of a certain arch in the A-Ma Temple, and compare the density of different materials"; Task Two: "Use GeoGebra to draw the axis of symmetry of the main buildings in the Historical Urban Area of Macau, and analyze their aesthetic"; Task Three: "Simulate the expected return of gambling games under different odds through programming, and explore the relationship between probability and decision-making"; Task Four: " a math game based on Macau cultural elements, such as "Dragon Ring Portuguese Tiles Mosaic Challenge", which requires players to use geometric knowledge to complete pattern assembly" These tasks guide students to actively construct mathematical knowledge in the process of solving practical problems, deepen their understanding of local culture, and achieve the dual goals of cultural heritage and mathematical literacy.

Practice Case:

Portuguese Tiles Probability Case:

Cultural Symbol: Blue and white tiles pattern (such as traditional Portuguese tiles classic patterns, such wave pattern, sailboat pattern, geometric floral pattern, herringbone pattern, etc., which not only have the characteristics of Portuguese marine culture but also contain the geometric aesthetics of symmetry and repetition)

Mathematical Concept: Geometric transformation probability (including the application of basic geometric transformations such as translation, rotation, reflection, etc., in the of tiles pattern and the corresponding probability calculation), combinatorial counting (calculating the ratio of the number of permutations and combinations of specific symmetric patterns to the total possible number of patterns)

Digital Tool: GeoGebra simulation pattern generation (using the geometric drawing function and probability simulation module of GeoGebra, students can set the basic blue and white tiles unit pattern transformation rules, and generation scale on their own, and generate virtual patterns of 10x10 tiles walls in real-time, and through data statistics and analysis of the of symmetric patterns appearing)

Task: "Design a 10x10 tiles wall, and calculate the probability of symmetric patterns appearing" (specific task requirements students to select one or more basic blue and white tiles unit patterns, determine its possible geometric transformation methods (such as horizontal flip, vertical flip, 180-degree rotation, etc), use GeoGebra tools to randomly generate multiple 10x10 tiles wall samples, record the number of patterns that meet the specific symmetry conditions such as axis symmetry centrosymmetry, and then calculate the theoretical probability by the principle of combinatorial counting, and compare it with the simulation results, and explore the key factors affecting the probability of symmetric patterns such as the complexity of transformation rules, the symmetry of unit patterns, etc.).

(II) The strategy of deep application of basic digital tools

Cultural modeling of calculators

Case: Use regression analysis to study the relationship between the historical results of the "Macau Grand Prix and the number of corners on the track (Data source: Macau Statistical Yearbook). The specific operation process includes: First, students collect the official performance data of the Mac Grand Prix races from 1990 to 2020 (such as fastest lap time, average speed, etc.) and the corresponding number of corners on the in the corresponding year through the Macau Statistical Yearbook and other authoritative data, and establish a dataset that includes independent variables (number of corners) and dependent variables (race results) ; Then, using the regression analysis function of the graphing calculator, try linear regression, quadratic function regression and other models, and determine the mathematical equation that best reflects the relationship between two by calculating correlation coefficients, residual sum of squares and other indicators; Finally, based on the fitted equation, predict the optimization of track design, such as analyzing how to adjust angle or length of the corner to improve the race results under the premise of maintaining a certain number of corners, or predict the impact on the safety and watchability of the event if certain number of corners are added, so as to combine mathematical tools with sports culture and engineering design, and deepen the understanding of the rules behind the data.

Real-world exploration supported by sensors

Case: Use the sonar sensor to measure the reflection angle of the sound field of the "Gangding Theater" dome, and verify the law of of light. The specific implementation steps are: The student team carries sensor equipment equipped with a sonar module to the Gangding Theater, selects different positions of the dome as sound source, transmits ultrasonic waves through the sensor and receives the signals reflected back from the surface of the dome, records the incident path and reflected path of the sound wave; Use built-in positioning system and time difference calculation function of the sensor to obtain the precise numerical values of the incident angle and reflection angle; At the same time, use the laser range and angle measuring instrument to assist in measuring, to ensure the accuracy of the data; then organize and collate the multiple sets of incident angle and reflection angle data collected, draw incident angle-reflection angle relationship diagram, and compare the experimental data with the theoretical value of the law of reflection of light (the reflection angle is equal to the incident angle) and analyze the source of error (such as differences in sound wave propagation media, sensor precision limitations, etc.), and finally draw the conclusion: Under ideal conditions, the reflection sound waves on the surface of the dome follows a similar law to the reflection of light, thus applying abstract physical laws to actual architectural acoustic scenarios, and enhancing the understanding and ability to real problems.

(Ⅲ) Innovative Process Evaluation System

Construct a "Three-stage Nine-dimensional" evaluation model:

    title Student Mathematical Literacy Evaluation D

    axis Cultural Relevance, Model Construction, Tool Application, Data Interpretation, Cooperative Innovation

    "Experimental Class Pre-test" [3, 4,2, 3, 3]

    "Experimental Class Post-test" [7, 8, 7, 8, 8]

Implementation carrier:Digital learning portfolio: Includes video of the exploration process, dataset analysis report, cultural reflection diary

Interdisciplinary evaluation rubric: Math teachers and history/art teachers jointly develop cultural understanding

4. Practice Achievements and Reflections

(1)Quantitative data comparison (Experimental cycle:2024.9-2025.6）

(II) Qualitative Achievements

Student Work Innovation:

"The Function Model of the Flow of Pilgrims the Ma Kok Temple" won the Macao Youth Science Award

"The New Street Shop Spacing Optimization Plan" was adopted for pilot implementation by the Municipal Affairs Bureau

Te Professional Growth:

"Using the tiles of the Sino-Portuguese Friendship Garden to teach the Fibonacci sequence, students' eyes light up - this is the class that Macao needs."

                                        ——Reflections Notebook of Mr. Chen, a teacher at Pui Ching Middle School

(III) Deepeningenges

Technological Appropriateness Issues

The wireless network coverage of the old school is only 65%, resulting in unstable sensor data transmission in some teaching areas with phenomena such as delay or loss affecting real-time monitoring and feedback effects. Especially when carrying out mathematics experiment teaching based on the Internet of Things, it is difficult to guarantee the and accuracy of data collection, which restricts the comprehensive implementation of smart teaching scenarios.

Uniformity of Evaluation Standards

It is necessary to develop the "Macao Culturalical Literacy Benchmark" (referring to the mainland's Cui Yunhu evaluation model 4), and construct an evaluation index system covering knowledge understanding, problemsolving, mathematical thinking, cultural infiltration, etc., in combination with Macao's local education characteristics and the requirements for core literacy in the mathematics subject, to ensure the mathematics teaching evaluation of different schools and different grades has comparability and scientificity, and to provide a basis for precise teaching improvement.

Conclusion

The digital transformation of Mac's mathematics education should be rooted in cultural identity, and real-world problem exploration should be activated through basic technical tools. Specifically, in the process of digital teaching, Macaos local historical and cultural elements need to be fully integrated, such as converting the geometric structure of Macao's historical buildings, the quantitative relationship in traditional festivals, and the and statistics cases in the development of the gaming industry into mathematical exploration materials, so that students can naturally perceive the charm of local culture in the process of solving real-world problems, cultural confidence and identity. At the same time, we should actively promote the use of basic technical tools such as smart whiteboards, mathematical modeling software, and online collaboration platforms, provide with intuitive and interactive learning experiences, and encourage them to use digital means for data collection, analysis, and visualization, thus deepening their understanding of mathematical concepts and application capabilities.

There is an urgent need to establish a “Macao Cultural Mathematics Resource Bank” in the future, which should systematically integrate Mac's unique cultural resources and mathematical education resources, including but not limited to the symmetrical beauty and geometric principles in Macao's traditional crafts, the measurement and spatial layout of sites such as the A-Ma Temple, and the relevant mathematical models of Macao's economic development since its return to the motherland. This should form a structured teaching resource for teachers' teaching reference and students' independent learning. In addition, it is necessary to formulate localized evaluation criteria that meet the actual needs of Macao, increase the investigation of problem-solving ability in a cultural context in the evaluation content, and combine the application performance of digital tools in the evaluation method, to comprehensively assess students' mathematical literacy and understanding ability. Through these measures, we can make mathematics learning a bridge of thinking that connects tradition and modernity, inheriting and promoting Macao's excellent traditional culture, cultiv students' innovative thinking and comprehensive abilities needed in the digital age, and promoting high-quality development of Macao's mathematics education.

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