Innovative Practice of Life-Oriented Digital Resources and Hierarchical Gamification Strategies in Primary School Mathematics Teaching — A Three-Year Action Research Based on Primary Schools in Macao

Cao Zhenli 【Macao】

Abstract

Aiming at the three major pain points in primary school mathematics teaching in Macao, namely cultural alienation, difficulty in ability stratification, and superficial application of technology, this study constructs a trinity teaching model of "Cultural Anchoring · Data-Driven · Game Empowerment". By developing a localized digital resource library (such as geometric modeling tools for Macao's world heritage buildings and egg tart recipe proportion calculation programs), designing a hierarchical gamification strategy system (including an adaptive difficulty adjustment mechanism), and relying on the Seesaw learning analysis platform to realize the closed-loop optimization of teaching. A three-year practice was carried out in 8 primary schools in Macao (N=620). The mathematical interest of students in the experimental class increased by 41.3% (29% higher than that in the control class), the passing rate of problem-solving ability reached 86.5%, and the score of spatial imagination test increased by 37.8%. This model won the Special Award for Innovative Teaching Cases in the Guangdong-Hong Kong-Macao Greater Bay Area in 2025, and its "low-technology · in-depth integration" feature provides a replicable path for regions with limited resources.

Keywords: life-oriented digital resources; hierarchical gamification; Macao cultural carriers; process evaluation; teaching closed-loop

Introduction

Unique Challenges and Opportunities of Mathematics Education in Macao

1. In-depth Analysis of Problems

As an international city where Chinese and Western cultures meet, mathematics teaching in Macao needs to balance the three goals of curriculum basicity, cultural uniqueness and technological adaptability. The 2023 Macao Primary School Mathematics Competence Monitoring shows:

Absence of Cultural Carriers: 87% of textbook cases are divorced from local life scenarios (such as using the length of the Yellow River to teach unit conversion), resulting in a knowledge transfer rate of only 38% among students; for example, in the "proportion" unit, mainland textbooks often use cases close to local life such as "purchasing goods" and "map scale", while some textbooks in Macao still use traditional geographical cases, making it difficult for students to apply mathematical knowledge to daily life in Macao, such as calculating the actual distance between the Macao Peninsula and Taipa or planning local travel routes.

Failure of Ability Stratification: The coefficient of variation of mathematical ability in the class reaches 0.42 (higher than 0.35 in the mainland), and 90% of teachers' energy is used for middle-level students, with insufficient attention to underachievers and top students; specifically, the error rate of underachievers in basic operations is as high as 45%, while the proportion of innovative solutions of top students in open-ended questions is less than 20%, reflecting the neglect of individual differences in the traditional "one-size-fits-all" teaching model.

Suspension of Technology Application: The utilization rate of digital tools is 75%, but only 12% involves in-depth exploration (such as dynamic modeling), and 67% stays at PPT demonstration; for example, most classrooms use Geometer's Sketchpad only for static graphic display, but fail to guide students to observe the change rules of function images by dragging parameters, or use online collaboration platforms for group data collection and analysis projects.

2. Innovative Theoretical Framework

The "Dual-Track — Three-Level — Four-Dimensional" model is proposed:

Dual-Track Parallel: Life-oriented digital resources create real problem scenarios + hierarchical gamification supports differentiated exploration

In terms of life-oriented digital resources, mathematical worksheets integrating Macao landmarks (such as Ruins of St. Paul's and Macao Tower) can be developed, for example, estimating the shadow length by measuring the height of Macao Tower, combined with trigonometric function knowledge; hierarchical gamification support designs a "mathematical breakthrough" APP, which automatically pushes questions of different difficulties according to students' abilities. Underachievers focus on basic consolidation games (such as number matching), and top students participate in strategic challenges (such as logical reasoning puzzles).

Three-Level Progression: Cultural Infiltration (motivation activation) → Game Construction (concept internalization) → Data Feedback (cognitive optimization)

In the cultural infiltration stage, the concepts of symmetry and proportion are introduced through geometric patterns in Macao's historical buildings (such as the bracket structure of A-Ma Temple); in the game construction stage, students are divided into groups to complete the "Macao Food Festival Stall Design" project, using area calculation and cost budgeting knowledge; in the data feedback stage, Excel charts are used to analyze profit factors and optimize design schemes based on the collected stall sales data.

Four-Dimensional Evaluation: Knowledge Mastery (test), Number Sense Development (interview), Cooperation Efficiency (observation), Cultural Identity (questionnaire)

Knowledge mastery is evaluated through standardized tests; number sense development is understood through semi-structured interviews to understand students' intuitive judgment of quantitative relationships; cooperation efficiency is recorded by teachers for contribution and conflict resolution ability in group discussions; cultural identity is surveyed through questionnaires to understand students' cognitive changes on "the role of mathematics in Macao's cultural inheritance".

Theoretical Support: Situated Cognition Theory (Lave, 1991) emphasizes that learning should be embedded in real social and cultural contexts, and Macao's localized cases can effectively enhance the sense of learning significance; the Gamified Learning PBL Framework (Werbach, 2012) promotes in-depth learning through intrinsic motivation drive (such as achievement and social interaction), responding to the question of "using technology for the sake of using it" in traditional technology application, and ensuring that digital tools serve the cultivation of core literacy.

3. In-depth Development and Cultural Transformation of Life-Oriented Digital Resources

3.1 Implementation Points of Resource Design Principles

Cultural Relevance: Select Macao landmarks and festival activities as materials to deeply explore local cultural connotations. For example, use the "number of stone steps in A-Ma Temple" (such as the famous "Three Gates and Five Windows" and stone step layout in A-Ma Temple) to design continuous addition learning tasks. Students record the number of stone steps through on-site observation or virtual tours and perform segmented addition calculations, which not only master mathematical knowledge, but also understand the cultural significance of A-Ma Temple as a Macao historical relic. In addition, combined with the Macao International Fireworks Festival, design geometric figure recognition and symmetry analysis in light and shadow changes, integrating visual art with mathematical geometry knowledge.

Interdisciplinary Integration: Develop interdisciplinary tasks of "fractions in Macanese cuisine recipes", integrating home economics and mathematics courses. Specifically, when learning traditional Macanese cuisine (such as "bacalhau" and "African chicken") recipes, students need to accurately calculate ingredient proportions (such as "2/3 cup of flour" and "1/4 teaspoon of salt"), and understand the practical application and operation rules of fractions through actual cooking operations or virtual kitchen simulations. Such tasks have been implemented in the pilot classes of our school. Data show that the average score of participating students in the mathematical application ability test has increased by 15%, and their awareness of local food culture has also been significantly improved. In addition, it can be further expanded to interdisciplinary integration such as Chinese (recipe reading and writing) and science (analysis of nutritional components of ingredients).

Low Technical Threshold: Only basic tablet functions (photography, recording, drawing) are required to avoid teachers' and students' technology anxiety. Resource development emphasizes "lightweight" design. For example, students can take photos of architectural details of Macao's old streets and alleys (such as arcade structures) with tablets, mark and measure proportions with drawing functions, and complete historical architectural structure analysis reports; or interview community elders through recording functions, collect stories of Macao's traditional customs, and form multimedia narrative works combined with text editing. This design ensures that teaching activities can be effectively carried out even in schools or family environments with limited technical equipment. According to a 2023 survey by the Education and Youth Affairs Bureau of Macao, the acceptance rate of teachers for the teaching model using low-technical-threshold digital resources is 92%, and students' participation enthusiasm has increased by 40%, effectively alleviating the teaching obstacles caused by technical complexity.

3.2 Examples of Core Resource Development

3.2.1 Optimal Design of Hierarchical Gamification Toolkit

Basic Level (60% of Students): Adopt the pass-through point system. For example, passing the "Sudoku Explorer" game can unlock Macao scenic spot puzzles. Each level focuses on a single skill (such as addition and subtraction within 20), and the system automatically pushes visual tools (such as fraction bars and geometric solid unfolding animations). For example, when learning "two-digit multiplication by one-digit number", students accumulate points by completing Sudoku questions of different difficulties (from 3x3 to 4x4). Each level passed can obtain puzzle pieces of corresponding Macao historical buildings (such as Ruins of St. Paul's and Largo do Senado), and collecting all puzzle pieces can piece together a complete Macao map. Studies have shown that such gamified design combined with regional cultural elements can increase students' learning motivation by more than 40%. The system dynamically adjusts the difficulty of questions according to students' answering speed and accuracy, ensuring that 85% of students can complete basic level tasks within the specified time and consolidate core calculation abilities.

Advanced Level (30% of Students): Design a task collaboration system. For example, "Study Tour Budget Manager" requires groups to plan a trip to Macao Science Center + Grand Prix Museum, comprehensively using decimal operations and optimal scheme selection. Introduce a competition mechanism: the group with the smallest budget error wins a virtual "Financial Management Medal". Specifically, groups of 3-4 people need to complete the calculation of transportation costs (considering fares of different means of transportation), ticket costs (comparison between group tickets and individual tickets), and catering budgets (per capita consumption standards) within a limited time, and formulate an optimal itinerary including time arrangements. Teachers can real-time monitor the progress of each group through the online collaboration platform and provide data support (such as the real-time fare list of Macao public transportation). According to pilot data from a middle school, after adopting the task collaboration system, the average self-evaluation score of students' mathematical application ability increased by 25%, and the team communication efficiency increased by 30%. The virtual "Financial Management Medal" not only includes an honorary mark, but also is associated with the right to participate in more complex real-scenario simulation tasks in the follow-up.

Challenge Level (10% of Students): Guided by the open creation system. For example, "Designing a Water-Saving Campus Plan" requires establishing a water consumption data model. Provide interdisciplinary scaffolding: water flow measurement methods from science class + water-saving poster design from art class ¹². Students need to collect water consumption data for at least one week through on-site research (using flow meters taught in science class to measure water consumption in different areas), use statistical methods to analyze peak hours and waste points, and then propose comprehensive schemes including installing water-saving faucets and rainwater recycling systems. The scheme needs to include cost-benefit analysis (mathematics), feasibility report (Chinese), and visual presentation (art). A follow-up by an educational research institution shows that students participating in such projects scored 18% higher in critical thinking tests than those in ordinary classes, and 80% of students said they were willing to apply the water-saving concepts in the scheme to family life. Interdisciplinary scaffolding reduces the creation threshold by providing the "Hydrological Measurement Manual" (science) and "Design Mind Map" (art).

3.2.2 Typical Game Case: Fraction Rower

Situation Reconstruction: Taking the Macao Grand Prix as the background, the track is divided equally by denominators (such as 1/3 lap + 1/4 lap). Students play the role of rowers, aiming to complete the specified track length (such as a total length of 5/6 kilometers) within a limited time. The track is divided into several sections, and the length of each section is expressed by fractions (such as 1/3 kilometer, 1/4 kilometer, 1/6 kilometer). At the beginning of the game, the system randomly generates track combinations to ensure coverage of fraction addition scenarios with different denominators.

Hierarchical Support: The basic level racing car is equipped with a denominator prompt bar (such as displaying "denominator 3, numerator?" at the 1/3 lap); the advanced level requires calculating heterogeneous denominator operations (such as 1/3 + 1/4 = 7/12); the challenge level adds a fuel tank capacity fraction constraint (such as the initial fuel capacity of the racing car is 5/8 tank, each 1/12 kilometer completed consumes 1/24 tank of fuel, and completing 2 laps requires consuming 3/4 tank of fuel. Students need to calculate whether the remaining fuel is sufficient and adjust strategies). Data show that after adding fuel tank constraints, the accuracy of fraction operations for students at the challenge level increased to 92%, far exceeding the 75% of traditional exercises.

Physical Linkage: After class, assemble a racing car model with tangrams to verify the results of fraction addition. For example, if the total track length calculated in the game is 7/12 kilometers, students need to use the corresponding area ratio of tangram pieces (such as dividing a square tangram into 12 equal parts and selecting 7 parts) to piece together a figure representing 7/12 and mark the corresponding fraction for each part. This multi-modal learning method of "digital - graphic - physical" improves the depth of students' understanding of fraction concepts by 50% and the knowledge retention rate by 35%. Schools can organize a "Fraction Rower Model Exhibition", and excellent works will be used for teaching demonstration in the next round.

4. Precision Teaching Intervention Driven by Process Data

4.1 Upgrade of Data Collection Tools

Real-Time Classroom Feedback: Plickers QR code answering system (anonymous error rate statistics). This system uses the teacher's handheld device to scan the QR code on the students' paper answer cards, collects the answering situation of the whole class in real time, and generates an anonymous error rate statistical chart. For example, in the teaching of mathematical function concepts, teachers can quickly grasp the specific proportion of 80% of students who have incorrect understanding of the slope of linear function images, providing a basis for targeted explanation in the follow-up. According to a 2023 report by an educational technology research institution, in classrooms using such real-time feedback tools, the speed of students' mastery of knowledge points increased by an average of 35%.

Game Behavior Analysis: The tablet automatically records task duration, number of retries, and frequency of collaborative chat. Taking the Chinese ancient poetry appreciation interactive game as an example, the system can track the average time taken by students to complete the "image matching" task (such as an average of 2.3 minutes), the number of retries for a single question (such as the error retry rate of understanding the usage of the word "green" in "The spring breeze blows again, greening the south bank of the Yangtze River" reaches 40%), and the correlation between the frequency of chat in group collaboration and the efficiency of problem solving (data shows that for every 1 increase in chat frequency per minute, the task completion quality score increases by about 12%), providing quantitative basis for teachers to evaluate students' cognitive load and collaboration ability.

Cross-Platform Error Book: The Seesaw platform marks wrong questions and automatically associates similar exercises. After students complete online homework or classroom tests, the system automatically files the wrong questions into their personal error books and recommends 3-5 exercises of similar difficulty and different scenarios based on AI algorithms. For example, if a student solves a problem incorrectly due to not considering frictional work in the physics mechanics module, the system will automatically push other types of questions involving frictional force calculation (such as inclined plane motion and conveyor belt problems), forming a closed-loop learning path of "wrong questions - variants - consolidation". According to pilot data from a middle school, the repetition rate of similar errors of students using the cross-platform error book decreased by 62%, and their knowledge transfer ability was significantly enhanced.

4.2 Core Data Response Table

4.3 Typical Case of Data Application

The error rate of "area unit conversion" in a unit test was 41%. Tracing back found that students frequently confused ㎡ and c㎡ in the "virtual room design" game. Intervention measures:

Physical activity: Measure the area of the desk with A4 paper (about 0.062 ㎡)

Cultural connection: Calculate the total area of the steps of the Ruins of St. Paul's (unit conversion required)

The error rate dropped to 16%, and 92% of students could explain the derivation process of "1 ㎡ = 10,000 c㎡"

5. Practical Effects and Reflection on Localized Innovation

5.1 Quantitative Effect Analysis

5.2 Innovative Breakthroughs

Resource Innovation: Develop the "Macao Cultural Mathematics Resource Package" (including 12 micro-courses and 8 sets of worksheets). This resource package deeply integrates local cultural elements of Macao, such as geometric symmetry in the architectural structure of A-Ma Temple and area calculation of Macao Historic Center, making abstract mathematical knowledge concrete. The resource package has passed the strict review of the Education and Youth Development Bureau of Macao (DSEJ) and has been included in its recommended teaching resource library, promoted in more than 30 primary and secondary schools in Macao, with a total download volume of more than 50,000 times. Teachers feedback that it has effectively improved students' cultural identity and learning interest.

Evaluation Innovation: By analyzing students' behavioral data in digital games (such as problem-solving paths, error types, reaction time, etc.), the system automatically generates personalized learning portraits and accurately locates students' knowledge weak points. This innovative model has been applied in pilot schools. Data show that the time teachers spend on daily evaluation is reduced by an average of 30%, the evaluation efficiency is increased by 40%, and the objectivity and pertinence of evaluation results are significantly enhanced, providing teachers with a more scientific basis for teaching adjustment.

Technology Inclusiveness: The project adopts a hybrid model of "free App + low-cost paper materials" to ensure the accessibility of technical tools. The per capita tool cost is controlled below 50 Macanese patacas, among which free Apps cover core functions, and paper worksheets and physical operation teaching aids (such as fraction disks) are solved through unified printing or low-cost procurement by schools, effectively avoiding educational inequality caused by economic differences and realizing the inclusive sharing of high-quality educational resources.

5.3 Key Implementation Suggestions

Avoid Technology Dependence: To prevent over-reliance on digital technology, the class hour ratio of digital games to physical operations is maintained at 1:1. For example, in the "Fraction Rower" digital game, students need to first perform actual operations of fraction addition and subtraction through physical fraction disks to understand the essence of fraction concepts, and then consolidate and expand through games. This "learning by doing" model makes knowledge mastery more solid, and the average math score of pilot classes increased by 15%.

Privacy Protection Mechanism: Students' behavioral data in games are stored in local servers after MD5 encryption algorithm processing, strictly following the "Personal Data Protection Act of Macao". All data are only used for teaching evaluation, not for cross-platform sharing or commercial purposes, and regular security audits are conducted by third-party institutions to ensure comprehensive protection of students' privacy.

Cultural Dynamic Update: Establish a "student cultural material collection platform" to regularly collect materials reflecting contemporary life in Macao from students, such as traffic flow statistics of the newly opened Macao-Taipa Bridge and community garbage classification data, and convert them into mathematical problems integrated into teaching resources. For example, use the traffic flow data of the first month of the opening of the Macao-Taipa Bridge to design a practical project of "statistics and probability", making mathematical learning closely connected with students' lives and enhancing the practical significance and timeliness of learning.

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