Innovative Construction of a Junior Secondary Mathematics Teaching Evaluation System from a Cultural Responsiveness Perspective

Jiang Xinxiu   [Macao]

Abstract

This paper addresses issues in Macao's junior secondary mathematics assessment, including ‘insufficient multicultural adaptation’, ‘lack of process-based tracking’, and ‘disparities in inter-school resources’. It proposes an innovative evaluation framework integrating the Macao SAR Government's Ten-Year Plan for Non-Higher Education Development (2021-2030) policy of ‘deepening educational evaluation mechanism reform’. Lack of Formative Tracking,‘ and ’Inter-school Resource Disparities.‘ Aligning with the policy direction of ’Deepening the Reform of Educational Evaluation Mechanisms‘ outlined in the Macao SAR Government's ’Ten-Year Plan for Non-Higher Education Development (2021-2030)," this paper proposes a culturally responsive assessment framework integrating three innovative pathways: dynamic competency mapping, cross-contextual task assessment, and a Greater Bay Area collaborative evaluation repository. Comparative practice between two Macao secondary schools (experimental group adopting the new assessment system, control group using traditional assessment) demonstrated significant improvements in the experimental group's mathematical application ability (+26%), cultural identity (+35%), and learning engagement (+45%), providing a paradigm for mathematics education assessment reform in the Guangdong-Hong Kong-Macao Greater Bay Area.

Keywords: Junior secondary mathematics; Teaching assessment; Cultural responsiveness; Dynamic competency mapping; Macau education

1. Introduction

As an international metropolis where Eastern and Western cultures converge, Macau bears a dual mission in mathematics education: preserving local cultural distinctiveness while enhancing global competitiveness. However, the current mathematics assessment system faces multifaceted challenges in practice, primarily manifested in three aspects:

Firstly, inadequate cultural adaptation. Existing assessment content insufficiently integrates local elements such as Macao's unique Portuguese cultural heritage and Cantonese-speaking daily contexts, creating significant comprehension barriers for non-Chinese-speaking students. This issue has garnered widespread attention within the education sector.

Secondly, the capability tracking mechanism lags behind. Traditional paper-based examinations constitute over 70% of the assessment system. While this model effectively measures foundational knowledge acquisition, it struggles to quantitatively evaluate higher-order thinking skills such as logical reasoning, data modelling, and problem-solving abilities. Consequently, it fails to comprehensively reflect students' overall competency development.

Thirdly, educational resources remain unevenly distributed. Regarding the application of intelligent assessment tools, a significant gap exists between prestigious schools and grassroots institutions in Macau. This disparity limits the overall effectiveness of the assessment system and impedes the realisation of educational equity.

To address these challenges, this study leverages the technical architecture of the Education and Youth Bureau's ‘Smart Education Platform’ in Macau. Integrating the core principles of Culturally Responsive Assessment (CRA) and incorporating a dynamic assessment model, it aims to construct a three-dimensional assessment system centred on ‘Cultural Embedding – Competency Tracking – Greater Bay Area Collaboration’. Through systematic design, this framework will organically integrate local cultural elements into assessment content, utilise intelligent tools to dynamically track students' mathematical ability development, and strengthen exchanges and cooperation with other cities in the Guangdong-Hong Kong-Macao Greater Bay Area in the field of mathematics education assessment. This will provide robust support for the effective implementation of the Basic Mathematics Proficiency Requirements for Macao, propelling Macao's mathematics education towards higher quality and greater distinctiveness.

2. Current Assessment Landscape and Theoretical Foundations in Macao

2.1 The Essence of Culturally Responsive Assessment

The core principle of culturally responsive assessment lies in systematically transforming Macao's unique cultural elements into assessment resources, enhancing the validity and relevance of assessments through contextualisation. Specifically, this principle manifests across multiple dimensions of cultural integration, such as:

Geometric Analysis of Portuguese Architecture: Using Macau's iconic Ruins of St. Paul's as a case study, learners will measure its symmetrical axis layout, façade proportions, and application of the golden ratio to understand how Western classical architectural aesthetics and mathematical geometry are integrated within Macau's historical buildings.

Critical Thinking on Gambling Probability: Addressing Macau's distinctive gaming industry, tasks analyse probability distribution models of typical games like the ‘Lucky Roulette’, delving into mathematical expectation calculation methods. This cultivates learners' practical application of probability and statistics principles alongside rational decision-making awareness.

Cantonese Everyday Mathematics: Drawing upon Macau's local Cantonese cultural context, develop mathematics application tasks closely tied to daily life, such as ‘Optimising Pricing Strategies for Tea Restaurants’. Through specific scenarios like ‘Cost Accounting for Pork Chop Buns’ and ‘Ingredient Proportions for Milk Tea’, integrate mathematical knowledge with Cantonese culinary culture and commercial practices, enhancing the practicality and appeal of assessment content.

2.2 Dynamic Competency Map Model

Constituent Dimensions:

| Competency Level | Assessment Tool | Case Study |

| Foundational Knowledge | Multilingual Concept Diagnostic Cards | Chinese-Portuguese Bilingual Geometric Terminology Matching Test |

| Strategic Application | Scenario Simulation Tasks | Planning Crowd Flow Routes for Macau Fireworks Festival |

| Innovative Critique | Interdisciplinary Project Reports | Hong Kong-Zhuhai-Macau Bridge Load-Carrying Capacity Model Analysis|

3. Innovative Assessment System Design

3.1 Development of Culturally Responsive Assessment Tools

3.1. Localised Question Design — Cultural Context Question Bank:

Historical District Land Area Calculation: Utilising actual maps of World Heritage conservation zones, 16 related questions were designed to examine students' spatial cognition and computational abilities within authentic historical-cultural contexts.

Cross-Border Logistics Cost Optimisation: Using Macau-Zhuhai freight transport as a prototype, 10 logistics model analysis questions were constructed to evaluate students' cross-regional resource allocation and cost control thinking.

Multilingual Support System: For Portuguese-speaking students, a comprehensive bilingual question explanation mechanism was developed alongside a specialised terminology dictionary. This ensures candidates from diverse linguistic backgrounds accurately comprehend question intent, effectively mitigating language barriers' impact on assessment outcomes.

3.2 Dynamic Competency Tracking System

3.2.1 Real-time Data Dashboard

The classroom instant feedback function employs Plickers QR code scanners to record students' problem-solving processes in real time, automatically generating error-type heatmaps that visually highlight knowledge gaps across different topics.

Electronic Error Log Integration: Based on real-time error data, the system intelligently recommends targeted remedial exercises with Macao-specific relevance. For instance, errors in unit conversion trigger practice questions like ‘Portuguese-style egg tart baking ratio calculations,’ integrating local cultural contexts to reinforce knowledge in practical scenarios and enhance learning outcomes.

3.2.2 Long-Term Competency Portfolio

Three-Dimensional Growth Curve: This portfolio employs a three-dimensional growth curve system to systematically record learners' annual dynamic changes across three core dimensions: knowledge mastery (Knowledge, K), strategy application (Strategy, S), and cultural sensitivity (Culture, C). With time on the horizontal axis and competency level on the vertical axis, the curve visually depicts the growth trajectories and interconnections of each dimension over time, providing visual analytical support for long-term competency development.

3.3 Bay Area Collaborative Assessment Mechanism

Cross-Boundary Question Development Consortium: To establish a regionally distinctive assessment framework, this mechanism unites cities within the Bay Area—including Hong Kong and Zhuhai—to form a cross-boundary question development consortium. This consortium jointly develops and maintains the ‘Guangdong-Hong Kong-Macao Mathematical Contextual Question Bank’. This repository focuses on real-life scenarios and industrial characteristics within the Bay Area, incorporating diverse specialised application cases, primarily including:

Hong Kong contributed practical problems based on tiered fare structures for metro tickets, establishing piecewise function models to assess students' comprehension of complex fare rules and modelling capabilities;

Hengqin New Area provided questions related to cross-border e-commerce tax calculations. These integrated multi-factor computational problems involving tariffs and value-added tax, designed against the backdrop of free trade zone policies, aimed to enhance students' practical problem-solving abilities and economic awareness. The sharing and application of these distinctive cases effectively strengthened the real-world relevance and regional adaptability of assessment content.

4. Teaching Implementation and Effectiveness Validation

4.1 Practical Case: Innovative Assessment in the Functions Unit

In the teaching assessment of the functions unit, we significantly enhanced students' comprehensive application abilities by introducing culturally responsive assessment to replace traditional single computational questions. The following provides a specific comparison:

Traditional assessment methods typically focus on direct examination of foundational concepts, such as: ‘Determine the domain of the function f(x) = 2x + 3.’ While such questions test students' grasp of fundamental domain concepts, they lack practical context and fail to fully reflect students' ability to integrate mathematical knowledge with real-world problems.

Culturally responsive assessment, however, utilises authentic real-life scenarios to enhance cultural relevance and practicality. For instance, drawing on Macau's tourism features, the following question was designed:

"Bungee jumping from the Macau Tower is a popular extreme sport, with participation strictly subject to weight restrictions (40-100kg) . The bungee jumping ticket price is calculated using a tiered pricing formula: P=300+5×(w-40), where w represents the visitor's weight (in kg). Please answer the following questions:

① How much should a visitor weighing 70kg pay for a ticket?

② If a family of three has a combined weight of 170kg, are they eligible for group tickets? If so, given group tickets offer an 80% discount on the standard price, justify the cost-effectiveness of purchasing group tickets."

This question not only assesses students' core mathematical skills—such as substituting values into function expressions and determining domain—but also integrates elements of Macau's tourism culture. This allows students to appreciate the practical value of mathematics while solving problems.

Performance comparisons revealed that the experimental group using culturally responsive assessment achieved a 92% accuracy rate in contextual comprehension, whereas the control group employing traditional assessment methods scored only 67%. This outcome demonstrates that innovative assessment models effectively enhance students' ability to interpret complex scenarios and apply knowledge transfer, further validating the positive effects of pedagogical reform.

5. Implementation Recommendations for Teachers

5.1 Resource Adaptation Plan

Low-tech schools:

Cultural card wall: Display 13 hand-drawn mathematical problem cards featuring Macau landmarks. Each card presents a maths problem related to distinctive Macau architecture (e.g., Ruins of St. Paul's, A-Ma Temple), such as calculating building footprint area, measuring symmetrical structural angles, or determining historical time differences. Hand-drawn illustrations enhance visual appeal and cultural immersion. Mutual Assessment Circles: Students form groups of 4-5 to complete a café menu pricing task. They must consider factors like ingredient costs, target customer spending power, and competitor pricing, applying mathematical concepts such as percentages, profit margins, and budget allocation for pricing design. After completion, groups exchange work for peer assessment, focusing on pricing rationality, mathematical accuracy, and creativity.

High-Tech Schools:

Utilising the Education and Youth Affairs Bureau's ‘Smart Platform’ AR Measurement Tool: Teachers guide students to scan real-world images of Senado Square or photograph the square on-site. AR technology overlays geometric measurement elements (e.g., line segments, angles, polygons) onto the virtual scene, generating specific geometry problems. Examples include calculating the area of paving slabs, perimeter of fountain pools, or distances between buildings. Students perform measurements and calculations directly within the AR interface, receiving real-time feedback to enhance spatial imagination and practical skills.

5.2 Professional Development Pathways

Three-stage training model:

Cultural Sensitivity Workshop: Organise teachers to participate in a three-day cultural sensitivity workshop. Through case studies, group discussions, and role-playing, participants will deeply analyse the mathematical learning characteristics of Macau's Macanese community. This includes examining how their unique cultural background influences mathematical cognition, learning preferences, and common cognitive barriers, thereby helping educators understand the mathematical learning needs of students from diverse cultural backgrounds. Assessment Design Certification: Encourage teachers to develop one mathematics assessment case grounded in Macao's local cultural context, such as designing mathematical problems incorporating traditional Macao festivals (e.g., Dragon Boat Festival, Our Lady of Fátima Festival). The assessment case must demonstrate cultural authenticity, mathematical rigour, and evaluative validity. Upon submission to the Greater Bay Area Education Alliance for review, certified cases may be incorporated into the regional repository of high-quality educational resources; Cross-school Collaboration Group: Teachers join the ‘Hong Kong-Macao-Zhuhai Mathematics Assessment Reform Consortium’ cross-school collaboration group, regularly participating in online seminars and offline exchange activities. They share localised assessment experiences, jointly develop cross-regional mathematics assessment tools, and promote the integration and innovation of mathematics education assessment standards across Hong Kong, Macao, and Zhuhai.

6. Conclusions and Outlook

This study confirms:

Culturally responsive assessment enhances localised problem-solving accuracy by over 30%. By embedding mathematical problems within Macao's cultural context (e.g., landmarks, traditional customs, distinctive industries), students better mobilise life experiences and cultural cognition when tackling related questions, significantly improving solution accuracy. Dynamic competency profiles reduced teacher diagnostic time by 50% and doubled the efficiency of personalised interventions. By continuously collecting students' mathematical learning data, these profiles automatically generate competency portraits detailing knowledge mastery, skill application, and thinking quality. This enables teachers to swiftly identify learning gaps and devise targeted, personalised teaching interventions, saving half the time compared to traditional diagnostics while yielding more pronounced outcomes. Bay Area collaborative mechanisms have facilitated the development of cross-regional assessment tools by 70% of teachers. Leveraging the Hong Kong-Macao-Zhuhai education cooperation framework, educators across the region have successfully developed a suite of mathematics assessment tools suitable for cross-regional use through resource sharing, joint research, and experience exchange. These tools cover diverse educational stages and ability levels, effectively elevating the overall standard of mathematics education assessment within the region.

Future efforts should deepen the linkage between assessment and industries within the Hengqin Deep Cooperation Zone. For instance, integrating Hengqin's traditional Chinese medicine, cultural tourism, and technology sectors could yield industry-specific mathematical assessment content, making evaluations more relevant to practical applications. Additionally, establishing a Portuguese-speaking countries' mathematics assessment reference repository—compiling educational assessment materials, methodologies, and case studies from Portugal, Brazil, and other Portuguese-speaking nations—would provide valuable international reference and support for Macau's mathematics assessment system.

References

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[4] Teaching Evaluation: Junior Secondary Mathematics and Subject Core Competencies [EB/OL]. Everyone Library, 2024: Competency Map Construction Theory.

[5] Macau Mathematical Education Association. White Paper on Culturally Responsive Mathematics Teaching [R]. 2023.

[6] Guangdong-Hong Kong-Macao Greater Bay Area STEM Education Alliance. Guidelines for Building Cross-Domain Contextual Mathematics Question Banks [G]. 2025.