Rethinking the Elementary Mathematics Assessment Framework Embedded in Cultural Context: A Hong Kong School-Based Practice

Han Meixiang 【Hong Kong】

Abstract

This paper addresses the issues of excessive emphasis on calculation and lack of connection to real life in Hong Kong elementary mathematics. A "Cultural Situation-Process Observation-Diverse Feedback" tridimensional assessment model is constructed. By developing 12 localized assessment tasks (such calculating consumption in a diner and designing a cruise route in Victoria Harbor), an action research was implemented in six Hong Kong elementary schools. The data show that students in the experimental have significantly improved in mathematical modeling ability ( 35.2%), cultural relevance awareness ( 41.8%), etc., providing an empirical solution for the implementation of thelife-oriented assessment" concept in the "Mathematics Curriculum Guide (2022)".

Keywords: Cultural Situation Assessment; Formative Assessment; Hong Mathematics Education; School-Based Assessment Tool; Diverse Feedback

1. Introduction

Hong Kong's "Mathematics Curriculum Guide (2022)" proposes to "establish a situational assessment mechanism", but the current assessment is still dominated by standardized paper-and-pencil tests. According to the report of the Kong Examinations and Assessment Authority (HKEAA), 72% of the questions in the entire Hong Kong P3 TSA focus on the speed of the four arithmetic operations and only 8% involve real problem solving, reflecting the insufficiency of the current assessment model in cultivating students' mathematical application ability. At the same time, as an metropolis, the assessment needs in the context of Hong Kong's multicultural background are becoming increasingly prominent, such as the inconsistent starting points of learning brought about by differences in educational for cross-border students, and the diverse needs for real-life mathematical application scenarios in different cultural backgrounds, which have not been effectively met. This study is based on Hong Kongs unique cultural genes, deeply analyzes the limitations of the existing assessment system, reconstructs the assessment objectives, develops situationalized assessment tools, optimizes the feedback mechanism, explores how to empower students' comprehensive development of mathematical literacy through assessment, providing practical paths and theoretical support for the reform of Hong Kong's mathematics education.

2. Current Sit and Challenges of Mathematics Assessment in Hong Kong

(a) The Objective of Assessment Deviates from Core Competencies

Excessive emphasis on mechanical operations

The TSA shows that 75% of the questions in the "Fractions" unit for Grade 4 are about common denominator calculations, ignoring the "mathematical reasoning and data processing capabilities required by the "Guidelines". Case: Students can calculate the result of frac{3}{4} times 12, but cannot solve the actual problem "1/4 of a pineapple bun is divided among 3 people, how much does each person get", which reflects the lack of ability to apply mathematical knowledge to real.

Serious lack of cultural situation

The current textbook assessment questions are mostly fictional situations (such as "Xiao Ming has 20 apples and divides them equally 5 children, how many does each person get"), lacking elements of Hong Kong life4, such as common scenarios in Hong Kong, such as ordering in diners, public transport fares, and allocating quantities in local festivals and activities. Student questionnaire surveys show that only 15% of students believe that the content of the mathematics assessment is " to life", indicating that the content of the assessment is disconnected from Hong Kong's local culture and daily life, and it is difficult to stimulate students' interest in learning application consciousness.

(b) The Monotonization of Assessment Tools

The weakness of process-based records

80% of teachers rely on unit test scores, lacking standardized recording tools for classroom observations, resulting in insufficient dynamic tracking of students' daily learning behaviors, engagement, and thinking processes, making it difficult to fully capture non-quantitative performances such as cooperative abilities exhibited in group discussions, hands-on skills demonstrated in experimental operations, and critical thinking revealed during classroom questioning. Insufficient Differentiated Assessment.

International schools and local schools use the same assessment rubrics without considering the cultural background differences of students (e.g., cross-border students' experience with currency conversion). For instance, when solving math word problems involving currency unit conversion in different countries, students from different cultural backgrounds may struggle to accurately understand the problem due to a lack of relevant life experience, leading to assessment results that do not truly reflect their mathematical abilities. It also overlooks the unique cognitive styles and problem-solving strategies formed by students in a multicultural environment.

3. The Construction of the Cultural Situated Assessment Model

(a) The Reconstruction Framework of Assessment Objectives

Design Principles: Based on the "Mathematics in Life" theory by Xie Xijin, Kong elements such as cha-chaan-teng (tea cafés) and Star Ferry are transformed into assessment carriers. Xie Xijin's "Mmatics in Life" theory emphasizes that mathematics learning should be closely integrated with real life, cultivating students' mathematical thinking and application ability through problem-solving in authentic situations, so mathematical knowledge moves from abstraction to concreteness and from the classroom to life. Under this theory, the design uses Hong Kong's representative cultural symbols and daily life scenarios as core carriers. For example, common issues in tea cafés such as ordering and pricing, ingredient proportions, and seat arrangement optimization can be transformed into practical applications of mathematical knowledge points such as relationships, geometric figures, and probability and statistics. The route planning, fare calculation, and passenger flow prediction of the Star Ferry can effectively integrate mathematical content such as function modeling data analysis, and optimization ideas. Through the concrete presentation of these local Hong Kong elements, students can not only feel the practical value of mathematics in familiar life scenes, enhancing their interest learning, but also examine their ability to apply mathematical knowledge to solve practical problems in the assessment process, achieving a deep integration of theory and practice, and transmitting Hong Kong's unique cultural characteristics, making the assessment process educational, interesting, and cultural.

(b) Development of School-based Assessment Tools

Process Observation Checklist

A[Classroom] --> B["Explain the meaning of negative numbers using the Octopus card consumption case"]

C[Group Task] --> D[Accuracy of angle calculation in the design of the Victoria Harbour cruise route"]

E[Cultural Relevance] --> F["Use the Dragon Boat Race Lantau to explain the speed model"]

The checklist has been validated by experts from the Hong Kong Institute of Education (Cronbach's α=0.8).

Tiered Task Manual

Basic Tier: Calculate the combination of cha-chaan-teng meal packages (e.g., the lowest consumption of AB C meal, considering the unit price of different meal packages, discount rules, and customer ordering restrictions, such as "designated meal packages cannot be used with other promotions at same time" and other real-life situations)

Advanced Tier: Simulate the investment "Red Chip Stock" monthly return statistics (integrating interest rate and statistical knowledge, it necessary to collect the daily closing price data of a certain Red Chip Stock in the past 12 months, calculate the monthly rate of return, average rate of return, standard deviation the rate of return, and analyze the impact of market volatility on investment decisions)

Challenge Tier: Optimize the design of the Star Ferry timetable (comprehensive use optimization and probability, it is necessary to design a timetable plan that minimizes operating costs while ensuring that passenger waiting time does not exceed 10 minutes, based on historical passenger data (such as 7:00-9:00 during the morning rush hour, one ferry every 15 minutes, passenger flow is about 300 peopleferry; during off-peak hours, one ferry every 30 minutes, passenger flow is about 150 people/ferry), combined with weather factors (y day passenger flow increases by 20%), holiday factors (such as the passenger flow on the anniversary of Hong Kong's return doubles), and the probability distribution of).

(c) Dynamic Feedback Mechanism

"Sandwich Feedback Method"

Affirmation (pecific): You accurately calculated the average expenditure per person at Temple Street Night Market at $68.5, organized the data clearly, presented the charts intuitively and understandably, were able to quickly grasp the core consumption level, demonstrating good data processing skills and meticulous observation!

Improvement (Precise): It is suggested to add a statement explainingwhy the mode was chosen instead of the average to represent typical consumption", such as analyzing the distribution characteristics of Temple Street Night Market consumption data, for example, whether there are extreme or low price orders that cause the average to be interfered with, and the mode can more reflect the actual consumption habits of the majority of tourists, such an explanation can enhance theasion and professionalism of data interpretation.

Challenge (Transfer): What variables need to be considered in the budget plan design for the discount season at the Sham Shui Po electronic? When designing the budget plan, it is necessary to consider variables such as market passenger flow forecast (such as historical data of the same period, holiday factors), commodity purchase (including discount strength, supplier credit period), labor cost (promotion personnel, temporary worker wages), marketing and promotion expenses (online advertising, offline event materials), venue and maintenance costs, expected profit margin targets, and possible emergency reserve funds (such as weather impact, inventory backlog disposal costs), etc., through multi-dimensional variable analysis develop a scientific and reasonable budget framework to ensure the smooth development of the discount season activities and the achievement of profit targets.

Culturally Responsive Interviewing

Discussing strategies converting Renminbi/Hong Kong dollars with cross-border students

When discussing strategies for converting Renminbi and Hong Kong dollars with cross-border students, culturally responsive interviewing respect and understanding for the bilingual and bicultural backgrounds that students are in. First, by asking open-ended questions, guide students to share real-life scenarios involving both, such as family shopping, payment experiences during cross-border travel, etc., so that the conversion problem is closely connected to their life experience. Next, combined with the difference the price level of Hong Kong and the mainland, examples are given to illustrate the price comparison of different commodities in the two places, to help students establish an intuitive understanding of the value the currency. At the same time, encourage students to use their existing mathematical knowledge, such as multiplication, division, and decimal operations, to explore conversion methods on their own, and their respective calculation ideas, and the teacher provides guidance along the way, correcting possible misconceptions such as the impact of exchange rate fluctuations on actual conversion. In addition, through group, let students explain the conversion steps to each other to promote the internalization and transfer of knowledge and cultivate their ability to solve real problems.

The spatial concept application is evaluated through the Daao boat shed mapping task. The Daao boat shed, as a unique group aquatic architecture, provides a real and rich scenario for evaluating the application of spatial concepts by pupils. In the mapping task, pupils are required to use tools such as rulers and protors to measure and record the length, width, height, and roof slope of the boat shed. The task design focuses on guiding pupils to combine abstract spatial concepts (such as plane, solid geometry, and scale) with the actual architectural structure. For example, by drawing the plan and elevation of the boat shed, they can understand the relationship between two-dimensional three-dimensional spaces; by calculating the floor area and building area of different boat shed units, they can master the calculation methods of area and volume. At the same time, pupils encouraged to observe the layout characteristics of the boat shed, such as the arrangement mode between houses and the width design of the passage, to analyze the spatial utilization logic behind it, and cultivate their spatial imagination and problem-solving ability. Teachers comprehensively evaluate the application level of their spatial concepts by observing the standard operation of pupils in the measurement process, the of data recording, and the depth of understanding of spatial relations, and adjust the subsequent teaching strategies according to the evaluation results, so as to further improve the spatial thinking ability of pupils

4. Practice Effectiveness and Evidence

(a) Quantitative Data Improvement：

Data source: School-based assessment database (2025.01-202.06), p<0.01 significant difference

(b) Qualitative evidence emerges

Student feedback:

“When designing the ticket price plan for mountaintop cable car, I finally understood that percentages are not just textbook exercises, they need to be combined with factors such as actual operating costs, tourist traffic, and ticket price discount for different age groups to make comprehensive calculations and adjustments, for example, children's tickets can be set at 50% of the adult ticket price, and senior tickets can set at a 70% discount, so as to ensure both the economic benefits of the cable car operation and social fairness, and this process has given me a deeper understanding of application of percentages.”

——A fourth-grade student at a school in Wong Tai Sin

Teacher's reflection:

“In this project-based learning, the task design needs to consider more local cultural venues, such as measuring interactive exhibits at the Science Museum, students can solve real problems by measuring the area of different exhibition areas, the height volume of exhibits in the Science Museum, and applying the knowledge of length unit conversion, area formula calculation and other mathematical knowledge, which can not only enhance students' interest in learning but also let them experience the close connection between mathematics and life in practice, and at the same time, it can also better understand the local cultural resources and improve comprehensive quality.”(III) Cross-school application case.

International school: Replace traditional currency exercises with the currency exchange task at the Stanley Market. In the math classroom of the international school, the led the students out of the classroom and into a simulated Stanley Market scene. The students held virtual currencies of different countries and converted currencies for "tourists" from all over the world to the real-time updated exchange rate data displayed on the electronic screen. For example, a "tourist" needed to buy a souvenir worth 100 Hong Kong, and the student needed to first check the exchange rate between the US dollar and the Hong Kong dollar on that day, calculate the required amount of US dollars, and round it to decimal places. In the process, the students not only practiced decimal multiplication and division, but also intuitively felt the impact of exchange rate fluctuations on actual transactions, with the sh and bargaining dialogues of the simulated market ringing in their ears, and the touch of the virtual currency in their hands forming a sharp contrast with the jumping numbers on the electronic screen, the abstract currency conversion vivid and concrete.

Rural elementary school: Combine the calculation of the area of the Yuen Long rice field with the application of the yield. The math of the rural elementary school extends the classroom to the fields. The teacher led the students to the Yuen Long rice field, where they observed the shape of the rice field — some rectangular with neat edges; some are slightly irregular due to the terrain. The students measured the length and width of the rice field in groups, marked the measuring points on the moist soil a tape measure, and recorded the data. Back in the classroom, they calculated the area of the rice field according to the measurement results, and then combined with the average yield per of rice field in the local area (such as 500 kilograms of rice per mu), to estimate the total yield of the entire rice field. The sun sh on the golden rice ears, and the air was filled with the fragrance of rice. The students deeply understood the conversion relationship between the area units "mu" and "square meter" and the actual application of mathematical knowledge in agricultural production through hands-on measurement and calculation, with a sense of achievement of combining theory with practice on their faces.

5. Reflection and Suggestions

Implementation Challenges

Insufficient teacher situational design capability: Only 5% of teachers can independently develop culture-related assessment tasks, reflecting a clear professional shortcoming in current teachers' ability to effectively integrate local cultural elements into mathematics teaching and assessment. results in a disconnection between the assessment content and students' actual lives, making it difficult to truly reflect students' ability to apply mathematical knowledge to solve local problems.

Counteasures: Establish a "Hong Kong Life Mathematics Assessment Case Bank," by collecting, organizing, and promoting mathematics assessment cases of local cultural contexts (such as traditional festivals landmark buildings, community activities, etc.). This provides teachers with directly referenceable resources to improve their situational design efficiency and quality.

System Optimization Direction

Incorate cultural situation assessment into the compulsory module of teacher professional development, systematically teach the design principles, methods, and practical cases of cultural situation assessment in teacher training courses, and enhance teachers practical skills through workshops, teaching and research activities, etc., to ensure that every teacher masters the core skills for developing culture-related assessment tasks.

TSA increases the of local situation application questions by 10%-15% (e.g., data statistics of the Hong Kong-Zhuhai-Macao Bridge, meteorological analysis of the Hong Kong Observatory, calculation of public transport fares, profit calculation of local business activities, etc.), making the assessment closer to the daily life experience of Hong students, enhancing the practical significance and educational value of the assessment, and guiding schools to focus more on the localization of mathematical knowledge application in teaching.

Conclusion

The core of lies in understanding how students use mathematical thinking to connect with the world. Hong Kong's unique cultural background provides a natural situational resource for mathematics assessment. By basing on life, recording the thinking process, and implementing culturally responsive feedback, assessment can be transformed from a "standard answer detector" to a "math literacy incubator." Teachers should become interpre of cultural situations and "detectives" of students' thinking, so that assessment can truly illuminate the learning journey.

References

[1] Zhang Minxuan.Research on Quality Assurance of Cross-Border Education" [M]. University of Hong Kong Press, 2023: 77-89. (Ass theory)

[2] HKEAA. "Report on the Whole-of-Hong-Kong System Assessment" [R]. 2024:15-21. (Current data)

[3] Xie Xijin. "The Theory and Practice of Life Mathematics" [M]. Lianhuastore (Hong Kong), 2022: 102-115. (Situational design)

[4] Zheng Meihong "Case of Hong Kong School-Based Curriculum Development" [J]. Journal of the Hong Kong Teachers' Centre, 2023(4): 3341. (Localized practice)

[5] OECD. "PISA Mathematics Literacy Assessment Framework" [S]. 2025: 6-70. (International reference)

[6] Mo Yachen. "Research on Mathematics Education in Hong Kong" [M]. Hong Kong Educational Books, 024: 144-152. (Cultural responsive strategy)