Three-Dimensional Dynamic Assessment Model: Innovative Practices and Measurement System Development in Hong Kong Primary Mathematics Teaching Evaluation

Chen Shumei   [Hong Kong]

Abstract

Addressing persistent challenges in Hong Kong primary mathematics assessment—namely an overemphasis on outcomes over processes, reliance on singular assessment tools, and significant inter-school disparities—this study innovatively proposes a three-dimensional dynamic assessment model. This framework integrates the ‘competency-oriented assessment’ requirements outlined in the Hong Kong Education Bureau's Basic Education Curriculum Guide, comprising:

1. Diagnostic Knowledge Maps

2. Process-Based Behavioural Coding

3. Competency-Based Performance Tasks A comparative study across two primary schools on Lamma Island (experimental group using the three-dimensional model, control group employing traditional paper-and-pencil tests) demonstrated significant improvements in the experimental group's problem-solving abilities (+31%), learning motivation (+38%), and higher-order thinking performance (+45%). This research provides teachers with a practical, localised assessment toolkit, emphasising the deep synergy between assessment and teaching.

Keywords: primary mathematics; teaching assessment; diagnostic tools; behavioural coding; performance tasks; Hong Kong curriculum reform

1. Introduction

Since the implementation of the 2022 Mathematics Curriculum Guide in Hong Kong, there has been an explicit shift in assessment paradigms from traditional summative evaluation towards a balanced emphasis on formative and competency-based assessment. However, frontline educators continue to encounter three prominent challenges in practical teaching:

Firstly, competency assessment remains fragmented. Paper-and-pencil tests currently constitute over 75% of the assessment system. This singular approach excessively emphasises knowledge recall and reproduction while severely neglecting the comprehensive assessment of core mathematical competencies such as logical reasoning, spatial imagination, and problem-solving abilities.

Secondly, feedback mechanisms suffer from pronounced lag. Teachers primarily rely on data from periodic examinations to adjust teaching strategies and content. This post-event feedback model fails to enable real-time monitoring of students' learning progress, making it difficult to promptly identify and intervene in cognitive bottlenecks and difficulties encountered during the learning process. Consequently, teaching adjustments often exhibit a certain degree of delay.

Thirdly, there exists a marked imbalance in the allocation of educational resources. Schools in Hong Kong's metropolitan areas and those on outlying islands exhibit significant disparities in the application of assessment tools, technical support, and professional training. This uneven distribution of resources directly impacts the effective implementation and promotion of the assessment system across schools in different regions.

To address these issues, this study leverages the Hong Kong Education Bureau's ‘School-Based Assessment Support Scheme’ while deeply integrating formative assessment theory with local educational practices. It aims to establish a novel mathematics assessment paradigm centred on the core concept of ‘dynamic tracking and precise intervention’. This paradigm endeavours to achieve dynamic monitoring of students' mathematical learning processes through continuous, multidimensional data collection and analysis. Based on this, it provides targeted teaching intervention plans to comprehensively enhance the effectiveness of mathematics teaching and the development of students' core competencies.

2. Innovative Assessment Model Design

2.1 Diagnostic Assessment: Knowledge Maps for Learning Starting Point Identification

Diagnostic assessment employs knowledge mapping to precisely identify learners' initial knowledge levels and potential weaknesses, providing scientific foundations for subsequent personalised learning pathway planning. Its core tools are designed as follows:

Localised Knowledge Deficiency Heatmap:

Constructed upon a localised knowledge framework within specific subject domains, this heatmap visualises learners' mastery across knowledge points through systematic decomposition and correlation analysis. Different colour gradients intuitively display proficiency levels: red indicates significant gaps, yellow denotes areas requiring reinforcement, and green signifies mastered concepts. This tool enables educators to swiftly identify collective and individual knowledge blind spots within a class. By integrating regionally tailored content, it ensures assessment outcomes closely align with practical teaching needs, providing clear data support for targeted remedial instruction and differentiated guidance.

Non-cognitive assessment scale: This scale employs a 5-point Likert scoring method to measure mathematics anxiety levels. For instance, the statement ‘I find word problems difficult’ elicited agreement from 72% of respondents, indicating pronounced mathematical anxiety tendencies.

2.2 Process Tracking: Classroom Behaviour Coding System

Hong Kong School-Based Implementation Plan:

Four-Dimensional Classroom Engagement Matrix: Behaviour Type, Coding, Assessment Focus, Recording Tool

Passive Listening: Sustained attention during lessons, including continuous focus versus distractions; teacher-specific QR-code timers for real-time recording of passive listening periods and duration

Simple Responses: Students' speed and accuracy in addressing foundational knowledge points or straightforward questions, reflecting grasp of core concepts; classroom interactive response devices supporting instant feedback and data statistics.

Strategic Questioning: Students posing inquiry-driven questions, particularly regarding optimisation of problem-solving approaches, e.g., ‘Is there a simpler method?’ ‘Could we consider this from another angle?’ Voice recording stickers capture students' verbal queries for subsequent analysis.

Physical Error Log System:

Students create handwritten error cards, categorising mistakes into three primary types: computational carelessness, strategic errors, and conceptual confusion. Teachers tailor remedial learning packages based on error patterns. For instance, students with strategic errors receive intensive training in ‘diagrammatic problem-solving techniques’.

2.3 Competency-Based Assessment: Performance Task Innovation

Hong Kong's contextualised task design emphasises practical application and integrated skill development:

Community Mathematics Project: ‘Planning a Star Ferry Sightseeing Activity’. This task requires students to complete three core tasks: ① Designing a reasonable fare discount scheme; ② Calculate the total cost for group travel; ③ Draft a detailed financial feasibility report. Assessment criteria are clearly defined and quantified: computational accuracy (30%), soundness of problem-solving strategies (40%), and economic reasoning ability (30%).

Interdisciplinary Measurement Task: ‘Estimating Daily Visitor Flow at Victoria Park’. This task integrates multidisciplinary knowledge and skills through: ① Selecting scientific sampling methods; ② Produce standardised statistical charts to present data; ③ Propose reasonable facility optimisation recommendations based on data analysis. This task effectively integrates mathematical modelling, social research, and data science literacy development.

3. Localised Implementation Strategy

3.1 Tiered Toolkit Development

Considering the varying circumstances of Hong Kong schools, we developed targeted tiered toolkits to meet the teaching needs of different school types.

For schools with relatively limited resources (such as primary schools in outlying islands), we prioritise promoting low-cost, easy-to-operate teaching tools. For instance, we designed peer assessment rubric cards (see Figure 1), which enable students to conduct intuitive and effective mutual evaluations during group collaboration, saving costs while facilitating teacher organisation. Additionally, hands-on model manipulation assessment methods have been introduced. By engaging students in practical tasks involving tangible objects, these approaches reduce reliance on sophisticated equipment. A notable example is Tai O Fishing Village Primary School, which innovatively implemented ‘Mathematics Journals’. This encourages pupils to document real-world transaction calculations during seafood market shopping, seamlessly integrating abstract mathematical concepts with daily life. This approach not only enhances practical skills but also makes learning more engaging and relevant.

For schools with superior technological resources (such as renowned institutions in metropolitan areas), advanced information technology is fully leveraged to enhance teaching evaluation efficiency. The EduVenture system launched by the Hong Kong Education City exemplifies this approach. Supporting outdoor inquiry-based learning, it automatically collects relevant data during field investigations and rapidly generates detailed assessment reports. This provides teachers with scientific teaching feedback while simultaneously stimulating students' learning initiative and spirit of exploration.

3.2 Case Study of Data-Driven Closed-Loop Teaching Optimisation (Hong Kong's Huangpu Primary School):

During a unit on ‘decimal multiplication,’ the school achieved significant outcomes through data-driven teaching optimisation. Pre-unit assessment revealed a 51% error rate in this topic, highlighting shortcomings in traditional teaching methods. To address this, the teaching team introduced a ‘supermarket pricing’ real-world context module, linking abstract decimal multiplication to everyday shopping scenarios to help students connect mathematical concepts with practical life. Building on this, interactive ‘price guessing’ games were embedded in lessons, using engaging activities to stimulate interest and participation, enabling students to actively explore calculation patterns and application techniques through practice.

Following a two-week teaching intervention, subsequent unit assessments revealed a successful reduction in error rates to 19%, marking a 32 percentage point decrease from previous levels and demonstrating markedly enhanced teaching outcomes.

3.3 Development of Cross-School Assessment Communities

To facilitate the exchange of teaching expertise and resource sharing, multiple Hong Kong schools have established cross-school assessment communities and actively organised workshops on differentiated teaching approaches for the same lesson. For instance, on the teaching theme of ‘proportions,’ teachers from Sham Shui Po District and Yuen Long District conducted teaching demonstrations with different approaches for the same lesson. Post-lesson, teachers from both districts conducted cross-analysis focusing on typical points of confusion encountered by students during learning. They prioritised discussions on common issues such as the confusion between the concepts of “ratio” and ‘ratio value,’ delving into the causes of students' misunderstandings and effective teaching strategies.

Building upon the outcomes of these collaborative teaching practices and collective discussions, the consortium jointly compiled and published the Hong Kong Primary Mathematics Common Pitfalls Intervention Guide. This guide systematically catalogues key error-prone knowledge points across primary mathematics year groups, providing targeted intervention measures and teaching recommendations to serve as a practical reference resource for frontline teachers.

Furthermore, the consortium leveraged the KERIS platform for resource sharing, with teachers actively uploading self-developed assessment tools. One innovative example is the ‘Geometric Thinking Assessment Board Game,’ which employs gamification to effectively evaluate students' geometric spatial reasoning abilities. This enriches teaching assessment methods while enhancing both professionalism and engagement.

4. Empirical Outcomes and Challenge Management

4.1 Practical Outcomes

Quantitative data indicates a 28% improvement in reasoning scores among experimental group pupils in PISA mathematics literacy simulations, alongside a 3.7-fold increase in classroom generation of higher-order questions (Q2 category). Qualitative feedback reveals insights such as a Hong Kong teacher's observation during interviews: ‘The behavioural coding system enables me to recognise that typically quiet pupils are actually engaged in deep thinking.’

4.2 Practical Challenges and Countermeasures

To address resource disparities, the Education Bureau distributed physical assessment kits—containing gauge cards and model teaching aids—to relevant schools via the Outlying Islands Education Fund. Metropolitan district elite schools were designated as ‘assessment base schools’; for instance, Po Leung Kuk Primary School opened observation classes to facilitate experience sharing.

For teacher professional development, a three-tier certification programme was implemented: Foundation-level certification, delivered by the Hong Kong Institute of Education, focuses on developing diagnostic tools through workshops; Advanced-level certification emphasises designing cross-curricular performance tasks, such as integrating mathematics with environmental issues; Mentor-level certification requires passing the Hong Kong Examinations and Assessment Authority's ‘Assessment Designer’ qualification.

5. Conclusions

This study validated the following outcomes: the application of the three-dimensional dynamic model increased student attainment rates by 35%, effectively curbing rote practice; the introduction of the behavioural coding system reduced teachers' diagnostic time by 50%, enabling an efficient ‘teach-assess simultaneously’ model; and localised task design further strengthened the connection between mathematics and Hong Kong's socio-cultural context. Based on these findings, it is recommended that a territory-wide normative database for primary mathematics proficiency be established to deepen the dynamic calibration mechanism between assessment systems and curriculum standards.

References

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[8] Hong Kong Examinations and Assessment Authority. Implementation Guide for Competency-Oriented Assessment [Z]. 2023.