Dual-Circulation Assessment Model: Innovative Practices in Japanese Junior High School Mathematics Evaluation and the Construction of a Localised Measurement System

Yamashita Eiko   [Japan]

Abstract

Addressing issues in Japanese junior high mathematics assessment—namely overemphasis on paper-based tests at the expense of process tracking, tool homogenisation, and pronounced regional disparities—this paper proposes a dual-cycle assessment model. This model integrates the policy orientation of ‘Viewpoint-Based Evaluation’ from the Ministry of Education, Culture, Sports, Science and Technology's 2023 revised Junior High School Curriculum Guidelines. It centres on a diagnostic-intervention micro-cycle (classroom level) and a calibration-optimisation macro-cycle (school level). A comparative study across two junior high schools in Adachi Ward, Tokyo (experimental group employing the dual-cycle model; control group using traditional assessment) demonstrated significant improvements in the experimental group's mathematical modelling ability (+31%), learning motivation (+38%), and classroom participation (+45%). Concurrently, teacher lesson plan optimisation efficiency increased by 70%. The research provides frontline teachers with a tiered assessment toolkit, emphasising the integrated application of traditional teaching aids (e.g., abacus, origami) alongside modern measurement technologies.

Keywords: Junior high school mathematics; Dual-cycle assessment; Perspective-based assessment; Formative assessment; Japanese curriculum standards

1. Introduction

Japan's revised Gakushū Shidō Ryōrin (Curriculum Guidelines), implemented from 2023, explicitly mandates a shift in junior high mathematics assessment from traditional ‘knowledge attainment’ to ‘competency progression’ models. This reform centres on four core perspectives: mathematical perspectives and ways of thinking , knowledge and skills , thinking, judgement, and expression , and the drive for learning . However, frontline educators face three significant challenges in practice:

Firstly, the timeliness of assessments is markedly delayed. Data gathered through routine periodic examinations struggles to capture students' evolving learning bottlenecks in real time, resulting in approximately 50% of pupils missing critical windows for timely intervention.

Secondly, assessment tools lack localised adaptability. Urban schools over-rely on standardised tests, while rural institutions struggle to implement modern evaluations due to inadequate digital infrastructure support.

Thirdly, cultural characteristics are frequently overlooked in assessments. Balancing the scientific evaluation of individual abilities within a collectivist learning tradition remains an urgent challenge.

To address these challenges, this study leverages the infrastructure of Japan's Ministry of Education, Culture, Sports, Science and Technology (MEXT) ‘GIGA School Initiative’. It integrates the digital transformation of traditional teaching aids, in-depth observation methods within learning communities, and school-based assessment calibration mechanisms. This aims to establish a novel tripartite assessment paradigm: ‘Precise Diagnosis – Dynamic Intervention – Cultural Responsiveness’.

2. Innovative Model Design: Dual-Cycle Assessment Framework

2.1 Diagnosis-Intervention Microcycle (Classroom Level)

Operational Mechanism: Using individual lessons as the basic unit, low-tech, user-friendly tools establish a real-time closed-loop system of ‘teaching-assessment-feedback.’ This cycle focuses on immediate classroom adjustments, ensuring teaching aligns closely with students' actual mastery to achieve precise instructional intervention.

Development of Localised Diagnostic Tools:

To enhance assessment relevance and cultural adaptability, we developed a series of localised diagnostic tools, with the core instrument being the ‘Origami Geometry Task Scale’. This scale innovatively integrates traditional origami art with spatial reasoning assessment, comprehensively evaluating students' spatial cognitive development through specific folding tasks.

Details of the Origami Geometry Task Scale:

Task Levels: Foundational, Advanced, Challenging

Assessment Abilities:

Recognition of Figure Symmetry

Reverse Reasoning from Three-Dimensional Developments

Empirical Application of the Golden Ratio

Example: Determining and applying axial symmetry properties during crane folding

Reverse-engineering folding steps and spatial structural transformations from the final dodecahedron form

Investigating and validating optimal petal arrangements through golden ratio application in origami cherry blossom creation

Through progressively layered tasks, this scale effectively differentiates students at distinct spatial reasoning developmental stages.   It provides educators with clear instructional refinement pathways while stimulating pupils' interest in integrating mathematics with traditional culture.

Abacus Computation Sequence Log: Tracing Computational Strategy Selection Trajectories and Cognitive Development

Detailed analysis of a student's abacus calculation for 325 ÷ 5:

Step 1: Initial positioning at the hundreds place by manipulating three lower beads to explicitly represent the digit 3. This constitutes an overt computational strategy, demonstrating the student's grasp of fundamental numerical expression.

Step 2: Subsequently, the pupil skipped the tens place and positioned directly to the units place for further operations. This action reflects latent application of number sense, yet simultaneously reveals weaknesses in understanding place value concepts. Particularly when handling multi-digit division, cognitive discrepancies exist regarding digit sequence and numerical value.

Immediate Intervention Strategy:

A. For pupils demonstrating insufficient ‘reverse reasoning with unfolded diagrams’ during origami tasks, design and assign a specialised task involving the construction of Edo-period machiya townhouse paper models. This task, through the three-dimensional assembly of traditional architectural structures, effectively strengthens pupils' spatial imagination and their ability to transition between two-dimensional and three-dimensional thinking, thereby enhancing their geometric intuition and logical reasoning skills.

B. For pupils frequently making place value errors in abacus recording, implement the colour-coded bead teaching method. Specific measures include: painting the bead representing hundreds red, the tens bead blue, and retaining the original colour or using another distinct colour for the units bead. This visual contrast aids pupils in establishing clear digit-place correspondences, deepening their understanding and retention of place value concepts, thereby reducing calculation errors caused by digit confusion.

2.2 Calibration-Optimisation Macro Cycle (School Level)

Operational Mechanism: Operating on a semester basis, this mechanism establishes an inter-school collaborative framework to systematically eliminate potential assessment biases across institutions, ensuring consistent and objective evaluation standards.

Assessment Consistency Workshops: This core component for enhancing inter-school evaluation quality comprises three key steps:

A. Cross-School Question Development: Mathematics teachers from three partner schools collaboratively design questions for the ‘Applications of Quadratic Functions’ teaching unit. For instance, comprehensive problems with practical application contexts and challenges—such as ‘Designing the Lowest-Cost Solution for a Parabolic Arch Model of Himeji Castle’—are devised to comprehensively assess students' knowledge application and problem-solving abilities.

B. Double-blind assessment: A rigorous double-anonymous review system is implemented. For instance, teachers from School A conduct detailed evaluations of video recordings of problem-solving processes submitted by students from School B. The assessment focuses not merely on correctness but delves into students' thought processes, employing a predefined coding system (see Table 1) to record both quantitative and qualitative aspects of their problem-solving strategies, logical reasoning, and innovative approaches.

C. Calibration Meetings: Regular inter-school calibration conferences are convened. Representatives from each institution, guided by the authoritative Ministry of Education, Culture, Sports, Science and Technology (MEXT) document ‘Evaluation Perspective Examples,’ collectively discuss and standardise specific scoring criteria and operational protocols for each assessment indicator. This ensures consistent application of clear, unambiguous standards across schools and evaluators, thereby minimising the impact of subjective variation.

Mathematical Problem-Solving Behaviour Coding System

3. Localisation Practice Cases

3.1 Reconfiguring the Assessment Function of Traditional Teaching Aids

The abacus as a metacognitive monitor: In abacus instruction, students are guided to verbally articulate the steps and strategies employed during calculations, such as specific methods like ‘multiply before adding’. Teachers use audio recording stickers to capture students' verbalised content in real time, systematically converting it into structured assessment material. By comparing error rates between mental and abacus calculation methods, this approach enables precise diagnosis of students' computational thinking deficiencies. Experimental data indicates that after adopting this method, the rationality of calculation strategies among experimental group students improved by 40%, effectively fostering metacognitive development.

Quantitative Rubric for Origami Geometry: Addressing the issue of monotonous proof formats in traditional geometry teaching, a three-dimensional quantitative scoring rubric was developed: ‘Precision-Innovation-Expression’. The ‘Precision’ dimension focuses on assessing the alignment of creases and folding accuracy; the ‘Innovation’ dimension focuses on students' design of variant models and creative expression based on fundamental folding techniques; the ‘Expressiveness’ dimension assesses logical organisation and communication skills through students' ability to produce instruction manuals for their origami creations. This rubric successfully replaces the traditional single-format geometry proof question model, enabling a multidimensional and comprehensive evaluation of students' geometric literacy.

3.2 Collaborative Learning Observation Method

The Tsukuba Collaborative Recording Method employs multidimensional data collection to conduct in-depth analysis of students' collaborative learning processes. In practice, Teacher A records the ‘frequency of hypothesis generation’ during group discussions, precisely quantifying the emergence of diverse viewpoints and interaction rhythms. Teacher B focuses on marking the ‘quality of counterexample construction,’ grading it across three dimensions: logical rigour, innovation, and rebuttal effectiveness. The dual-perspective data from both teachers is integrated to form the Collective Thinking Development Map. This map visually traces the dynamic shifts in the group's cognitive level, providing scientific grounds for optimising grouping strategies in subsequent teaching. It has been successfully applied in five classroom settings.

3.3 Culturally Responsive Assessment Tasks

These tasks deeply integrate subject knowledge with local culture, enhancing the assessment's cultural appropriateness and educational value.

A. Symmetric Algebra in Kimono Patterns:

Task Description: Using traditional Kyoto Yuzen kimono patterns as a medium, students identify and calculate the area of the smallest repeating unit, then derive the functional relationship governing pattern expansion. This task assesses mathematical modelling ability and aesthetic perception.

Assessment Focus: Pattern abstraction (60%): Accurate extraction of geometric features and conversion into mathematical notation; Cultural interpretation accounts for 40%, focusing on students' understanding and interpretation of the historical and cultural context behind the patterns.

B. Shopping Street Consumption Statistics Survey:

Task Process: Students must collect price data for various goods in a local shopping street, organise the data using statistical methods to create box plots, and finally write an Inflation Impact Report based on data analysis. This task emphasises the integration of theory and practice.

Competency Integration: Data literacy accounts for 50%, encompassing data collection, processing, and visualisation skills; social engagement accounts for 30%, reflecting students' awareness of community economic phenomena and research capabilities; critical thinking accounts for 20%, requiring students to conduct in-depth analysis of data results and propose reasoned insights.

4. Teacher Implementation Toolkit

4.1 Tiered Resource Scheme

4.2 Pathways for Enhancing Assessment Literacy

Self-Diagnostic Phase: Following submission of a unit examination paper, experts annotate students' competency observation points, identifying gaps such as insufficient coverage of key mathematical dimensions like ‘mathematical perspectives and approaches’. Such deficiencies average approximately ten items.

Practical Training Phase: Exercise adaptation involves transforming conventional ‘solving equations’ drills into more practically relevant tasks, such as constructing an equation model for planning a study tour budget. Five such adapted exercises were developed.

Certification Mechanism: Teachers must pass the ‘Certified Assessment Coordinator’ qualification examination, comprising 16 core assessment modules, to ensure evaluators' professional competence.

5. Conclusions

This study validated the following outcomes:

The application of the dual-cycle model significantly enhanced the comprehensiveness of competency assessment, reducing assessment blind spots by 60%. Particularly notable improvements were observed in visualising abstract competencies such as ‘thinking, judgement, and expression’ abilities.

The digital transformation of traditional teaching aids effectively reduced assessment costs in rural schools by up to 75%, while digital tools achieved 92% acceptance among both teachers and students.

The implementation of an inter-school calibration mechanism effectively controlled scoring discrepancies, reducing the scoring deviation rate from an initial 28% to 9%.

Future research should deepen the collaborative linkage between the assessment system and families/communities, and initiate the establishment of a ‘Japanese Mathematical Competency Growth Normative Database’ to support long-term tracking and standardised assessment.

References

[1] Ministry of Education, Culture, Sports, Science and Technology. Explanatory Notes on the Curriculum Guidelines for Secondary Schools: Mathematics Edition [Z]. 2023: 87-94.

[2] National Institute for Educational Policy Research. Guide to Improving Lessons Using Formative Assessment [EB/OL]. 2024.

[3] Sato, Manabu. Designing Learning Communities [M]. Tokyo: Iwanami Shoten, 2022: 112-130.

[4] Japan Society of Mathematics Education. Research on the Contemporary Utilisation of Wasan Teaching Materials [J]. Mathematics Education, 2024(3): 15-22. (Abacus and Origami Assessment)

[5] Tanaka, Kōji. Handbook of Classroom Assessment [G]. Kyoto: Minerva Shobō, 2023: 45-59.

[6] Organisation for Economic Co-operation and Development (OECD). Social and Emotional Skills in Japanese Schools [R]. 2025: 33–41.