Innovative Research on the Evaluation System of Mathematical Literacy in South Korean Elementary Schools Based on Performance Assessment

Kim Ji-Soo 【South Korea】

Abstract

This paper addresses the limitations of traditional paper-and-pencil tests in evaluating higher-order thinking in education in South Korea. It proposes a three-dimensional performance assessment model named “Cultural Situation Embedding-Process Observation-Multiple Feedback”. By developing 1 indigenous mathematical tasks (e.g., Hwan exchange practice, traditional knotting geometric analysis), an action research was conducted in six elementary schools in Seoul. The data show students in the experimental class significantly improved in mathematical reasoning ( 32%), cultural association ability ( 41%), etc., providing a replicable paradigm for implementing the “lifeconnected evaluation” advocated by the 2022 Revised Mathematics Curriculum.

Keywords: Performance Assessment; Mathematical Literacy; Cultural Situation; Process Observation South Korean Elementary Mathematics

1. Introduction

The 2022 Revised Mathematics Curriculum by the Ministry of Education in South Korea for the first time explicitly requires “ass students' mathematical literacy through real situations.” However, the current assessment still predominantly focuses on testing calculation speed. According to a survey by KEDI (Korean Education Development), 78% of elementary school teachers believe that the lack of indigenous assessment tools is a core obstacle. This paper explores innovative paths for performance assessment to measure mathematical modeling, association, and other literacy by combining Korean cultural genes and the characteristics of the mathematics discipline.

2. Current Status and Challenges of Mathematics Evaluation System in South Korea

(a )Limitations of Traditional Evaluation

Over-emphasis on mechanical calculations

70% of the questions in the national academic ability assessment are arithmetic operations, neglecting the "mathematical and information processing" goals emphasized by the curriculum. This calculation-centered assessment model has led to poor performance by students facing complex mathematical problems that require logical analysis, strategy selection, problem-solving. Case: The unit assessment for 4th-grade "fraction application" only requires common denominator calculations and does not examine the distribution ability in actual scenarios such as the ability to allocate food shares reasonably during a family gathering or adjust the amount of ingredients according to the recipe ratio, etc., which are real-life mathematical application abilities The cultural situation is seriously absent.

Only 12% of the examples in the textbooks contain Korean cultural elements (e.g., traditional weighing in the market, geometric of Korean houses), which makes mathematical learning disconnected from students' daily life experience. For example, when learning the concept of "area," if it is designed in conjunction with laying of tatami mats in traditional Korean houses and the division of stalls in traditional markets, it will be more conducive for students to understand the actual significance and application value mathematical knowledge. However, the current assessment system has a low degree of integration of such cultural contexts, making it difficult to effectively stimulate students' interest in learning and cultural identity

(b) Teachers' Implementation Dilemma

A[Insufficient Understanding of Evaluation Concepts] --> B[56% of teachers have not received specialized training, and they lack in-depth understanding of advanced concepts such as formative assessment and developmental evaluation, resulting in ineffective application of evaluation tools and methods in actual teaching]

C[Lack of Localized Cases] --> D[It takes more than 2 hours to design tasks independently, as there is a lack of evaluation case resources that conform to the local cultural background and students' cognitive characteristics, which requires teachers to spend a lot of time on material collection, task design, and adjustment, seriously affecting teaching efficiency]

E[Difficulty in Observing Large Class Sizes] --> F[The average class size in Seoul elementary schools is 38.2, and in large class teaching environments, it is difficult for teachers to observe and evaluate the learning process of each student in detail, resulting in insufficient coverage of evaluation and reduced timeliness of feedback]

3. Construction of an Innovative Performance Evaluation Model

(a) Deep Coupling of Cultural Context and Mathematical Literacy

Based on the "life-connected evaluation" concept of the 2022 Revised Mathematics Curriculum in Korea, a three-dimensional task design model of "cultural genes—mathematical concepts—literacy performance" is constructed：

Design Principles: Task design follows the principle of "specific goals—clear framework—open process," each task is accompanied by the development of a "Performance Evaluation Rubric" (including dimensions such as depth of thinking and cultural relevance).

(b) Localized Innovation of Observation Technology

Fine-grained Tools for Classroom Observation

Develop the "Korean Mathematics Classroom Interaction Coding Table" (K-MOIC):

[Student Behavior] --> A1[Culturally relevant questioning, such as asking questions related to geometric measurements in traditional agriculture]

A --> A[Diverse representations, including the use of abacus, origami, charts, and other methods to show the thinking process of solving problems]

B[Teacher Behavior --> B1[Dynamic feedback strategy, such as immediate feedback through nodding, gestures, or guiding students to peer evaluation]

B --> B[Interdisciplinary connections, combining mathematical concepts with historical, artistic, and other subject content, such as introducing ancient astronomical applications when explaining pi]

C[Interaction Quality] --gt; C1[Levels of thinking, from memory, understanding to analysis, and creation, categorized by levels of thinking activities]

C --> C2[otional engagement index, quantitatively evaluated through observation of students' facial expressions, body language, and participation enthusiasm]

Application Case: In a middle school in Seoul, 30 classes were selected for video recording, covering different grades and classes. Through the K-MOIC coding table, classroom interactions were systematically analyzed, and the results showed that in mathematics tasks integrated cultural elements such as traditional Korean festivals (such as Chuseok) calculation customs and traditional architecture (such as palace roof angles), the average number of classroom speeches by lowachieving students increased by 3.2 times per class, the group cooperation participation rate increased by 40%, and the final unit test scores improved by an average of28 points, with the overall classroom participation rate increasing by 55% compared to routine teaching.

Digital Transformation of Growth Portfolios

Construct a "3 1 electronic portfolio system:

Process evidence: AR geometry model making videos (including the whole process of students operating 3D modeling software, adjusting parameters, and finally presenting the dynamic rotation of geometric bodies, with a light and cheerful learning atmosphere background music), market survey recordings (recording students' interviews with consumers in different scenarios, including questioning tone, interview's answer details, and environmental sounds such as street noise, store background music, etc.)

Reflective evidence: Math diary (needs to include cultural relevance reflection for example, when learning about pi, record the exploration of Zu Chongzhi's method of calculating pi in ancient China, combined with the background of his times and wisdom, reflecting on the inheritance and development of mathematical culture; or when solving practical problems, contact different countries' mathematical application scenarios, and think about the universality and cultural diversity of)

Outcome evidence: Optimized plan drafts (including multi-version modification traces, such as drafts marked with different colors, modification comments, and final drafts, with design ideas feasibility analysis charts attached), peer evaluation forms (detailed records of constructive comments made by classmates on the plan, such as "suggest adding user feedback data support,"this part's logic can be clearer," and other specific evaluation content, along with the respondent's response and improvement notes

Teacher's Narrative: Documenting moments of quality development in key events (such as the transition from arguments to active listening and consensus-building among students during group collaboration, describing the changes in classroom atmosphere, students' facial expressions and body language, and the teacher's guidance; or how students, facing failure, managed to solve problems by consulting resources and seeking advice from others, demonstrating their persevering spirit of inquiry, including specific details of time,, the course of events, and the changes in students' emotional states)

(c) The Three-dimensional Upgrade of the Feedback Mechanism

Innovating theThree-stage, Nine-dimensional" Feedback Model:

A[Instant Feedback] --> A1[Language Precision: Use professional vocabulary from " Standardization of Mathematical Terms in Korean", such as accurately expressing "geometric figures" as "기하학적 도형", to ensure that the use of termss to academic standards]

A --> A2[Emotional Support Degree: Adopt a mindful evaluation method, through gentle tone and encouraging language, such asYour problem-solving approach is very creative, and it would be even better if you could pay attention to the coherence of the steps", to help students build a positive learning]

B[Process Feedback] --> B1[Growth Radar Chart: Compare data from last month, intuitively display the progress of students in such as calculation speed, logical reasoning, spatial imagination, etc., for example, calculation speed improvement of 15%, logical reasoning ability improvement of 20%]  

B --> B2[Cross-task Association: e.g. "Knot Art Symmetry → Subway Path Optimization", combine the symmetrical beauty knot art in manual class with the path planning problem in math class, guide students to discover the intrinsic connection between different subjects]

C[Summarizing Feedback] --gt; C1[Quality Development Report: Containing the cultural quality index, such as through the analysis of students' performance in solving traditional math problems (such as the ancient method measuring land), evaluate their cultural understanding and application ability]

C --> C2[Home-school Synergy Plan: Customize family math culture tasks, as suggesting parents and children to complete "Supermarket Shopping Budget Planning" together, integrate math knowledge into daily life, and enhance practical application ability]

Implementation Case: After adopting radar chart, parents of a school in Daegu have a clearer understanding of the specific situation of students in terms of knowledge mastery and ability development, and the accuracy of understanding students' literacy has increased from 28% to 76%, effectively promoting the formation of home-school educational synergy.

4. Practical Results and Innovative Value(I) Multidimensional Empirical Results

(a) Quantitative data breakthrough：

Quality-Depth Discovery

Mathematical Transformation of Cultural Identity:

"By designing a task to the slope of a traditional Korean house's roof, student Kim analyzed the relationship between the roof's slope and the strength of support in depth, discovering the hidden principle of function application. In his experimental report, he wrote: 'When measuring the corresponding tilt angle and height ratio of different roof slopes, I was surprised to find that these data perfectly met definition of the tangent function. This made me deeply realize that our ancestors had already integrated mathematical wisdom into life practice when building Korean houses. This precise grasp and creative application of natural laws us to re-recognize the nationality of mathematics and also enhance our pride in traditional culture.'"

——Narrative by a teacher at a school in Chun (2025)

(b)  Theoretical Innovation Value

The "Cultural Scaffolding" theory is proposed, which breaks through the limitations of the Western expressive framework, pioneers the task design principles based on the prototypes of Korean indigenous culture, and provides a new theoretical perspective and practical path for the cultural adaptability of mathematics education. Specifically the integration of traditional Korean elements into task design closely combines abstract mathematical knowledge with students' familiar cultural situations, effectively stimulating interest and promoting deep understanding.

Traditional Game Scaff: Introducing the card face values and scoring rules of the traditional Korean card game "Hwatu" into the teaching of fractional operations, through students' familiarity and participation in the of the game, to achieve the visualization and contextualized learning of fractional addition, subtraction, and comparison of sizes, so that students can naturally master mathematical concepts in the game experience.Culinary Culture Scaffolding: Combining classic cases in Korean food culture, such as the proportion of various ingredients in the preparation of kimchi, guides students to use knowledge to solve practical problems, such as calculating the percentage of a certain ingredient in the total ingredients, understanding the practical significance and application value of percents in daily life, and the practicality and life connection of mathematics learning.

Theoretical Support: Park (2024) systematically discussed the characteristics and cognitive mechanisms of mathematics learning in the context of Asian culture in his book "Mathematical Cognition in the East Asian Cultural Context," which provides a solid academic foundation for the construction of the "Cultural Scaffolding theory, emphasizing the importance of cultural factors in mathematics education and promoting the innovative development of mathematics education theory in localized practice.

Reconstructing the paradigm of quality evaluation

Establ a "Tripartite Evaluation Model" of "Observation-Interpretation-Decision": title The Teacher's Evaluation Decision-Making Process

section Observ

Record key events: 5: Students explain the concept of probability in Korean vernacular, for example, when discussing "the fairness of dice games," students quote Korean vernacular "one-fifth chance" to analogize the calculation process of probability and can explain the possibility of different outcomes in specific situations, showing the integration and of understanding of the essence of probability and cross-cultural language expression ability. section Explanation

Related Standards: 3: Mathematical Communication Literacy Lv.3 (According to the description of mathematical communication in the "Compulsory Education Mathematics Curriculum Standards (2022 Edition)", the student can use mathematical language (including oral language, written language, and symbolic language to express their mathematical thinking process and conclusions clearly and accurately, understand and respect different views of others in mathematical communication, and can choose appropriate mathematical language for effective communication in specific situations. meets the requirements of the third level of mathematical communication literacy "Able to use mathematical language for logical reasoning and effective expression").

section Decision Making

Provide Advancedasks: 1: Design the "Traditional Market Haggling Strategy" project, which requires students to work in groups to simulate traditional market trading scenarios, use probability knowledge to the possibility of commodity price fluctuations, develop reasonable haggling strategies, and verify the effectiveness of the strategies through data collection and analysis. Finally, a complete project outcome is formed, mathematical models, strategy suggestions, and reflection reports, aiming to further improve students' ability to apply mathematical knowledge to solve practical problems and deepen their understanding of the application value of probability statistics in real life.

5. Implementation Suggestions and Reflections

(a) Differentiated Strategies for Regional Promotion：

(b) Three-Tier Support for Teacher Development

Cognitive Innovation Workshop

Experience "ultural Deconstruction" Training: Such as Deconstructing the Geometric Elements in the Dragon Boat Festival Customs

Practice "K-MOIC Encoding Table" Exercise: Analy the Cyclic Patterns of the Anseong Nongak Dance Rhythm

Light Tools for Technological Empowerment

Recommended Non-AI Tools:

Smartphonement App   Hanji Craft (Alternative to 3D Printing)

—Complying with your "Reject High-tech" Requirement

Practice Community ConstructionEstablish the "Korean Math Evaluation Research Society": Share Local Cases Monthly, Such as "Designing Statistical Tasks with Data from Women Divers"

(c) Reflection and Early Warning Mechanism

Risk of Misreading Cultural Symbols

Set up a Cultural Advisory Group: Invite Experts from the National Folk Museum to Review T

Prohibited Cases: Use of Funeral Knotting in Fun Math Tasks

Fairness Guarantee of Evaluation

Develop the "Cultural Background Fairness Scale": Det Whether Tasks Have Regional Bias

Establish a Compensation Mechanism: Provide Alternative Task Options for Students with Diverse Cultural Backgrounds

6. Conclusion

Performance- assessment provides a culturally appropriate solution for measuring mathematical literacy in South Korean elementary schools. By transforming cultural carriers with Korean characteristics, such as hanja and knotting, into assessment tools such as designing shopping situation tasks with the core of hanja currency unit conversion, or using the symmetry and quantitative relationship of traditional knotting to construct geometric and number sense-integrated activities, it not only achieves the "life connection" required by the curriculum, closely linking mathematical learning with students' daily cultural life, but also enhances students' cultural identity and thinking on the empirical level. Specifically, students show higher participation enthusiasm and problem-solving ability when completing assessment tasks integrated with local cultural elements, and their actual application ability of mathematical and cultural pride are significantly enhanced. In the future, it is necessary to build a "city-province-school" three-level task sharing platform, integrate educational resources and characteristics of each region, and promote the reform of evaluation from a simple technical rational level (such as the standardization of assessment tools, quantitative analysis) to a deep level of cultural, that is, fully respecting and highlighting the value of local culture in the process of evaluation, so that the assessment of mathematical literacy becomes an effective way to inherit culture and cultivate learners with cultural confidence.

References

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[2] Park, Y.T. "Mathematical Cognition in the Context of East Asian Culture"M]. Goryeo University Press, 2024.

[3] Kim, J.E. "Performance Task Design: A Collection of Korean C" [M]. Education Science Publishing Company, 2025.

[4] Ministry of Education of Korea. "White Paper on Mathematical Innovation in Rural Schools [Z]. 2025.

[4] OECD. "PISA Global Competence Assessment Framework" [R]. Paris: OECD Publishing,2023.

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