Construction and Practice Research of Hierarchical Evaluation Model for Mathematics in Korean Middle Schools Based on Situation Background

Zheng Zhengmin  【Korea】

Abstract

This paper aims to address the problems of excessive emphasis on mechanical operations and neglect of thinking processes and applications in mathematics assessment in South Korea. By integrating the "life-connected evaluation" philosophy of the "2022 Revised Mathematics Curriculum", this study constructs acultural situation embedding-process tracking-differentiated feedback" three-dimensional evaluation model. Through the development of localized assessment tasks, such as Korean traditional house geometry analysis and traditional market application, action research was conducted in six middle schools in Seoul and Busan. The data show that students in the experimental class have significantly improved in mathematical modeling ability ( 36%) cultural relevance awareness ( 43%), providing an innovative path to solve the "only computing speed" evaluation dilemma.

Keywords: Cultural situation; Hierarchical evaluation; Process; Korean mathematics education; Differentiated feedback

1. Introduction

The "2022 Revised Mathematics Curriculum" of the Korean Ministry of Education clearly proposes to " students' mathematical literacy through real situations". However, there are still three major discontinuities in the current assessment:

Goal Discontinuity: 68.7% the questions in the national proficiency assessment focus on the speed of four-arithmetic operations, which is out of touch with the "reasoning-modeling-application" goals advocated the curriculum. This is reflected in the excessive proportion of mechanical calculation questions, such as 72% of the questions in the fraction operation section of the elementary school stage directly examine steps of generalizing and simplifying, while less than 15% of the questions involve solving actual problems, resulting in students' difficulty in transferring mathematical knowledge to real problems

Cultural Discontinuity: The assessment content generally adopts internationalized situations (such as Euro exchange rate, international competition scores), lacking mathematical deconstruction of local cultural elements such Korean traditional clothing proportions, traditional architecture (such as geometric symmetry in the palace structure of Jingfu Palace), and Korean food ratios (such as the weight distribution of bibimb ingredients). For example, in the statistics and probability module, only 3% of the questions involve Korean local cultural data, while more than 60% of the questions foreign holiday and sports competition data, making it difficult for students to establish a sense of meaning in mathematical learning within cultural identity.

Disparity Discontinuity: The unified test intensified the frustration of students with learning difficulties (according to the survey by the Korea Education and Development Institute KEDI, the rate of math aversion among junior two students has 41%). This "one-size-fits-all" assessment method ignores the individual differences of students with different cognitive levels. Students with learning difficulties are prone to a negative perception of "math is useless" when facing questions beyond their ability, which in turn forms a vicious cycle. For example, in the concept evaluation of functions, students are to establish a quadratic function model according to complex real-life situations, and the correct rate of students with learning difficulties is only 12%, while such questions account for as as 25% of the total score, significantly increasing their learning pressure.

This study reconstructs the assessment system based on local cultural genes, responding to the call of curriculum to "root mathematics in the soil of Korean culture". By exploring the proportion calculation in the production of Hanbok, the periodic law in traditional agricultural activities, and the spatial in folk festivals and celebrations, we design mathematical tasks with cultural recognition, aiming to achieve the unity of assessment goals and curriculum philosophy, the integration of cultural identity and mathematical ability, the balance between differentiated needs and the principle of fairness, and ultimately promote the comprehensive development of students' mathematical literacy.

2. Current Situation and Innovative Direction of Assessment in Korea

2.1 Analysis of the limitations of traditional assessment：

2.2 Theoretical Foundation of Cultural Situation Assessment

Cultural Responsive Teaching Theory (Kim, 023): Mathematical assessment should carry the cognitive transfer function of cultural symbols. This theory emphasizes the integration of cultural symbols and life situations familiar to students into mathematical assessment, such using symmetrical patterns from traditional festivals, geometric structures from folk crafts, and spatial layouts of local characteristic architecture as assessment materials. It guides students to achieve the cognitive transfer from cultural to mathematical concepts in the process of solving mathematical problems. For example, when assessing "Translation and Rotation of Figures," a task can be designed with the transformation of patterns paper-cutting art as the background, allowing students to not only master mathematical knowledge but also deeply understand the mathematical wisdom contained in cultural symbols, thus enhancing cultural identity and interest in learning It makes the assessment process an organic unity of cultural inheritance and the development of mathematical thinking.

Process-tracing Evaluation Model (Park, 2024): Replace singleresult judgment by multi-time point observation of thinking development trajectory. This model advocates breaking the limitations of "one test determines everything" in traditional assessment by setting multiple key time nodessuch as the beginning, middle, end, and expansion stages of unit learning) in the teaching process to continuously and dynamically observe and record students' thinking processes in solving mathematical problems., students' changes in problem-solving strategies can be recorded through classroom observations, their cognitive confusion can be understood through interviews, and their logical construction process can be analyzed through collecting' draft paper and concept maps. This systematically traces students' thinking development trajectory from intuitive perception to abstract generalization and from single method to diverse strategies. For example, in the unit of "Fraction Division," not only the accuracy of students' final calculation results is concerned, but also the depth of students' understanding of "the meaning of division," diversity of problem-solving strategies, and the transformation of error types at different time points are compared to fully describe the growth path of their mathematical thinking, thus providing a basis for improvement.

3. Innovative Construction of a Three-dimensional Evaluation Model

3.1   Design of Cultural Situation Carrier

Based on Korean cultural symbols, develop a "-level situation task library":

A[Living Culture] --> B[Discount rate calculation in traditional market (comparing supermarket vs. market prices)]

[Material Culture] --> D[Angle measurement of the eaves of a Korean house (combined with the Pythagorean theorem)]

E[Spiritual Culture --> F[Geometric symmetry analysis of the letters in "Training the People with Correct Sounds"]

The cases provide more targeted evidence, realizing the transformation of from "result-oriented" to "process-oriented."

Case:

Elementary task: Calculate the golden ratio of the hem of a traditional Korean Chogori (top) (Integ similar figure knowledge)

In the design of traditional Korean Chogori (top), the shape of the hem often embodies subtle aesthetic proportions. Taking the hem of a typicalogori as an example, its edge profile can be approximately regarded as composed of multiple similar geometric figures, such as trapezoids, sectors, or combinations of curved segments. By the width data at different positions of the hem, such as the vertical distance from the waist to the bottom of the hem as L, and the horizontal width of the hem at the positions are a, b, c (where a is the width at the narrowest part of the waist, c is the width at the widest part of the hem bottom, b is the width at a certain key position in the middle), it can be known from the nature of similar figures that the ratio of these widths to the corresponding heights satisfies the or nonlinear change law. Further, the width change curve of the hem is abstracted as a continuous function f(x), where x is the distance from the waist to the of the hem, and f(x) is the width at the corresponding position. According to the definition of the golden ratio (about 0.618), it necessary to find two key width values on the hem, so that the ratio of the length of the smaller interval to the length of the larger interval is close to 0.68. For example, if there exist positions x1 and x2, such that the ratio of f(x2)-f(x1) to f(x1) close to 0.618, then it can be verified that the hem design conforms to the golden section aesthetics. This task not only requires students to master the determination properties of similar figures, but also to combine the idea of function modeling, to transform the actual clothing structure into a mathematical problem for solution, and deeply understand the application of the golden in traditional art.

Advanced task: Optimize the packaging plan for Jeju citrus (Integrating solid geometry and function extremum.

As a famous citrus-producing area in Korea, Jeju Island needs to transport a large amount of citrus in boxes every. In order to reduce transportation costs and improve space utilization, it is necessary to design the optimal boxing scheme. Suppose the citrus is a sphere with a diameter of d, and the is a cuboid with an internal size of length l, width w, and height h. First, from the perspective of solid geometry, there are two dense packing methods for the in the cuboid: one is simple cubic packing (each sphere is located on the grid point), and the other is hexagonal close packing (more space-saving). simple cubic packing, m×n spheres can be placed on each layer, where m=⌊l/d⌋, n=⌊w/d⌋, the number of layers=⌊h/d⌋, and the total number N1=m×n×k. For hexagonal close packing, the spheres on each layer are arranged in a honey pattern, and the spheres on adjacent layers are placed staggeredly. At this time, the number that can be placed on each layer is slightly more than simple cubic packing, and height of every two layers in the height direction is √(3)/2 d, so the number of layers k'=⌊h/(√(3)/2 d)⌋ and the total number N2 needs to be calculated according to the specific arrangement. Next, the objective function is established: maximize the total number of citrus N under the constraint of the box volume V=l×w×h (or the load limit of the transport vehicle). Let the ratio of length, width, and height of the box be a::c (a,b,c are constants), then l=a×t, w=b×t, h=c×t (t is the proportionality coefficient, substitute into the expression of N, and get the function N(t) about t. By finding the derivative N'(t) and setting it equal to 0, the point of the function N(t) can be obtained, and then the optimal t value, that is, the optimal box size ratio, can be determined. In addition, it also necessary to consider the actual size difference of citrus, introduce the error range, and adjust the expected value of the number of boxing by the probability model. This task comprehensively uses space-filling problem in solid geometry, the solution of function extreme value, and the treatment of constraints in actual problems to cultivate students' ability to integrate multi-disciplinary knowledge and complex real-world problems.

3.2  Process Tracking Evaluation Tools

Development of dynamic observation scale:

Visualizing the Thought Process Tool

Origami Protocol Method: Folding Korean paper to record the path of solving geometric problems (such as steps in proof)5

Audio Diary: Recording audio of problem-solving ideas (e.g., "How I used ratios to calculate the interval relationship of musical instruments ancestral temple rituals")

3.3  Differentiated Feedback Mechanism

Constructing a "Dual-Channel Feedback System":

A[Instant Feedback --> A1[Cultural Metaphor Prompt: "Like maintaining the balance of the equation as in making kimchi"]  

A -->2[Error Type Marking: Symbol “❊” = Cultural Situation Misreading]  

B[Long-term Feedback] --> B1[Personized Growth Map: Labeling “Traditional Pattern Design Capability Progress”]  

B --> B2[Cultural Application Portfolio: Collecting physical outcomes as market research reports]  

4. Practical Effectiveness and Reflection

4.1  Quantitative Effect Verification:

4.2 Qualitative Outcome Analysis

Enhanced Student Cultural Identity

"I used to think mathematics was just about solving problems, but now I can use it to analyze the structural design of Korean houses – it turns out our ancestors have been using the Pythagorean theorem since they building houses!"

——Interview record of students from Busan Experimental School (October 2025)

During the course implementation, students' sense of identity with the culture significantly enhanced. By combining mathematical knowledge with cultural elements such as Korean house architecture and traditional crafts, students not only mastered mathematical concepts like the Pythagorean theorem and geometric figures also gained a profound understanding of the application value of mathematics in traditional culture. For example, when exploring the design of the roof slope of a Korean house, students used trigonometric to calculate the stability of different angles and discovered that the slope ratio formed by traditional craftsmen through empirical accumulation highly coincided with mathematical principles. This discovery stimulated students' sense pride in local wisdom. In addition, the course also introduced the application of mathematics in traditional farming, such as the calculation of farm tool dimensions and the planning of crop planting area, enabled students to recognize that mathematics is an important tool that runs through daily life and cultural heritage, thereby enhancing their cultural identity and confidence.

Teacher's Assessment Paradigm Shift"Process tracking has allowed me to discover: calculation errors often occur after cultural understanding deviations, which overturns the previous grading method that only focused on numbers."

—— Feed from Daegu Teacher Training Workshop

Curriculum reform prompts a fundamental shift in teachers' assessment paradigms. In traditional teaching, teachers often focused on whether students' calculations were, while neglecting the depth of cultural understanding and the thinking path during the process of knowledge acquisition. By introducing process-oriented assessment tools such as learning logs, group discussion records, and project reports, teachers can comprehensively track students' performance in solving mathematical problems integrated with cultural elements. For example, when analyzing the mathematics problems in traditional festival celebrations, teachers found that students had deviations in data collection and model construction due to insufficient understanding of festival customs, which affected the final calculation results. This discovery made teachers realize that cultural understanding is the foundation mathematics learning, and assessment should shift from a single result-oriented approach to focusing on students' cultural cognition, problem-solving strategies, and interdisciplinary thinking abilities. Teachers to adopt more inclusive evaluation criteria, encouraging students to incorporate cultural perspectives into their mathematics learning and guiding students to deepen their understanding of the relationship between culture and mathematics through diversified methods, thus achieving a virtuous cycle of integrated teaching and assessment.

4.3  Reflection and Challenges

Existing problems

Cultural context task development is time-consuming (averaging 6.5 hours per task), mainly reflected in the in-depth mining of cultural elements, the precise integration of mathematical knowledge points, and the repeated pol of task logic, which requires multi-party collaboration among educators, cultural researchers, and mathematics experts, resulting in a longer development cycle. Rural school cultural resource acquisition is limited (such the lack of traditional architectural cases in Jeju Island schools), due to remote geographical locations, economic constraints, and insufficient awareness of cultural heritage, many rural schools find it difficult to rich local cultural resources, such as geometric structures in traditional architecture, quantitative relationships in folk activities, etc., which directly affects the diversity and authenticity of cultural context tasks. Optimization path

Establishing a "Korean Mathematical Cultural Resource Database" (integrating digital exhibits from national museums, cultural relics data from local cultural centers, non-legacy databases, etc.), through systematic collection and digital processing, categorizes and stores and shares Korean mathematical cultural resources from all over the country, providing educators with convenient sources of materials shortening task development time. Developing a "Mobile Math Culture Workshop" for use in remote areas, using portable multimedia devices, online interactive platforms, and mobile display and teaching materials transforms the content of the Math Culture Database into interactive experience projects suitable for classroom and extracurricular activities, allowing rural school students to closely contact and experience local math culture,ating for geographical limitations in the acquisition of cultural resources.

Conclusion

The deep coupling of local cultural context and hierarchical assessment has shifted mathematics assessment from "cold, hard numerical games" "warm, cultural practices." In the future, it is necessary to further explore: how to balance the assessment weights of traditional culture and modern mathematical ideas? How to convert "allyu" cultural elements into mathematical modeling materials? This is not only the deepening direction of assessment reform but also a vivid application point of cultural confidence in mathematics education.

References

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[4]Ministry of Education of Korea. National Report on Mathematical Proficiency Assessment [R]. 2025: 17-21.

[5] Choi, Sang-Ze. Hands-on Mathematics: Mathematical in Traditional Crafts [M]. Pusan National University Press, 2022: 77-85.

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