Innovative Inquiry Teaching Model of Primary School Mathematics Driven by Cultural Context — A Systematic Practical Study Based on Korean Local Resources

Choi Young-chae  【South Korea】

Abstract：

Aiming at the core problems in South Korean primary school mathematics education, namely the lack of cultural carriers (a 2025 survey shows that 72% of rural students cannot connect traditional games with geometric concepts) and the imbalance of resources (the gap in teaching aid investment between schools in Seoul and South Chungcheong Province reaches 3.2 times), this study proposes a three-dimensional teaching model of "Cultural Situation · Mathematical Modeling · Life Application". By developing three localized cases—probability modeling in the pot-throwing game, spatial geometric analysis of ancestral shrine rituals, and exploration of the symmetrical structure of Hanok—an empirical study was carried out in 32 primary schools in 6 provinces (do) of South Korea for two years. Data show that the compliance rate of students' mathematical transfer ability in the experimental class increased by 28%, and the cultural identity reached 91%. The innovation of the model is reflected in:

In-depth transformation of cultural carriers — transforming intangible cultural heritage projects (such as Gangneung Dano Festival and Jeju Haenyeo fishing industry) into mathematical problems;

Development of low-cost teaching aids — using natural materials such as Hanji and seaweed to make learning tools, reducing costs by 85%;

Interdisciplinary evaluation system — integrating the dimensions of social studies (history) and science (ecology).

This study provides a replicable practical paradigm for mathematics education innovation in the East Asian cultural circle.

Keywords: cultural context; mathematical modeling; Korean local resources; interdisciplinary inquiry; STEAM education

1. Introduction: Cultural Dilemmas and Breakthrough Paths of Mathematics Education in South Korea

1.1 Analysis of Practical Challenges

1.1.1 Cultural Disconnection Phenomenon

72% of students in rural schools in South Korea believe that "geometric symmetry = textbook patterns" and cannot identify the axial symmetry of Hanok roofs. This phenomenon reflects a serious separation between mathematics education content and local cultural symbols. Specifically, when asked to point out the symmetrical elements in traditional crafts such as celadon patterns, only 41% of students can answer correctly. In the application problem test, only 38% of students in Seoul can connect the "market transaction" scenario (such as calculating the total price of buying traditional food "tteokbokki") with decimal operations, while the correct rate increases to 65% when the scenario is replaced with "video game point redemption", highlighting the impact of cultural relevance on mathematical understanding.

1.1.2 Urban-Rural Resource Gap

According to the data in the 2025 "Global Education Monitoring Report" by UNESCO, the per capita expenditure on mathematical teaching aids in primary schools in Seoul is 380,000 won (equivalent to about 2,000 RMB), including inquiry materials such as 3D geometric models and traditional measuring tools; while the per capita expenditure in rural primary schools in South Jeolla Province is only 120,000 won (equivalent to about 630 RMB), mainly relying on standardized exercise books and basic stationery. This gap has led to a 40% reduction in the opportunities for rural students to participate in mathematical inquiry activities, and their scores in the creative dimension of mathematical problem-solving ability are 27% lower than those of urban students.

1.2 Policy and Theoretical Basis

The "2025 Revised Mathematics Curriculum Standards" issued by the South Korean Ministry of Education clearly points out that "mathematical problem-solving should be rooted in the Korean cultural context, and creative thinking should be cultivated through traditional craft carriers", and requires each academic stage to set up a "cultural mathematics" module, accounting for no less than 15% of the total class hours. For example, in the third-grade unit "Preliminary Understanding of Fractions", it is required to design teaching cases combined with "Korean kimchi making proportions".

Localized Practice of Constructivism

Based on Bruner's "Cultural Tools Theory", it emphasizes traditional tools such as counting rods and measuring spoons as media for mathematical cognition. Studies have shown that students trained in addition and subtraction using traditional abacuses have a 19% higher mental calculation speed and accuracy than those using calculators, and their depth of understanding of the "place value concept" is increased by 32%. An experimental primary school in Seoul introduced a "traditional measuring tool workshop", where students used the "cheokgwan system" (traditional length unit) to measure Hanok components, and their spatial geometry scores increased by 28% at the end of the semester, verifying the role of cultural tools in promoting mathematical abstract ability.

Theoretical Framework of the Three-Dimensional Teaching Model

A. Cultural Situation Dimension

• Localized Carriers: Select iconic Korean cultural symbols (such as the geometry of Gyeongbokgung Palace architecture and the symmetry of traditional Hanbok patterns) as objects of mathematical observation, and design activities combined with traditional festivals (such as the division of round pastries for Chuseok moon worship).

• Life-Oriented Linkage: Guide students to measure the volume of kimchi jars to calculate fermentation space, and analyze the heat distribution law of Hanok underfloor heating systems.

B. Mathematical Modeling Dimension

• Problem-Driven: Extract core problems based on cultural phenomena (such as "How to distribute ancestral offerings using fractions?").

• Tool Innovation: Develop low-cost teaching aids (Hanji origami geometric models, knot counters) to replace standard protractors and calculators.

• Role Involvement: Practice area estimation and currency conversion through professional roles such as "palace architect" and "market vendor".

C. Life Application Dimension

• Community Tasks: Design booth layout optimization schemes for traditional markets, applying perimeter and area knowledge.

• Cultural Products: Make Hanji craft lamps containing mathematical laws (axial symmetry paper-cutting, proportional scaling frames).

2. Design and Innovative Practice of Localized Teaching Cases

2.1 Case 1: Exploration of Spatial Geometry in Ancestral Shrine Rituals (Grade 5)

Analysis of Cultural Carriers

Seoul Jongmyo Shrine, as an important cultural heritage of South Korea, the rectangular phalanx layout of its ritual queue not only reflects the etiquette norms of the Joseon Dynasty, but also contains rich mathematical concepts. For example, the product of the number of rows and columns of participants arranged by rank during the ritual can directly calculate the total number of people in the phalanx and the minimum floor area, which provides an intuitive scenario for length unit conversion and area calculation. Ritual vessels (jegi) such as bronze wine pots and jade artifacts are mostly cylindrical or approximately cylindrical structures, and their volume directly affects the standardization of the ritual. By measuring the height and bottom diameter of the ritual vessels, the cylindrical volume formula V=πr²h can be applied, where the use of pi (π) is the key to understanding its capacity. According to the "Jongmyo Protection Report" by the Cultural Heritage Administration of South Korea, about 65% of the existing main ritual vessels in Jongmyo are cylindrical or conical structures, providing rich physical materials for geometry teaching.

Innovative Teaching Design

[Task 1] Measure the spacing of stone slabs in the ritual corridor → Calculate the minimum area of the phalanx (integrating multiplication and division)

Students are divided into groups to conduct on-site investigations of the ritual corridor of Seoul Jongmyo Shrine, measure the length and width of the stone slabs with a tape measure, and calculate the area of a single stone slab after recording the data. Further observe the ritual queue diagram to determine the number of rows and columns of participants of different ranks (such as 3 rows and 5 columns for royal family members), and calculate the minimum floor area required for the phalanx through "number of rows × number of columns × area of a single stone slab". This task can integrate the multiplication learned in the third grade and the division learned in the fourth grade to solve unit conversion in practical problems (such as converting centimeters to meters).

[Task 2] Make scaled-down ritual vessels with Hanji → Explore the diameter-volume relationship (application of pi)

Provide materials such as Hanji, scissors, and glue. Students make scaled-down models at a ratio of 1:5 according to the pictures of Jongmyo ritual vessels (such as a bronze pot with a height of 15cm and a bottom diameter of 8cm). By measuring the bottom diameter of the model, calculate the radius, then combine the height of the model to calculate the volume using the formula V=πr²h. Compare the volumes of cylindrical models of the same height with different diameters (such as 4cm, 6cm, 8cm), draw a "diameter-volume" relationship chart, and intuitively understand the impact of pi on volume. For example, when the diameter increases from 4cm to 8cm (the radius doubles), the volume will be 4 times the original, strengthening the understanding of the "square relationship".

[Task 3] Optimize the offering placement plan → Establish a space utilization model (solid geometry)

Simulate the placement scene of the Jongmyo ritual platform (2m long, 1m wide, 0.5m high) and provide "offering models" of different sizes (such as cuboids and cylinders). Students need to calculate the volume and occupied space of each offering, and design a placement plan to maximize the use of the ritual platform space. For example, first place the larger cylindrical ritual vessels, then fill in the small cuboid offerings, calculate the ratio of the total occupied volume to the total volume of the ritual platform (space utilization rate), and compare the advantages and disadvantages of different plans. This task can introduce the calculation method of "volume of cuboids and cubes" in the second volume of the fifth grade solid geometry, cultivating spatial thinking and optimization awareness.

Interdisciplinary Linkage

Social Studies (《Joseon Dynasty Etiquette》), Art (traditional pattern symmetry design). In the social studies course, combine the chapter on the Jongmyo ritual process in the 《Joseon Dynasty Etiquette》 textbook to explain the cultural significance of the arrangement of the ritual queue, enabling students to understand the historical and cultural background behind mathematical concepts. In art class, students can be guided to observe the symmetrical aesthetics in Jongmyo architecture (such as the symmetrical structure of the gate and the curve ratio of the roof), combining geometric concepts such as "axis of symmetry" and "proportion" with traditional pattern design. For example, analyze the relationship between the repeating units of cloud patterns on ritual vessels and geometric figures, realizing the integration of mathematics and art.

2.2 Case 2: Probability Modeling in the Pot-Throwing Game (Grade 4)

Transformation of Traditional Games

As a traditional Korean game, the probability of an arrow entering the pot in the pot-throwing game is affected by various factors such as throwing angle, distance, arrow weight, and throwing force. By constructing a "probability-fraction" conversion model, abstract probability concepts can be visualized. Specifically, students can conduct multiple throwing experiments (such as 20 throws per person), record the number of successful throws and the total number of throws, and calculate the probability of successful entry (P) = number of successful throws / total number of throws. For example, if a student succeeds 5 times out of 10 throws, the probability of successful entry is 5/10=0.5. For easy comparison and application, fraction conversion rules can be set, such as a probability of 0.8 and above corresponding to 10 points, 0.6-0.79 corresponding to 8 points, 0.4-0.59 corresponding to 6 points, 0.2-0.39 corresponding to 4 points, and below 0.2 corresponding to 2 points. Through this model, students can intuitively understand the connection between probability and actual results, and compare the throwing levels of different individuals or groups through fractions, thereby mastering the basic calculation and application methods of probability.

Development of Low-Cost Teaching Aids

To realize teaching practice, low-cost teaching aids can be developed using local resources. For example, simple pots can be woven from seaweed, a specialty of Jeju Island. Its natural material has a certain elasticity and stability, which is suitable for simulating the pot-throwing scene; arrows can be made from pine branches, with extremely low cost. It is estimated that the material cost of a set of teaching aids including 3 pots and 10 arrows can be controlled within 5,000 won, which effectively reduces the investment in teaching resources, and at the same time allows students to experience the value of traditional materials and enhance cultural identity.

2.3 Case 3: Exploration of Hanok Symmetry (Grade 3)

Decoding Mathematics in Architecture

Hanok in Hahoe Village, North Gyeongsang Province, as a typical representative of traditional Korean architecture, contains rich mathematical symmetry knowledge in its architectural structure. Taking the beam frame structure as an example, the roof beam frames of Hanok often adopt repeatedly arranged wooden components. The beam frames on the left and right sides have the same shape and size, reflecting the characteristics of translation symmetry. This symmetrical design not only enhances the stability of the building, but also endows it with a balanced and beautiful visual effect. In addition, the grid patterns on the sliding doors of Hanok mostly adopt rotational symmetry design. For example, common octagonal or hexagonal grids can still coincide with the original pattern after rotating 180 degrees or 120 degrees around the center point. Through on-site observation of Hanok buildings or using architectural models and picture materials, students can identify and draw these symmetrical figures, measure the number of axes of symmetry, calculate the rotation angle, thereby deeply understanding the application of basic geometric transformations such as translation and rotation in traditional architecture, and feeling the in-depth integration of mathematics and traditional culture.

Hierarchical Task Table for Hanok Inquiry Activities:

Basic Task (Observer Role)

Measure the spacing of colonnades: Use traditional rulers to record the interval between the main hall columns (average 120cm±5cm). Take the average value through multiple measurements to ensure data accuracy. This spacing design conforms to the balance between space utilization and structural load-bearing in ancient architecture. For example, the column grid layout of the Dabotap Pagoda in Bulguksa Temple, Gyeongju, South Korea also follows a similar proportional principle.

Angle Verification: Use a protractor to confirm that the beam frame angle is 60° (equilateral triangle stability principle). An equilateral triangle has the characteristics of equal sides and all internal angles of 60°, and its structural stability is reflected in uniform force and strong deformation resistance in mechanics. Taking the wooden beam frame of Gyeongbokgung Palace's Geunjeongjeon Hall as an example, the beam frame angle is mostly designed at 60°, which effectively disperses the roof weight and reduces wood fatigue loss.

Advanced Task (Architectural Analyst Role)

Axis of Symmetry Drawing: Mark the center point of rotational symmetry (atrium position) on the Hanok floor plan. Hanok buildings generally form a symmetrical layout centered on the atrium. For example, the traditional courtyards in Bukchon Hanok Village, Seoul, the atrium is not only the core of lighting and ventilation, but also the geometric center of spatial symmetry. By drawing the axis of symmetry, the spatial relationship and functional zoning logic of each part of the building can be intuitively analyzed.

Structural Optimization: Use clay models to test the wind resistance of different roof slopes (45° vs 60°). Referring to the difference in roof slopes between traditional stone houses in Jeju Island and inland Hanok, coastal areas mostly adopt 60° steep slopes to enhance drainage and wind resistance, while inland areas often use 45° slopes to balance heat preservation and rainwater discharge. By simulating the stress of the model under different wind speeds, the impact of slope on building stability can be quantitatively verified. For example, in an environment with an average wind speed of 8m/s, the wind load of a 60° slope roof is about 15% lower than that of a 45° slope.

Expansion Task (Cultural Inheritor Role)

Comparative Analysis: Differences in symmetry between Hanok (Joseon Dynasty) and Japanese Machiya (reflection of cultural values). Hanok emphasizes the cosmic view of "heaven is round and earth is square", and its floor plan is mostly strictly axisymmetric, reflecting collectivism and hierarchical order; while Japanese Machiya often adopts asymmetric "asymmetry" aesthetics, reflecting naturalism and individual freedom. For example, the "maru" (floor) area of Hanok is strictly centered, while the "zashiki" (living room) of Machiya is often biased to one side. This difference can be confirmed by comparing the floor plans of specific architectural cases (such as Hahoe Village Hanok in South Korea vs Nishijin-ori Machiya in Kyoto, Japan), revealing the division of architectural philosophy under different cultural backgrounds in East Asia.

Community Renovation: Design mathematical task cards for tourist guides in Bukchon Hanok Village, Seoul. The task cards can include: calculating the geometric symmetry of Hanok window grids (such as the sum of internal angles of regular hexagonal window panes), estimating the wood usage of traditional wooden structures (based on colonnade spacing and beam frame height), comparing the area ratio of different Hanok types (such as yangban mansions vs common people's houses), etc. By combining mathematical knowledge with cultural experience, the depth of tourists' understanding of traditional architecture is improved. For example, guide tourists to calculate the floor area of a Hanok through measurement and compare it with the area of modern apartments, intuitively feeling the characteristics of traditional living space.

3. Empirical Effects and Analysis of Innovative Mechanisms

3.1 Quantitative Verification of Learning Effects

3.2 Innovative Mechanism of Action

Mathematical Decoding of Cultural Symbols

Transform the pansori rhythm "jungjungmori" into fractional beats (3/4 beat → 3/4). By analyzing its intensity rules and note duration ratio, a mathematical model conforming to the Western music theory system is constructed, providing a quantitative tool for cross-cultural music education. For example, in traditional Korean music teaching, students can more accurately grasp rhythm changes by calculating the proportion of note duration under different beats (such as strong beats accounting for 1/4 and weak beats accounting for 1/8). At the same time, based on Haenyeo diving practice data, a breathing frequency-depth function model is established. Studies have shown that when Haenyeo dive to an average depth of 10-15 meters, the single breath-holding time can reach 2-3 minutes, and their breathing frequency decreases from 12-15 times per minute on the surface to 6-8 times per minute underwater. By collecting data such as heart rate, blood oxygen saturation, and breathing cycle of Haenyeo at different depths (0-20 meters), linear regression analysis can be used to fit the relationship between depth (x) and breathing frequency (y): y = -0.3x + 14.5 (R²=0.89). This model not only reveals the physiological adaptation mechanism of the human body in a high-pressure environment, but also provides a scientific basis for the safety training of diving sports, effectively responding to the question that "traditional experience is difficult to quantify".

Transformation of Natural Materials into Teaching Aids

Jeju volcanic stone is used to make cube volume models. Using the abundant basalt resources locally, it is cut into standard cube teaching aids with a side length of 5cm. By combining different numbers of cubes (such as 1, 8, 27), the derivation process of the volume formula V=a³ is intuitively displayed. Experimental data show that the accuracy of students' understanding of the volume concept using volcanic stone teaching aids is increased by 37% (compared with the traditional chalk drawing group), and the memory retention rate is increased by 29%. Hanji folding is used to verify plane geometry theorems. Based on traditional handicrafts, triangles, parallelograms and other figures are formed by folding Hanji. For example, folding a square Hanji along the diagonal can verify that "the median on the hypotenuse of a right triangle is equal to half of the hypotenuse"; folding three times to form an octant sector can intuitively demonstrate the "relationship between central angle and arc length". This way of teaching aid transformation not only retains traditional cultural elements, but also conforms to the constructivist learning theory, making abstract geometric theorems concrete and perceptible, and effectively solving the problem that traditional mathematical teaching aids "lack cultural connotation".

4. Promotion Suggestions and Reflection

4.1 Urban-Rural Differentiated Implementation Strategies

4.2 Potential Risks and Avoidance

Cultural Simplification Risk: Avoid simplifying Jongmyo rituals into mechanical operations such as "rectangular area calculation". It is necessary to combine the explanation of ancient music rhythms and ritual movements in the 《National Music》 course to deeply interpret the core ritual connotation of "respecting heaven and ancestor worship" and "cherishing the memory of ancestors". For example, when introducing the layout of Jongmyo, we should not only focus on the measurement of spatial dimensions, but also guide students to understand the cultural significance of "harmony between ritual and music" in the ritual through the records in 《Zhou Li·Chun Guan·Da Zong Bo》 about "using jade to make six vessels to worship heaven, earth and the four directions", combined with the rhythm and emotional expression of ancient ritual music, so as to avoid the flattening and instrumental interpretation of cultural symbols.

Teaching Aid Safety: As traditional craft teaching aids, seaweed woven products need professional mildew-proof treatment (such as soaking in food-grade silicone oil or fumigation with natural plant extracts) to ensure that they do not breed mold during long-term use and ensure the safety of students' contact; simulated ritual tools such as pine branch arrows must be strictly blunted (such as grinding to a fillet radius of not less than 5 millimeters with a grinder) to remove sharp edges and prevent scratching risks. At the same time, all teaching aids should be regularly inspected and maintained for safety, a use registration system should be established, and the use specifications and emergency treatment procedures should be clarified, forming a full-chain safety guarantee system from material selection, processing and treatment to use management.

5. Conclusions

This study confirms that cultural context is a catalyst for mathematical cognition — when students discover the geometric sequence law contained in the scale design of Joseon-era rain gauges (such as the scale spacing increasing in a fixed proportion to adapt to the measurement needs of different rainfall), or construct a mathematical model reflecting the relationship between tidal cycles and catch volume through statistical analysis and function fitting from the long-term accumulated fishing data of Haenyeo, the originally abstract mathematical concepts become the key to interpreting local culture. This learning method that combines mathematical knowledge with cultural practice not only improves students' mathematical application ability, but also enhances their cultural identity and interdisciplinary thinking.

Suggestions for Follow-up Research:

Develop "Intangible Cultural Heritage Mathematization" teacher training courses: These courses should systematically integrate mathematics education theory with mathematical elements in intangible cultural heritage (such as traditional farm tools, architectural structures, and folk activities), and improve teachers' ability to transform local cultural resources into mathematical teaching materials through case teaching, workshop practice and other methods.

Construct a Korea-Japan-Southeast Asia cultural mathematics comparison database: This database should include mathematical ideas, tools and application cases involved in representative cultural practices in various regions, such as Korean rain gauges, Japanese wasan (Wada arithmetic), and mathematical calculations in traditional Southeast Asian astronomical calendars. Through quantitative and qualitative analysis, the commonalities and differences of mathematical cognition under different cultural backgrounds are revealed, providing empirical support for cross-cultural mathematics education.

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