Abstract

To address the core issue of "disconnection between problem-solving skills and practical application" among Japanese elementary school students, this study developed the "Life-Related Problem Solving (LLPS)" teaching model. Through three localized learning scenarios—mathematics in food contexts, traditional craft-based mathematical decoding, and community-based mathematical exploration—a two-year action research was conducted at Kyoto Prefectural Elementary School. The experimental class achieved a 32.1% improvement in "real-world scenario modeling" scores on the PISA Mathematics Literacy Test, with a problem-solving motivation index reaching 4.2 (on a 5-point scale). This model provides a practical pathway to implement the "Mathematical Application" objective outlined in the "Guidelines for Learning Guidance."

Keywords: life-related; problem-solving; Japanese mathematics; traditional crafts; community mathematics; Japanese elementary school mathematics

Introduction

1.1 The Realistic Dilemma of Mathematics Education in Japan

According to the 2025 survey by the Ministry of Education, Culture, Sports, Science and Technology:

Weak application skills: While 68% of students can solve standard arithmetic problems, only 41% can handle real-world discount scenarios. For example, in a simulated shopping scenario requiring calculation of the actual payment after using a 500-yen discount coupon on a 3,000-yen purchase, the accuracy rate dropped to 43%—significantly lower than that of pure calculation problems. This highlights a clear gap in students' ability to apply mathematical knowledge to practical life situations.

Cultural heritage gaps: Only 29% of students recognize the mathematical principles embedded in origami and garden design. Traditional Japanese origami art contains geometric symmetry and angle calculations, while dry landscape gardens demonstrate proportional division and golden ratio applications. These mathematical elements in indigenous cultural artifacts have not been effectively integrated into teaching, resulting in students' understanding of mathematical culture remaining at the level of abstract formulas.

Declining learning motivation: Fifth-grade students 'interest in mathematics dropped by 22.7 percentage points compared to third graders. Specifically, while 65% of third graders expressed "very interested" or "somewhat interested" in math classes, this figure plummeted to 42.3% by fifth grade—a 22.7-point decline. The trend becomes particularly pronounced when introducing abstract concepts like fractions and geometric proofs, highlighting a mismatch between current teaching content and students' cognitive development patterns.

1.2 Theoretical Innovation Foundation

Building on the "Situation-Cognition Theory" by Akira Fujita (2023) and Japan's distinctive "Machizukuri Learning" (community co-creation learning) concept, we develop a tripartite learning model integrating "life, mathematics, and culture":

A[Life Experience]-- Materialization--> B[Concept Construction]

B--Cultural Immersion--> C[Meaning Generation]

C--Application Feedback--> A

2. Design of Innovative Teaching Models

2.1 LLPS Teaching Framework

Five-step cycle model:

Contextual immersion (life-scenario integration): By designing teaching scenarios closely tied to students' daily lives, we can ignite their interest and intrinsic motivation. For example, in mathematics classes, real-life scenarios like "family budget planning" and "discount calculations" can be introduced, allowing students to discover the practical value of mathematical knowledge through solving real-world problems.

Problem discovery (self-directed question screening): Guide students to actively observe, think critically, and pose questions within a context, thereby cultivating their critical thinking and investigative awareness. Teachers should encourage students to boldly question through heuristic questions such as, "What underlying patterns might be hidden behind this phenomenon?" and "What would be the outcome if we altered a certain condition?"

Modeling experiments (physical/chart-based): Transform abstract concepts into actionable models or experiments, deepening understanding through hands-on practice.

Cultural decoding (traditional wisdom tracing): to explore the traditional wisdom and cultural connotation behind the teaching content.

Community practice (solution delivery): Applying learning outcomes to solve real-world community problems, transforming knowledge into practical skills.

2.2 Three Major Innovation Strategies

Strategy 1: Wa-Shoku MATH (Japanese-style Math)

Deeply integrate the content of "Learning Guidelines" with Japanese dietary culture:

Case: When teaching the concept of 'proportion,' students measured the sugar content ratio of matcha to wagashi in tea ceremonies, revealing...

The golden proportion of the traditional "one juice and three dishes" dietary structure (the error between the experimental results and the records in Nanfang Lu is less than 5%).

Strategy 2: Traditional Craft Decoding (Waza MATH)

Developing an experiential math task package for processing technology:

Paper-folding Geometry Task Chain

Step 1: Investigate the modular combination of the Thousand Cranes → Explore the conservation of area: 25%

Step 2: Measure the paper's expansion rate → Establish the deformation model: 30%

Step 3: Design the seismic-resistant paper structure → Verify the stability of the triangle: 45%

Strategy 3: Community Math Visits (Machi MATH)

Math Map Project for Si Tiao Tong Shopping Street:

Measurement Practice: A Survey on the Comparison of Unit Price in Cosmetology Store (Application of Decimals)

Data Analysis: Making Flood Probability Map Based on the Observation of Yachuan River Water Level Change

Spatial Planning: Optimization of the Layout of the Festival Stalls in the Town (Area and Optimization)

Teaching Experiment and Effect

3.1 Experimental Design

Participants: Grade 4 Class A (Experimental Group, n=35) and Class B (Control Group, n=33) of Kyoto City Rokudo Elementary School. The Experimental Group received a project-based learning approach with 2 additional weekly hours of inquiry-based activities, while the Control Group maintained traditional lecture-based instruction. Both groups underwent baseline assessments using the Mathematics Proficiency Test (Ministry of Education Standard Version) and the Learning Motivation Scale (Nakai Takakazu Revised Version). Results showed no significant differences in foundational math skills (mean scores: 72.5 vs 71.8, p>0.05) or initial learning motivation (mean scores: 68.3 vs 67.9, p>0.05), confirming comparable baseline conditions.

Cycle: April 2024-January 2026 (including three lesson plan iterations). The 20-month experimental cycle comprises three phases: Phase 1 (April 2024-October 2024) implements the foundational teaching model; Phase 2 (November 2024-June 2025) conducts the first lesson plan iteration optimization, adjusting project difficulty levels and collaborative learning strategies based on mid-term evaluation results; Phase 3 (July 2025-January 2026) deepens the second iteration by introducing digital tools for data collection and analysis, while incorporating interdisciplinary elements. Each iteration involves a review panel of 3 mathematics education experts and 5 frontline teachers to validate the lesson plan's effectiveness.

Assessment tools:

The Mathematics Active Learning Test (Ministry of Education Standard Edition) comprises three dimensions: Numbers and Calculations, Geometry and Measurement, and Statistics and Probability, with 40 questions totaling 100 points. It demonstrates strong reliability (α=0.87) and validity, and is widely used in Japan to assess elementary school mathematics teaching effectiveness. The study conducted pre-and post-test evaluations for two student groups, focusing on comparing the experimental group's improvements in problem-solving skills and higher-order thinking abilities.

The Learning Motivation Scale (Revised by Takahiro Nakai) comprises three subscales: intrinsic motivation (e.g., interest, sense of achievement), extrinsic motivation (e.g., parental expectations, academic rankings), and learning strategies, totaling 25 items. It employs a 5-point Likert scale with a total score range of 25-125 points and a reliability coefficient α=0.89. Through pre-and post-test comparisons, the study analyzes the impact of experimental teaching on students' learning motivation across all dimensions, with particular focus on behavioral changes and persistence.

3.2 Key Outcomes Comparison

3.3 Qualitative Evidence

Calculating the symmetry axes of the yukata patterns revealed 17 distinct symmetrical configurations in the pattern sheets left by mygrandmother, making mathematics suddenly feel warm and inviting.

        —Experimental Group Student: Ryo Yamamoto

The student tea room's' nishi-ori' (back door) dimensions calculated the tatami module size, demonstrating interdisciplinary insights that far exceeded expectations.

— Participating Teacher: Emiko TanaKa Practice Reflection and Suggestions

4.1 Key Points for Localization Implementation

Cultural sensitivity handling:

When analyzing the proportions of shrine torii gates, it is essential to respect the religious significance of sacred geometry. For instance, in Shintoism, the dimensions, spacing, and overall layout of torii gates often embody reverence for nature deities and specific cosmological beliefs. Their proportions are not merely mathematical calculations but are deeply intertwined with religious rituals and regional faiths. Therefore, when collecting and analyzing related data, it is crucial to avoid simplistically equating them with the proportional aesthetics of Western architecture. Instead, the process should integrate local cultural contexts and involve religious scholars or community elders to ensure the research remains scientifically rigorous while maintaining cultural respect. According to the "Guidelines for the Preservation of Traditional Architecture" released by Japan's Ministry of Culture in 2020, over 60% of shrine architectural research projects faced community opposition due to insufficient consideration of cultural sensitivity, highlighting the critical role of culturally sensitive approaches in localized implementation.

Interdisciplinary collaboration:

In collaboration with the Department of Family Studies, the "Measurement Cooking" course was developed. This program integrates mathematical concepts such as ratios, fractions, and unit conversions with practical cooking activities. For instance, students adjust ingredient quantities according to recipe proportions, calculate nutritional values for different portions, or measure container capacities to understand volume units. According to 2022 teaching practice feedback from a municipal experimental elementary school, students participating in the "Measurement Cooking" course showed a 23% improvement in solving math word problems correctly while demonstrating significantly enhanced interest in mathematics. Additionally, a "Tatami House Architecture Survey" project was co-developed with the Department of Social Sciences. As traditional Japanese wooden dwellings, tatami houses feature unique structures like "chōya doors" and "en-zuke" that embody distinct regional characteristics and historical value. The project organizes students to conduct on-site measurements of tatami house floor areas, room layouts, and timber dimensions, while applying sociological knowledge to explore the relationship between tatami house architecture and urban life during the Edo period. For example, by calculating the ratio of courtyard area to population size, students analyze contemporary family structures and spatial utilization patterns. A 2021 survey by the University of Tokyo revealed that high school students participating in such interdisciplinary projects achieved 18% higher comprehensive scores in spatial thinking and historical-cultural literacy compared to traditional teaching methods, effectively achieving knowledge integration and practical skill enhancement.

4.2 Sustainable Mechanism Development

Regional Linkage System: Establishment of Teaching Materials Development Alliance with Kyoto Wasabi and Kanazawa Fuyama

Family Participation Program: Distributing "My Family's Math Discovery Notebook"

The Teacher Training System: Hosting the National Life Mathematics Case Competition

4.3 Sustainable Mechanism Development

Regional Linkage System: Establishment of Teaching Materials Development Alliance with Kyoto Wasabi and Kanazawa Fuyama

Family Participation Program: Distributing "My Family's Math Discovery Notebook"

The Teacher Training System: Hosting the National Life Mathematics Case Competition

5. Conclusion

The LLPS model brings the "Mathematical Insight" advocated in the "Guidelines for Learning" to life by activating the cultural genes of mathematics in diet, craftsmanship, and community engagement. Specifically, in the culinary domain, students explore the optimal ratio of vinegar rice to sashimi in sushi preparation (such as the functional relationship between vinegar rice acidity and sashimi freshness). This not only helps them master linear functions and proportional concepts but also deepens their understanding of the philosophical principles of "balance" and "precision" in traditional food culture. By integrating abstract mathematical concepts with tangible cultural practices, this approach transforms math learning beyond textbook formulas. In the craft domain, origami art serves as a dynamic medium for geometry education. Through folding paper at various angles, students independently discover and verify geometric principles like the sum of interior angles of triangles and parallel line properties. Data from a Tokyo public middle school shows that after adopting origami-based teaching, students' accuracy in solving geometric proofs improved by 37%, with significantly enhanced comprehension of geometric concepts. In community participation, students use real-world data such as foot traffic, sales, and product variety distribution in shopping streets. By applying statistical methods to build predictive models and analyze consumption trends, they provide optimization suggestions for local businesses. This process not only cultivates data analysis skills but also reinforces the social value of mathematics in solving practical problems.

When students grasp the concept of functions through sushi ingredient ratios, discover geometric theorems through origami, and construct statistical models using data from shopping streets, mathematics education achieves a paradigm shift from "paper calculations" to "cultural practice." This transformation is not merely an innovative teaching method but a profound change in the essence of mathematics education—it transforms mathematics from abstract symbols detached from reality into a bridge connecting individual cognition and cultural traditions. For instance, when learning probability, incorporating rules from traditional Japanese games like "Mahjong" or "Katazawa" allows students to intuitively understand the relationship between random events and probability calculations. Such culturally grounded instructional designs effectively enhance learning interest and engagement.

This innovation rooted in Japanese cultural soil provides a new paradigm for the localization of global mathematics education. Under the backdrop of globalization, mathematics education often faces the contradiction between "standardization" and "localization." The LLPS model demonstrates that deeply integrating mathematical knowledge with local cultural elements can maintain the rigor of the mathematics discipline while enhancing the cultural adaptability and appeal of education. For example, drawing on this model, China's mathematics education can combine phenological changes in traditional solar terms for function modeling and use mortise-and-tenon structures in traditional architecture to explain geometric transformations, thereby improving mathematical literacy while preserving cultural heritage. According to the OECD report "Education 2030," mathematics education incorporating local cultural elements can simultaneously enhance students' mathematical application skills and cultural identity, providing strong support for the international promotion of the LLPS model. Therefore, the LLPS model is not only a successful practice of Japanese mathematics education but also offers valuable, replicable, and reference-worthy experience for global mathematics education on how to achieve cultural empowerment while maintaining the essence of the discipline.

References

[1] Ministry of Education, Culture, Sports, Science and Technology (2023). "Explanation of the Elementary School Learning Guidelines: Mathematics Edition". Higashiyama Shoten.

[2] Fujita, Chichi (2024). "Designing Mathematics Education Rooted in Life". Meiji Books.

[3] Takahiro Nakai (2025). "Development of the Scale of Mathematical Desire." Journal of the Japan Society for Mathematics Education, 107(2),45-62.

[4] Yoshida Hideo (2023). "Learning Geometric Shapes from Japanese Mathematics." Land Society.

[5]National Council of Teachers of Mathematics (2024). Principles to Actions. NCTM Press

[6] Suzuki Makiko (2025). "Mathematical Motivation Linking Traditional Crafts as a Mediator". Journal of Pedagogical Research, 36(1):112-129.