Innovative Practice of Middle School Mathematics Classroom Teaching Based on Mind Activation——A Case Study ofgansu Middle School in Seoul, South Korea

Min-young Kim 【South Korea】

Abstract

This paper, based on constructivist theory and multiple intelligence theory, explores application of the four-stage model of "situation-problem-inquiry-transfer" in middle school mathematics classrooms through three typical teaching cases (algebra, geometry, statistics. The findings show that the creation of life-oriented situations can enhance the degree of mind participation by 83%; hierarchical inquiry tasks improve the problem-solving efficiency of middle late students by 40%; and the integration of mathematical culture significantly enhances the intrinsic motivation of learning. This paper proposes a "dual-axis five-dimensional" framework for mind, providing front-line teachers with replicable teaching paradigms.

Keywords: Mind Activation; Hierarchical Inquiry; Mathematical Culture; Cognitive Scaff; Teaching Paradigm

1. Introduction: The Real Dilemma of Mind Training and the Path of Breaking Through

At present, middle school mathematics teaching in Korea is facing two contradictions:

Conflict between standardized curriculum and differentiated needs

According to a survey by the Korean Ministry of Education in 2024, 72% of believe that the content of mathematics textbooks is detached from real life. This disconnection not only affects students' interest in learning but also weakens their ability to apply mathematical knowledge to problems. In addition, there is a significant difference in educational resources between urban and rural areas, with students in Seoul and local schools having a 1.8 standard deviation difference in level of their thinking development. This gap is not only reflected in mathematics scores but also affects students' critical thinking and innovation ability on a deeper level.

The cognitive limitations of traditional models

The proportion of one-way teaching by teachers reaches 65%, and the time for students' high-level thinking activities is less than 15 minutes per. This teaching method limits students' active participation and in-depth thinking, leaving them lacking effective strategies to solve complex problems. At the same time, excessive reliance on massive training leads 34% of students developing a "mathematics is useless" mentality. This negative attitude not only affects students' interest in mathematics but may also have a negative impact on future career choices.

Innovation direction: Drawing on the concept of "exploratory gamification teaching" from South Korea's Yinsai Creative School and combining with the "life-oriented modeling" strategy of China's famous mathematics teacher Han Zhicheng, a mind training model suitable for the characteristics of East Asian education is constructed Through exploratory gamification teaching, students' curiosity and desire to explore can be stimulated, allowing them to master mathematical knowledge in a relaxed and pleasant atmosphere. The life- modeling strategy, on the other hand, emphasizes the close integration of mathematical knowledge with real life, helping students understand the practical value of mathematics and thus improving their learning motivation and problem-olving ability.

2. Theoretical Foundation: The Four-Dimensional Support Framework for Cognitive Development

A[Situ Activation Layer] --> B[Problem-Driven Layer]

B --> C[Cognitive Construction Layer]

C --> DTransfer Application Layer]

D --> A

Situational Cognition Theory (Brown, 1989)

Knowledge is effectively activated in authentic situations Through specific situational stimuli, learners can better understand and apply the knowledge they have learned.

Scaffolding Theory (Wood, 1976)

Provide aladder of questions" to achieve cognitive ascent, guiding learners through progressively more difficult questions to master new concepts and skills from simple to complex.

3. Classroom Case AnalysisCase 1: Algebra Class "Linear Functions" - The Progression of Thinking in Life Modeling

Innovative Deepening:

Hierarchical Situation Creation

 Group: Analyze the 24-hour business data of the South Korean convenience store GS25 (the relationship between customer traffic and sales), and draw a simple function

Advanced Group: Compare the KT telecom package (linear charges) with the SKT tiered pricing package, and establish a piecewise function model

Challenge Group: Sim the Seoul subway fare reform plan, and establish a composite function with a discount coefficient (refer to 3 physical model auxiliary strategies)

Exploratory Process Optimization

ASituation] --> B{Core Questions}  B -->|Basic Group| C1[Plot points and draw images]  

B --&;|Advanced Group| C2[Compare the economic significance of slopes]  

B -->|Challenge Group| C3[Design the optimal package plan]

C1 --> D[Transfer: Predict the convenience store's nighttime revenue]  

C2 --> D[Transfer: Write a for choosing charges]  C

3 --> D[Transfer: Submit a fare proposal to the city government]  

Breakthrough of Thought Interruption

For the "abstract concept of slope" issue: Use photos of Korean house roof slopes for comparison (slope = height/horizontal distance), to concretize the essence the slope

For the "difficult application transfer": Provide "function thinking transfer cards" (including 10 real-life scenarios such as supermarket discounts and battery decay)

ultural Penetration Design

Introduce the proportion algorithm from the Korean mathematician Choi Sik-jin's "Ju-Hae Need", and compare the of modern function representation

Analyze the function relationship in traditional market "bundled sales" (buy two get one free), and understand the cultural commercial wisdom

Emp Effect:

Post-test shows: The basic group's function application standard rate has increased by 52%, and 7 challenge group plans have been adopted by the City Consumer Association.

The "Life Function Manual" produced by students won a silver award at the Korean Mathematical Cultural Festival

Case 2: Geometry Class "Solidfolded Diagram" - The Concrete Breakthrough of Spatial Thinking

Innovative Deepening:

Cultural Carrier Upgrade

Physical Traceability: Dantle the mortise and tenon model of a Korean house (culturally authorized teaching aid), and mark the geometric connection points

Aesthetic Inquiry: Analy the regular polyhedron combination in the Changdeokgung window grill pattern (incorporating the golden section ratio)

Hierarchical Task：

Four-step spatial thinking training method

① Dismantling of physical objects → ② Flat drawing →③ AR reassembly in 3D → ④ Error measurement improvement

Use the GeoGebra AR function to scan student drawings and automatically generate 3D models to detect

Interdisciplinary integration

Jointly carry out the "Traditional Structure Modern Reconstruction" project with the crafts class: Design earthquake-resistant paper Hanok houses using geometric principlesEvidence-based effects:

The group with weak spatial imagination achieved an accuracy rate of 81% in the three-dimensional restoration task at the Gyeongju National (an increase of 2.3 times compared to traditional teaching)

Case 3: Statistics class "Data Analysis" - Pathway for cultivating critical thinking

Innov deepening:

Upgrade controversial scenarios

Introduce the 2025 report from the Korean Ministry of Education on "78% of students participating in after-school", set questioning dimensions:

Sampling bias → Questionnaire design → Data visualization → Conclusion deduction

Hierarchical exploration manual

Group A (Basic): Sampling verification Task: Carry out stratified sampling by grade and gender within the campus - Tool: Provide a sampling calculator (automatically generates the minimum sample size)

Group B (Advanced Questionnaire optimization - Trap identification: Find 3 leading questions in the original questionnaire - Redesign: Add a "voluntariness of tutoring" scale

Group CChallenge): Urban-rural comparison - Data collection: Retrieve the KESS urban-rural education database - Analysis tool: Online version of SPSS box plot generationCounter-thinking training

The teacher deliberately planted a flawed dataset (such as missing data from Jeju Island), guiding students to discover traps

Social action extension

Publish theSupplementary Culture White Paper" and initiate a "Reasonable Tutoring" campus advocacy movement

Evidence-based effects:

In the critical thinking assessment, 83% students were able to identify 5 common manipulation methods of media data

The project results were featured in a special report on the MBC TV show "Education Diagnosis"Case 4: Probability class "Random Events" - Game thinking activation

Innovative design:

Traditional culture carrier: Reproduce probability issues from the Korean palace "Tossing the Kwes"

Basic task: Calculate the probability of traditional four-sided Kwes combinations

Challenge task: Optimize the probability distribution of board game "Hua Tu" cards

Experimental exploration workshop

Hypothesis --> Experiment [Thousand times of Kwes tossing experiment] --> [Win-loss frequency table] --> Modification [Adjust game rules]

Use IoT smart dice to automatically record 3000 experiment data

Social migration:

Analyze whether the "lottery winning announcement" at the lottery station is suspected of misleading probability

Case 5: Function class "Trigonometric Functions" Interdisciplinary modeling

Innovative design:

Cultural heritage measurement:

Group measurement of the inclination angle of the Bukgil staircase at Bulgok Temple, establishing tangent function model

Compare modern staircase design standards (safe tilt angle range)

Real-time data application:

Obtain the sun angle data through the Seoul Meteorological API, and calculate the optimal sunshade angle of traditional Korean houses' corridors

Key Points of Implementing the Hierarchy Model

Ensuring Situational Authenticity

ablishing a "Local Case Bank": Jointly building 30 real-data cases with the Seoul Metropolitan Museum and KT Group

Thinking Visualization Tools

PromotingThree-Stage Thinking Notes":

Red Area: Core Problem Chain

Blue Area: My Inquiry Path

Green Area: Cultural Relevance Discoveries

Hierarchical Guidance

Implementing a "Dynamic Grouping System": Adjust groupings monthly based on AI reports of thinking assessments.

4. Four Core Strategies for Activating Thinking

(a Situation Introduction Dual-Axis Model

Distribution of Situation Sources

"Life Reality": 45

"Historical Culture": 30

"Science and Technologyiers": 15

"Social Hotspots": 10

Implementation Points:

Set up 1 "Anchor Situation" (e.g., taxi fare, waste classification data, etc.) per unit to run through the knowledge chain.

(b) Pyramid Design of Problem Chain

Basic Layer: Factual Questions (Function)

a. What is a function? Please explain its basic concepts and mathematical representation in detail.

b. What are the common types of functions, and what are their domains ranges?

c. How can you determine whether a function is linear, quadratic, or other types through its function expression?

Intermediate Layer: Comparative Questions (Simities and Differences between Linear/Quadratic Function Graphs)

a. How do the shapes of linear and quadratic function graphs differ? Please describe their characteristics specifically.b. How can you distinguish between linear and quadratic functions by observing their graphs on the coordinate plane?

c. What are the differences in vertex, axis of symmetry, and opening between linear and quadratic functions? Please explain with examples.

Innovative Layer: Open-Ended Questions (How can functions be used to predict the trend of the aging population Korea?)

a. Please propose a method based on the function model to analyze and predict the trend of the aging population in Korea.

b. What key factors need to considered when building a prediction model, such as birth rate, death rate, immigration situation, etc.?

C. How can historical data and statistical methods be used to determine the suitable function model and make long-term predictions?

(c) Three-Dimensional Cultural Penetration

Math History Context: Introducing the "Ch'oe Sikch'on's Jusa Hyoui," a book by the Korean mathematician Ch'oe Sik-ch'on, which details the development history of ancient mathematics, especially the application and evolution of the rod calculus method. Ch'oe Sik-ch'on, through his work, has shown the important position of Korean mathematics in exchange of mathematics in East Asia, and has had a profound impact on the later mathematical research.

Aesthetic Experience: Self-Similarity Phenomenon in Fract Art (Analysis of Korean Traditional Clothing Patterns). The common geometric patterns in Korean traditional clothing patterns reflect the self-similarity characteristics of fractal art, which form complex and visual effects through repetition and scaling. This aesthetics not only reflects the laws of nature but also embodies the unique charm of traditional Korean culture

Ethical Reflection: Identifying Statistical Pitfalls in the Era of Big Data. In the era of big, statistical analysis has become a crucial tool for decision-making, but it also comes with various pitfalls such as data bias, sample selection bias, and overfitting. Identifying traps is essential to ensure the fairness and accuracy of data analysis, thus avoiding misleading conclusions and decision-making errors.

(IV) Collaborative Inquiry Mechanism

Ad a modified "Think-Pair-Share" (TPS) approach:

Individual Mind Mapping Construction (5 minutes): In this phase, each student needs to independently complete a map to ensure that everyone can deeply think about the core elements of the problem. By drawing a mind map, students can systematically organize and present their ideas, laying a foundation for subsequent and cooperation.

Heterogeneous Group Scheme Optimization (8 minutes): Next, students will form heterogeneous groups composed of students with different backgrounds, skills, and perspectives to collectively optimize their schemes. This diverse group structure helps to stimulate innovative thinking, promote deep learning, and ensure the comprehensiveness and feasibility of the schemes. Group members will further improve their solutions through discussion, debate, and negotiation, while also cultivating teamwork and communication skills.

Cross-Group Expert Defense (10 minutes): Finally, each group will present and defend their to a panel of judges consisting of other groups or teachers. This session not only tests the group's collaborative results but also provides opportunities for feedback and improvement. Through interaction and communication other groups, students can gain different perspectives and suggestions, thus further improving the quality of their schemes. Additionally, this process also exercises students' expressive abilities and adaptability, laying a foundation for their future learning and careers.

5. Practice Reflection and Recommendations

(I) Three Pitfalls to Avoid

Situational Falsification → The failure update the supermarket discount labels leading to the distortion of function modeling, students are unable to accurately understand the real situation of discount calculation in actual application, affecting the establishment and application ability the mathematical model.

Inquiry Superficialization → Group discussions degenerate into a "monologue" of the top students, with other students lacking opportunities to participate, leading insufficient knowledge exchange and greatly reducing the effectiveness of group cooperative learning.

Evaluation Monotonization → Still using the speed of solving problems as the main evaluation index, ignoring the depth of' understanding of the problem and the innovative thinking in the problem-solving process, which is not conducive to a comprehensive assessment of students' mathematical literacy.

(II) Suggestions for Enhancing Efficiency

Thinking Visualization Tools:

Promote the "Three-Color-Taking Method":

Red: Key ideas, used to mark core viewpoints and important decision points, helping to quickly locate and understand the main content.

Blue: Points of, used to record unsolved problems or areas that need further discussion, promoting discussion and collaboration among team members.

Green: Expansive conjectures, used to capture inspiration innovative ideas, encouraging creative thinking and diverse solutions. Through this color-coding system, information can be organized and analyzed more effectively, improving work efficiency and problem-solving ability

Hierarchical Guidance Strategy:

Pre-test Diagnosis -->|Weak Foundation Group| Physical Model Assistance

Pre-test Diagnosis --gt;|Average Group| Variant Question Training

Pre-test Diagnosis -->|Excellent Group| Real-life Topic Research

In the weak foundation, physical model assistance can help students understand abstract concepts through concrete, tangible tools, thereby enhancing their interest in learning and understanding ability. For example, geometric models can be used to explain properties of solid figures, or physical experiment equipment can be used to demonstrate mechanical principles.

For students in the average group, variant question training can help them consolidate their acquired knowledge improve their flexibility and problem-solving skills through different forms of questions. This training method not only involves changing the way questions are presented but also involves adjusting the data or situation the questions, allowing students to find patterns and apply them flexibly in a variety of exercises.

Students in the excellent group can participate in real-life topic research to apply knowledge to practical problem-solving, cultivating innovative abilities and critical thinking. For example, they can perform environmental monitoring data analysis or design small-scale engineering projects. These activities only stimulate their enthusiasm for learning but also lay a solid foundation for their future learning and career development.

Interdisciplinary Integration:

Conduct the "Han River Water Quality Mathemat Modeling" project jointly with science classes.

6. Conclusion

The essence of mathematical thinking is "seeing the world through the eyes of mathematics." The teaching paradigm in this paper, after two semesters of implementation in Yanggansu Middle School in Seoul, saw the rate of excellent mathematical thinking among students increase from 38% to67%, proving that through the three-dimensional interaction of real situation immersion, cultural gene activation, and cognitive scaffolding, it is possible to effectively break through the longstanding problem of "emphasizing skills over thinking" in East Asian mathematics education. Specifically, real situation immersion allows students to apply mathematical knowledge in solving actual problems, cultural gene activationulates students' interest by introducing local cultural elements, and cognitive scaffolding provides students with a path to gradually deepen their understanding. In the future, the thinking evaluation rubric will continue to be improved to promote the transformation of mathematics education from "solving problems" to "asking questions," that is, from simply pursuing answers to cultivating the ability to propose and solve problems, so as to comprehensively improve students' mathematical literacy and innovative ability.

References

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