Innovative Practice Research on the Teaching Model of "Living Situation Hierarchical Teaching" in School Mathematics Class——Localized Application of the Educational Thoughts of Park Geum-mi, a Korean Mathematics Educator

Choi Ji Young【Korea】

Abstract:

This paper addresses the problems of insufficient motivation and significant differences in abilities among middle school students in mathematics learning. It proposes a "Living Situation Hierarchical Teaching". This model integrates the life situation teaching philosophy of Park Geum-mi, a Korean mathematics educator, and combines it with a dynamic hierarchical strategy. Through reconstructing teaching content, gradient tasks, and a diversified evaluation system, it achieves individualized teaching. Practice in a middle school in Seoul shows that the interest of students in the experimental class in mathematics increased 37%, and the accuracy rate of high-order thinking questions increased by 21.3%, verifying the effectiveness of the model in improving classroom ecology and promoting equity.

Keywords: Middle School Mathematics; Hierarchical Teaching; Living Situation; Park Geum-mi's Educational Thoughts; Dynamic Evaluation

1. Introduction:Currently, middle school mathematics teaching faces two major pain points:

Exacerbated ability differentiation: The 2024 report of the Korean Education Curriculum Evaluation Institute shows the standard deviation of middle school mathematics scores is as high as 18.7 points, and the traditional "one-size-fits-all" teaching leads to poor students confidence and excellent students having limited thinking. This teaching model ignores the individual differences of students, fails to meet the learning needs of students at different levels, and further exacerbates the between students.

Disconnection between knowledge and life: Over 65% of students believe that mathematics is "abstract and useless." Park Geum-mi emphasized in "athematics Vitamin": "Mathematics education should reveal the beauty of thinking behind life phenomena." Traditional mathematics teaching often focuses too much on theory and formulas, while ignoring the practical of mathematics in daily life, making it difficult for students to feel the charm and practicality of mathematics.

This paper takes Park Geum-mi's "life mathematics" as the theoretical basis, innovatively designs a hierarchical teaching framework, and stimulates students' interest in learning and improves their mathematical literacy by closely integrating mathematical knowledge with real life. At the same time, a hierarchical teaching method is adopted to develop individualized teaching plans for students at different levels, to help poor students build confidence, promote the thinking development of excellent students and thus achieve the common progress of all students.

2. Theoretical Basis and Innovation Points

2.1 Practical Inspiration of Park Geum-mi's Thoughts

Creation of living situations: Extracting mathematical problems from historical events and daily phenomena (such as designing shopping plans using discount calculations or predicting future trends through analyzing population growth data allows students to apply mathematical knowledge in real situations, enhancing the practicality and interest of learning.

Transfer training of thinking: By cultivating spatial reasoning ability through activities such as tang puzzles and Sudoku, these activities not only inspire students' creativity and logical thinking but also help them develop stronger spatial imagination and strategic planning capabilities when solving complex problems. In addition more similar puzzle games, such as Rubik's Cubes and logic puzzles, can be introduced to further enhance students' comprehensive thinking abilities.

2.2 Design of Innov Teaching Model

2.2.1 Three-dimensional dynamic hierarchical framework

Note: Grouping is dynamically adjusted twice each semester to avoid labeling.

2.2.2ierarchical Task Design Case (Taking "Linear Function" as an Example)

■ C-Layer Task: Calculate the Monthly Fee of a Mobile Phone Plan (in the form y=ax b)

In the C-layer task, students need to calculate the monthly fee of different mobile phone plans based on different call minutes and data traffic. For, suppose there is a plan where each minute of call costs 0.1 yuan, each GB of data traffic costs 10 yuan, and there is a fixed fee of 50 yuan per month, then the monthly fee can be expressed as y=0.1x 10z 50, where x represents the number call minutes, and z represents the number of GB of data traffic used.

■ B-Layer Task: Analyze the Step Pricing Strategy of Shared Bicycle Fees

 the B-layer task, students need to analyze how shared bicycle companies optimize revenue through step pricing strategies. For example, a certain shared bicycle company stipulates that the first 5 minutes of each ride is free, and then each minute is charged 0.1 yuan. If the user purchases a monthly card, then the first 30 minutes of ride is free, and then each minute is charged 0.05 yuan. Students can draw a linear function image to compare the changes in fees under different pricing strategies analyze their impact on user behavior.

■ A-Layer Task: Design a "Lowest Cost Campus Activity Meal Plan" Function Model

In the A-layer task, students to design a function model to determine the lowest meal cost for campus activities. Suppose the cost of each meal box is 15 yuan, and the total cost increases linearly each additional meal box. If the expected number of participants in the event is n people, the total cost y can be expressed as y=15n. Students also need to other factors, such as transportation costs, taxes, etc., to further improve the function model and ensure that it can accurately reflect the actual cost.

3. Teaching Implementation Path

3.1 Pre-Class: Diagnostic Hierarchization

By using a "Life Math Interest Questionnaire" "Pre-Test Knowledge Graph" dual-dimension grouping to that the personalized needs of each student at the starting point of learning are met. The specific steps are as follows:

Firstly, using the "Life Math Interest Questionnaire" understand students' interests and preferences in different mathematical application fields, such as statistics, geometry, algebra, etc. This helps teachers design more attractive teaching content according to students' interests.Secondly, through the "Pre-Test Knowledge Graph", assess students' mastery of various mathematical knowledge points, including but not limited to statistical concepts, spatial thinking, logical reasoning etc. This step helps teachers identify students' knowledge blind spots and develop targeted teaching plans.

Example questions:

"Please estimate the number of plastic bags discarded by the family each (statistical concept)", this question aims to test students' data collection and analysis ability, while guiding them to pay attention to environmental protection issues.

"Describe the path from home to school (spatial thinking)", this question not only tests students' spatial perception ability but also encourages them to use mathematical knowledge to solve practical problems in their daily lives

Through the above methods, teachers can more effectively allocate teaching resources to ensure that every student can get the best learning experience at their own level,

3.2 In-class: Differentiated Instructional Strategies

Situational Introduction Phase (Unified for the Whole Class):Play a video of traditional market transactions, leading to percentage calculations

Hierarchical Inquiry Phase:

A[C Level: Calculate the discount amount] -->[Teacher provides a calculation template]  

B --> G[Students calculate the actual discount based on the template]  

C[B Level Compare membership card/coupon schemes] --> D[Group discussion on the optimal solution]  

D --> H[Analyze the advantages and of different schemes]  

E[A Level: Design promotional strategies] --> F[Data modeling   Profit maximization]  

F --> I[Simulate market response and adjust strategies]

Cross-level Interaction Mechanism:

Establish a "Math Advisory Group" (A group guides student Q&A. By setting up a "Math Advisory Group," interaction and communication between students of different grades and levels can be effectively promoted. This advisory group is composed of excellent students from higher, who not only have profound knowledge accumulation in mathematics but also possess good communication skills and teaching experience. These advisory group members will regularly provide one-on-one or group tutoring students in lower grades or with learning difficulties, answering the questions they encounter in mathematics learning. In addition, the advisory group can also organize special lectures, math competitions, and other activities stimulate students' interest in mathematics and improve overall mathematics levels. This cross-level interaction mechanism not only helps students with learning difficulties improve their grades but also allows excellent students to consolidate knowledge and cultivate their leadership and sense of responsibility.

3.3 After Class: Flexible Homework and Evaluation

Implementation Points: B/C level tasks are set with "Challenge Bonus Questions", which are designed to stimulate students' interest in learning and of exploration by introducing more difficult questions. This encourages them to further challenge themselves after completing the basic tasks. These questions can involve interdisciplinary knowledge, requiring students to apply a variety of to solve problems and enhance their comprehensive abilities. In the A level, real-world constraints such as budget limits are added to cultivate students' practical operation and decision-making abilities. example, in a project management course, A level students need to complete project planning and execution within a limited budget, which not only tests their financial management skills but also exercises their to respond to emergencies.

4. Analysis of Practical Results

After implementing it for a semester in a second-grade class in Seoul:

4.1 Quantitative（N=45）

4.2 Qualitative Feedback

Student interview record:

"During the process of designing the spring outing using functions, I not only learned how to apply mathematical knowledge to solve practical problems but also deeply realized the importance and practicality of mathematics in daily life." (Student from Group)

"When teaching my classmates to design the class badge using geometric drawing, I deepened my understanding of symmetry through practice and also improved my teaching and expressive abilities during the guidance." (Member of Group A's advising team)

Teacher's observation notes:

"After a period of guidance and encouragement, students in Group C gradually transition from initially avoiding questions to actively using 'Help Cards', which shows that they are more confident and willing to seek help when facing difficulties. Meanwhile, students in Group B showed diverse and methods in the problem-solving process, indicating that their flexibility and innovation in thinking have significantly improved."

5. Reflection and Suggestions

5. Countermeasures for Implementation Challenges

Risk of stratified labeling → Use "Rainbow Group" moniker/Regular reorganization: By grouping students by ability using the "Rainbow Group" moniker, we can reduce students' psychological pressure and labeling effects. Regular reorganization of group members ensures that every student has the opportunity to in teams at different levels, promoting an education philosophy that values well-rounded development.

Increased pressure of lesson preparation → Establish a school-based resource library: To reduce' lesson preparation burden, the school should establish a rich school-based resource library. This includes a collection of real-life case studies, such as using KPOP concert seat calculations to stimulate students' interest and application ability in mathematics. In addition, it should also provide a hierarchical exercise manual, with each problem marked with a difficulty coefficient, to help teachers targeted to students' ability levels.

5.2 Future Direction of Improvement

Develop a "Mathematics Practice Passport" to record growth trajectories, by detailedly students' actual operations and achievements in mathematics learning, to help teachers and parents fully understand the progress of students. At the same time, a points system can be introduced to encourage to actively participate in mathematics practice activities.

Co-design interdisciplinary projects with home economics and science classes (such as "Optimization of Family Water-saving Plan"), integrating knowledge from different subjects, to cultivate students' comprehensive problem-solving abilities. For example, in the "Optimization of Family Water-saving Plan" project, students can mathematical knowledge to calculate the amount of water used in the family, combine scientific principles to analyze the effectiveness of water-saving methods, and use home economics skills to implement specific water- measures, thus achieving in-depth interdisciplinary learning and application.

6. Conclusion

Living stratified teaching effectively breaks the abstract dilemma and the contradiction of ability differences in mathematics teaching through the-stage model of "situational activation of interest—hierarchical development of abilities—practice deepening understanding." Its core value lies in:

Realizing Baeung-mi's advocated "thinking cultivation": integrating the spirit of mathematics into life decisions, which not only helps students apply mathematical knowledge in their daily lives but also cultivates their thinking and problem-solving abilities.

Responding to the requirements of the "Korean Mathematics Curriculum Standards": cultivating "mathematical literacy" rather than problemsolving machines, emphasizing that mathematics education should focus on the overall quality improvement of students, rather than just mastering problem-solving skills, thus promoting the overall development of students

Providing a replicable operational framework: frontline teachers can adjust the stratification parameters according to the school's needs, making the teaching methods more flexible and targeted, meeting learning needs of students at different levels, and improving the teaching effect.

References:

[1] Bae, K. (2006). Mathematics Vitamin.: Education Science Publishing House. (Theoretical basis and living case)

[2] Korean Institute for Curriculum and Evaluation. (2024). Middle School Mathematics Quality Monitoring Report. (Data support)

[3] Han Teacher Teaching Practice Case. [EB/OL]. Tianjin, Yijiao Network, 205. (Interactive strategy reference)

[4] Research on the Application of Multimedia in Middle School Mathematics. (2023, No. 4). of Educational Technology. (Situational creation method)

[5] Construction of Hierarchical Teaching Model in Middle School Mathematics. (2025, No. ). Journal of Basic Education Research. (Dynamic grouping mechanism)