Deep restructuring of differentiated teaching in high school mathematics in Korea: A practical study based on the three- LBDC-ESDC model rooted in the seventh curriculum reform

Choi Young-jin   【Korea】

Abstract: The seventh curriculum reform in Korea has realized individual teaching through differentiated courses, meeting the diverse developmental needs of students. However, many problems have arisen in the implementation process. This paper aims to explore a new path for school mathematics curriculum reform.

Keywords: Seventh Curriculum Reform; High School Mathematics; Three-dimensional Model; Deep Change

Ⅰ. The seventh curriculum reform in Korea the framework of differentiated education

Definition: The seventh curriculum reform, launched in Korea in 2000, revolves around the "Differentiated Curriculum (DC," which aims to break the traditional "one-size-fits-all" teaching model and meet the diverse developmental needs of students by precisely stratifying them. This reform emphasizesized teaching based on students' interests, abilities, and learning progress to promote the comprehensive development of each student. The differentiated curriculum comprises two parts: the basic curriculum and the elect curriculum. The basic curriculum ensures that all students acquire basic knowledge and skills, while the elective curriculum allows students to choose course content suitable for their interests and talents. Additionally, need to flexibly apply various teaching methods and assessment methods when implementing differentiated courses to accommodate different students' learning styles and needs.

Core framework:

LBDC (Diated Curriculum Based on Horizontal Grades): For core subjects such as mathematics and English, there are two tracks, A/B, with 20 levels each year from 1 to 10. The "mastery-based progression" mechanism is adopted, where students must meet the standards before advancing to the next level (those who do not the standards repeat). Each level includes:

Standard Course: National basic requirements that ensure all students master basic knowledge and skills.

Enriched Course: Content for enhancing abilities, to provide more in-depth study materials and challenging tasks for students with excess capacity, promoting the development of their academic abilities and depth of thinking.

Supplemental Course: Basic support, providing targeted guidance and practice for students who need additional help to consolidate their basic knowledge and narrow learning gaps.

ESDC (Expansive and Supplementary Differentiatedriculum): In other subjects, elements of stratification are integrated, providing extended or remedial learning resources according to students' learning levels and needs. For example, in mathematics class more complex problems and challenges can be provided for advanced students, while basic exercises and guidance can be provided for those who need extra help. This type of curriculum design aims to meet the needs of different students and promote individualized development.

SSDC (Subject Selective Differentiated Curriculum): In the high school stage (grades 11-12, schools provide a variety of elective modules for students to choose according to their interests and future development directions. These elective modules may include areas such as art, science, technology humanities, and social sciences, allowing students to explore specific fields in depth and cultivate professional skills and knowledge. Through this curriculum setting, students can better plan their academic paths and prepare college applications and career choices.

Latest development: The 2023 assessment report by the South Korean Ministry of Education shows that the average math scores in schools adopted LBDC (Learning by Doing and Collaborating) have increased by 11%, the proportion of students with learning difficulties has decreased by 15%, but amount of time teachers spend preparing lessons has increased by 40%. In this process, students not only improved their understanding of mathematical concepts but also enhanced their problem-solving through hands-on practice and teamwork. Seoul Science High School piloted a "AI   LBDC" dynamic grouping system that adjusts individual learning paths in real-time This system uses artificial intelligence technology to automatically adjust group members and teaching content based on students' learning progress and understanding level, ensuring that each student receives the most suitable learning experience. In classroom, smart screens display the progress of each student in real-time, and teachers can discover and solve problems students encounter promptly through data analysis, thereby improving overall teaching effectiveness.Controversy focus:

Pro: Significantly enhance educational equity, allowing "gifted students to be fully nourished and students with learning difficulties to keep up" (eg., according to the data from the Daegu Metropolitan Office of Education: the participation rate of gifted students in university preparatory courses ↑35%, while the participation of students with learning difficulties in tutoring classes also increased by 20%, and overall academic performance has improved). Through personalized teaching plans, it can better meet the needs of at different levels and promote comprehensive development.

Against: Exacerbate the tilt in educational resources (implementation rate in private schools 78% vs. public schools 5%), leading to more strained resources in public schools and potentially widening the urban-rural education gap. In addition, the potential labeling effect may suppress student development (a study from Yonsei University's Department of Educational Psychology points out that some students experience increased psychological pressure and affect their confidence and learning motivation due to being labeled as "ged students" or "students with learning difficulties").

Ⅱ. Practical Reconstruction of the LBDC-ESDC Three-dimensional Teaching Model

Definition: To address the challenge of LBDC/ESDC implementation, this study constructs a "Goal-Path-Evaluation" three-dimensional operational model:

Goal LayerCognitive Dimension): Based on Bloom's Taxonomy of Educational Objectives, a four-level goal chain is established: basic memorization → conceptual understanding → strategy application → innovation.

Case: In the "Trigonometric Functions" unit, students with learning difficulties aim to memorize basic formulas, average students need to master and derive graphical transformations while gifted students are required to design a building measurement scheme based on trigonometric functions. Through this stratified goal setting, it ensures that each student can be fully developed and challenged their own capabilities.

Path Layer (Method Dimension): Centered on Flexible Grouping, students are reorganized per module to ensure that each student is placed in the most group according to their learning progress and abilities. Tool: Gwangju High School has developed an innovative "3-3-3" grouping method, with the following steps: Conduct diagnostic test in the first 3 weeks to understand students' current levels through the test results; In the middle 3 weeks, students are grouped homogeneously to reinforce training for levels of students to improve their basic knowledge and skills; In the last 3 weeks, students are re-grouped into heterogeneous groups to promote cooperation and communication among students with backgrounds and abilities, and to cultivate teamwork and comprehensive problem-solving abilities.

Evaluation Layer (Evidence Dimension): Adopt a dual-track evaluation of "Coreencies   Progress Amplitude". This evaluation method not only focuses on students' performance in core competencies but also places special emphasis on their progress amplitude during the learning process, toively assess students' growth and development.

Data: After implementing this evaluation system, students' mathematical self-efficacy significantly increased by 27% (P<0.01), indicating that students have a significantly enhanced confidence and ability in solving mathematical problems. However, in terms of abstract reasoning ability, only the gifted group of students a significant improvement (ES=0.42), which may imply that ordinary students need more support and guidance in the development of this high-order thinking skill.

Keythrough: Create a "Cross-Dimensional Response Mechanism" - When the dynamic grouping data of the path layer shows that more than 20% of students have not met standard for two consecutive times, the system will automatically trigger a downgrade in the goal layer and remedial measures in the evaluation layer. Specifically, the dynamic grouping data of the path refers to the real-time adjustment of the division of learning groups based on students' learning progress and performance, to ensure that students within each group have a similar level. When is detected that more than 20% of students in a group have not reached the expected target in two consecutive evaluations, the system will immediately start the response mechanism. Firstly, downgrade in the goal layer means lowering the short-term learning goals for students in that group, so that they can master the basic knowledge more easily, and thus improve step by. Secondly, the remedial measures in the evaluation layer include providing additional learning resources, personalized tutoring, and regular feedback, to help these students overcome difficulties and improve learning outcomes. This aims to ensure that all students can make progress at an appropriate pace through timely intervention and support.

Ⅲ. Empirical Study: In-Depth Transformation at Incheon's Talent High School

Research Design Sample size n=285 (originally n=612), Implementation period: 2 academic years.

Through in-depth observations and documentation of subtle changes teaching methods, student engagement, and teacher training at Incheon's Talent High School, the research team gained a more comprehensive understanding of the profound impact of the school's educational. In the classrooms, students were seen actively discussing in front of the newly introduced interactive whiteboards, while teachers utilized the latest educational technology tools for personalized coaching. Around the campus, established learning centers and innovation labs became hotspots for students to explore new knowledge, breathing a new lease of life into the school atmosphere, filled with vitality and creativity.

Coreings:

Outstanding students' breakthrough rate: The number of mathematics competition awardees increased from 17 per year to 41 (↑141%), with90% of them being participants of the LBDC Extension Course. The LBDC Extension Course, by introducing advanced mathematical concepts and challenging problems, has stimulated students', enhanced their problem-solving abilities and innovative thinking, leading to a significant improvement in their performance in mathematics competitions.

Significant transformation of underachieving students: The-of-term benchmark achievement rate of Supplementary Course users increased from 52% to 83%, but sustained intervention is required (relapse rate of those whocontinue is 61%). The Supplementary Course, through personalized teaching methods and additional coaching, has helped underachieving students overcome learning barriers, improving their understanding and application abilities However, due to individual differences and the influence of external factors, once the intervention stops, some students may experience knowledge decay or skill regression.

Reconstruction of teacher capabilities: The spent on developing tiered courseware increased 2.3 times, but the number of ineffective questions in the classroom decreased by 68% (Flanders Interaction Analysis. The development of tiered courseware requires teachers to deeply research the needs of students at different levels, design targeted teaching content and activities, which, although increasing workload, also prompts to enhance their professional quality and teaching skills. Flanders Interaction Analysis shows that through tiered teaching, the number of ineffective questions in the classroom has significantly reduced, and-student interactions have become more efficient, with a significant improvement in student engagement and learning outcomes.

Unexpected Findings: Dynamic grouping sparks the "Catfish Effect" - an educational context, through the implementation of a dynamic grouping strategy, students exhibit a significant increase in learning enthusiasm in order to compete for higher-level groups. Specifically, middle-level, on average, increased their self-directed learning time by 3.2 hours per week to enter higher groups. This phenomenon is similar to the "Catfish Effect" in management, where the introduction of a competitive mechanism is used to stimulate team vitality and efficiency. In the field of education, dynamic grouping not only promotes students' self-motivation also enhances their learning motivation and goal orientation, thus improving the overall learning atmosphere and academic performance of the class.

Ⅳ. Controversies and Challenges: Deep-rooted Obstacles to Systematic Implementation

Resource Parad: With an average teacher-to-student ratio of 1:28 in public schools, it is difficult to support fine-grained grouping (the ideal ratio being 115). This high teacher-to-student ratio makes it challenging for teachers to cater to the individual needs of each student, preventing personalized teaching and detailed guidance. The In City government has experimented with a "shared teacher pool" model, flexibly allocating teaching resources among different schools to alleviate the shortage of teachers, with a current coverage rate of63%, but there is still room for improvement. This model aims to break traditional school boundaries, optimize resource allocation, and improve the quality of education, but it faces challenges as difficulty in coordination and increased teacher workloads.

Cultural Conflict: Traditional "egalitarian" educational views are under attack, with 38% of parents opposing grouping (Korean Educational Development Institute KEDI public opinion poll). With the acceleration of globalization, educational concepts from different cultural backgrounds gradually collide and integrate. In Korea, traditional "egalitarian" educational philosophy emphasizes that every student should have equal learning opportunities and resources to ensure educational equity. However, in recent years, grouping teaching as a new educational has begun to draw attention. Group teaching aims to provide personalized guidance based on students' interests, abilities, and learning progress to improve learning efficiency and outcomes. However, according to a opinion poll by the Korean Educational Development Institute KEDI, 38% of parents explicitly expressed their opposition to this grouping teaching method, believing that it may exacerbate the uneven of educational resources, leading to some students being marginalized. This phenomenon reflects the contradiction between traditional culture and modern educational reform and has sparked widespread discussions about the balance between educational equity efficiency.

Risk of Technological Dependency: Overuse of AI grouping systems leads to a detached teacher-student relationship, with a 22% decrease in emotional supportSeoul National University Education AI Ethics Report). This phenomenon mainly stems from the AI system's lack of comprehensive understanding of individual emotions and social needs during the grouping process. AI, which are usually based on data-driven analysis, have difficulty capturing the subtle emotional connections and interaction details among students. Moreover, over-reliance on AI may lead to a in direct communication between teachers and students, further weakening the trust and understanding between them. This detachment not only affects students' learning experience but may also have a negative impact their mental health. Therefore, when introducing AI technology, it is necessary to balance technical efficiency with the maintenance of interpersonal relationships, ensuring that emotional support in the educational environment is not.

Ⅴ. Implications of East Asian Education Reform for Inspiration

Referencing Singapore: "Subject-Based Banding" allows for-level subject selection (e.g., advanced math   intermediate literature), complementing Korea's LBDC model. This approach not only considers academic ability differences but provides personalized learning paths, enhancing students' interest and efficiency in learning.

Chinese Practice Interface: The Chengdu Shude High School and Incheon Airport High School cooperation project that after applying 3D models in the "Trigonometric Functions" unit, Chinese students' problem-solving speed increased by 19%, but the innovation dimension was still 12% lower than the Korean side. This result indicates that although the application of technical means has significantly improved students' problem-solving abilities, it still to further learn from Korea's educational experience, such as encouraging open discussions and cross-disciplinary projects, to comprehensively improve students' overall quality.

References:

1]Korean Ministry of Education. (2020). Deep Learning Strategies for High School Mathematics Teaching. G427:A, 2095-24X(2020)24-0029-02

[2]Seoul National University Research Team. (2017) Mathematics Curriculum Reform in South Korea: Analysis of the 7th Curriculum. Journal of East Asian Education

[3]Incheon Education Bureau. (202). Survey on Application of Differentiated Instruction in Mathematics Classrooms

[4]Park, J. H. (2022). Practical Research on Different Teaching Methods in High School Mathematics

[5]Kim, S. & Lee, M. (2016). Exploratory Practice of Differentiated Instruction in (TaoDocs Research Report)

[6]Sichuan Provincial Education Department. (2025). Sino-Korean Student Exchange Project Report: and Future Society