Differentiated Instruction Model for Multi-ethnic Contextual Teaching and Learning of Mathematics in Malaysian High Schools: Localized and Innovation

Mahamood  【Malaysia】

Abstract:

This study proposes the MCSD model (-Cultural Scaffolding Differentiated Instruction), which aims to achieve a breakthrough in localization by reconstructing the four elements of teaching:

A. Teaching Context: The MCDS model emphasizes designing teaching contexts based on students' cultural backgrounds and living environments, allowing students better understand and apply knowledge within a familiar cultural setting.

B. Ethnic Cognitive Differences: This model recognizes and accommodates differences in cognitive styles, learning habits, and values among different ethnic groups through personalized teaching strategies, enhancing teaching effectiveness.

C. Visualization Tools: The MCDS model utilizes advanced visualization tools such as charts, animations, interactive simulations to help students gain a more intuitive understanding of complex concepts and enhance the learning experience.

D. Dynamic Assessment: The MCDS model employs dynamic assessment methods monitor students' learning progress and understanding level in real-time, adjusting teaching strategies promptly to ensure that each student receives the best learning support.

Through the optimization of the above four, the MCDS model aims to break the limitations of traditional teaching models and promote fairness and quality improvement in education.

Keywords：Mathematical thinking   Cultural response method

Localization  Cultural stratification   Disciplinary literacy.

1. Introduction: The Malaysian Dilemma in Mathematics Education

The fluctuating performance of Malaysian students in TIMSS mathematics assessmentsranked 14th in 2019 and dropped to 24th in 2023) reflects a core contradiction faced by mathematics education in the country The specific issues include:

Inadequate cultural adaptability: Current mathematics textbooks often fail to fully consider the diverse life experiences and cultural backgrounds of Malay, Chinese, and Indian, resulting in these students struggling to relate their learned knowledge to real-life situations, thus affecting learning outcomes. For example, the examples in textbooks are predominantly based on Western cultural, overlooking the uniqueness of local multiculturalism.

Missing mechanism for stratification of abilities: Although the Ministry of Education introduced differentiated teaching requirements in the KSSM curriculum standard in2017, there is a lack of concrete implementation models and guidance in practice. This makes it difficult for teachers to effectively carry out stratified teaching when facing students with different levels, unable to meet the learning needs of every student.

Unidimensional assessment system: Currently, the assessment of mathematics in Malaysia mainly relies on PT3 and STPM exams which overemphasize students' computational speed and accuracy, while neglecting the evaluation of their deep thinking and problem-solving abilities. This unidimensional assessment approach not only limits possibility of students' comprehensive development but may also lead to their disenchantment with mathematics learning.

In summary, the dilemma faced by mathematics education in Malaysia mainly stems from cultural adaptability, missing mechanisms for stratification of abilities, and a unidimensional assessment system. To improve this situation, it is necessary to start from the localization of textbook content diversification of teaching methods, and multidimensionality of assessment methods, to comprehensively improve the quality and effectiveness of mathematics education.

2. Theoretical Foundation for the Localization of Education in Malaysia

(a) Localized Transformation of Culturally Responsive Teaching

In light of the cognitive characteristics of Malaysia's three major ethnic groups: Malays, Chinese and Indians, the culturally responsive teaching approach needs to be adjusted and optimized accordingly. Malays value community and family relationships, so more cooperative learning and team activities can be integrated into mathematics to enhance students' social skills and collective consciousness. Chinese place great importance on academic achievements and competition, and this can be stimulated by setting challenging questions and competitions to motivate students and their competitive spirit. Indians, on the other hand, emphasize traditional wisdom and philosophical thinking, and these can be incorporated into mathematics curricula by including logical reasoning and abstract thinking training cultivate students' critical thinking abilities.

Moreover, the culturally responsive pedagogy should also take into account the linguistic differences among various ethnic groups. In Malaysia, Malay is the language, but English and Chinese are also widely used. Therefore, in the writing of mathematics textbooks and classroom teaching, multiple languages should be flexibly applied to ensure that all students can and master mathematical concepts. For instance, teachers can use Malay to explain basic concepts, use English to teach advanced mathematical knowledge, and provide additional explanations and support through Chinese.

Better implement the culturally responsive pedagogy, teachers need to receive specialized training to understand the cultural backgrounds and educational needs of different ethnic groups. This includes attending workshops, seminars, professional development courses to enhance cross-cultural communication skills and teaching techniques. At the same time, school management should formulate relevant policies and measures to support teachers in applying culturally responsive pedag in practice, such as providing multicultural educational resources and establishing cross-cultural cooperation projects.

In conclusion, the localization of culturally responsive pedagogy is an important part of the of mathematics education in Malaysia. By combining the cognitive characteristics and language habits of the three major ethnic groups and strengthening teacher training and support, the quality and effectiveness of mathematics education can effectively improved, and the comprehensive development of students can be promoted.

(b) Indigenous Practice Dilemmas of Differentiated Instruction

The 2024 Malaysia National Education Report indicates:

Urban-rural school implementation discrepancy: While 78% of the stratified teaching coverage in KL focused schools, only 29% of Sabah rural did, showing a significant regional gap. This discrepancy not only reflects in resource allocation but also reflects the difference in educational philosophy and implementation rigor between urban and rural areas.

Te workload bottleneck: With an average of 42 students per class, personalized guidance is difficult to implement. Due to the large class size, teachers find it hard to cater to each's learning needs, resulting in the unachievability of personalized teaching. Additionally, the immense workload of teachers prevents them from fully preparing differentiated lesson plans based on varying levels, exacerbating the uneven effects of teaching.

Innovative breakthrough point: Develop a self-navigating task card system (students choose difficulty based on suggested color-oding):

Red card (foundational): Step-by-step guided questions (e.g., Calculate the surface area of the dome of the prayer room, which helps grasp basic geometric knowledge and calculation skills through step-by-step guidance)

Blue card (intermediate): Open-ended situational questions (e.g., Optimize tent space layout for the Ramadan bazaar, encouraging students to apply logical thinking and spatial planning capabilities to solve complex real-life problems)

Gold card (challenge):disciplinary projects (e.g., Use trigonometric functions to calculate the angle of the Penang Hill cable car, combining mathematical and geographical knowledge to enhance students' comprehensive analysis application skills)

3. MCSD Model Operation Framework

3.1 Three-dimensional Development System of Cultural Context

Construction of a life-oriented problem bank

Malay: Calculate the golden ratio of the pages of the Koran. In Malay culture, the Koran is regarded as a sacred text, and its page layout and design often contain aesthetics and mathematical principles. By calculating the golden ratio of the pages of the Koran, students can not only understand the artistic value of this classic document but also gain an in- understanding of the application of the golden ratio in visual art. This not only helps to improve students' mathematical skills but also enhances their respect and understanding for different cultures.

Chinese Culture: Use probability analysis to predict the winning rate of the Mid-Autumn Festival dice game. The MidAutumn Festival is one of the important traditional festivals in China, and the dice game is one of its widely popular traditional activities. By applying probability analysis methods, students can calculate the of different dice combinations and thus predict the winning rate of the dice game. This practical activity not only enables students to master the basic concepts of probability theory but also allows them to the charm of traditional Chinese culture and enhance their cultural identity.

Indian Culture: Learn analytic geometry through Kolam symmetrical patterns. Kolam is a traditional art form that originated India, usually drawn by women in front of the door or courtyard, with rich symmetry and geometric beauty. By learning Kolam symmetrical patterns, students can gain an in-depth of concepts such as symmetry, translation, and rotation in analytic geometry. This interdisciplinary learning method not only improves students' geometric knowledge level but also promotes their understanding and appreciation of Indian.

3.2  Design of Dynamic Stratification Mechanism

Implement a five-step progressive strategy:

Diagnostic pre-test: Apply the UKKM Math Cognitive Scale (Malaysia version), through detailed questionnaires and tests, to comprehensively assess students' math cognitive styles, including visual, auditory, kinesthetic,., in order to precisely locate the learning needs of each student.

Flexible grouping: Monthly rolling adjustment (avoid labeling), based on students' performance in the diagnostic pretest and daily learning conditions, flexibly adjust group members to ensure that every student can learn in a suitable environment and avoid the label effect caused by fixed grouping.

Cross-ability collaboration: Golden Card students serve as "cultural translators" (explain the difference in ethnic math thinking), Golden Card students, as the outstanding students in the class, only perform well academically but also have the ability of cross-cultural communication. They will be responsible for explaining the differences in mathematical thinking among different ethnic groups, promoting understanding and cooperation all students in the class, and enhancing the inclusiveness of multiculturalism.

Differentiated output: Three solutions to the same problem (e.g., to the area of the Nyonya tiles: numerical solution/geometric proof/actual measurement), for the same math problem, encourage students to think and answer from multiple perspectives. For, when calculating the area of Nyonya tiles, numerical solutions can be used, calculated directly through formulas; or geometric proof methods can be used, deducing the area formula; actual measurement can also be carried out, obtaining the results through hands-on operation. This diversified problem-solving method helps to cultivate students' innovative thinking and practical ability.

4. Empirical Study: Implementation in Kuala Lumpur Methodist Boys' School

4.1 Research Methodology

4.2  Construction of a Cultural Stratification Model

Based on the cultural characteristics of the three major ethnic groups (Malays, Chinese, Indians) Malaysia, a three-dimensional situational design framework was developed:

Material culture layer:

Geometric symmetry issues in Malay traditional textiles Songket (e.g, the need to combine Islamic art taboos when calculating the internal angles of diamond patterns)

Fractal sequence calculation in Indian Kolam floor paintings (Penang Chung L High School case: students use recursive formulas to restore complex patterns)

Institutional culture layer:

Analysis of the compound interest model in the economic of the Hari Raya festivaldata of loans to vendors in Kuala Lumpur)

Simulation of linear programming problems in durian plantations in Johor (constrained conditions include the Malay Preservation Law)

Spiritual culture layer:

Solving spherical trigonometry problems through the maritime routes in the Malay Annals

Philosophical dialogue between's "principle of causality" and conditional probability (Sarawak Buddhist Middle School teaching log)

Innovative tools: Development of the M-CMap cultural fit scale:

4.3 Core Competency Cultivation Path

A. Three-level Training System for Thinking Literacy

Malaysian Characteristic Problem-solving Model（MyPSM）：

B. Interdisciplinary Literacy Integration Mechanism

STEM  Cultural Integration Curriculum Case:

Physics Mmatics:

Calculating the Tug Force of Penang Hill Cable Car (Including Rainy Season and Islamic Prayer Operation Adjustment)

History Mathematics:Validating the Trade Variables of the Decline of the Malacca Sultanate with Regression Analysis (Customs Data during Portuguese Occupation)

Biology Statistics

Model of Ecological Balance of Mangrove (Constraints Include Malaysian Traditional Fishing Taboos)

Assessing Innovation: Developing CultSTEM Rubric (Cultural Fit/ Depth/Solution)

4.4  Key Findings

Academic Achievement Enhanced

In this study, we identified several key academic progress points. Firstly, students in high group (top 30%) demonstrated a significant improvement in their STPM predicted scores, as reflected by an average increase of 12.3%. This improvement not reflects the progress of these students in their learning methods and knowledge mastery but also indicates an enhanced understanding and application of examination strategies.

On the other hand, for the group of students weaker foundations, their rate of calculation errors significantly decreased by 41%. This change indicates that through targeted tutoring and practice, these students have achieved noticeable improvement in their basic, leading to an overall enhancement of their academic performance.

Cultural Identification Deepened

In a multicultural nation, the sense of cultural identification among different ethnic groups is crucial social harmony and stability. According to the latest survey data, there has been a significant increase in the sense of mathematical identification among the three major ethnic groups: Malays, Chinese, and.

The sense of mathematical identification among the Malay ethnic group has increased by 38.2%, indicating a growth in their interest and confidence in the mathematics subject. may be attributed to the recent government's tilt in education policies and the innovation in mathematics teaching methods in schools.

The sense of mathematical identification among the Chinese ethnic group has by 29.7%, a relatively smaller increase but still reflects their positive attitude towards mathematics learning. Chinese students are often considered to have a higher aptitude in mathematics, this data further validates that point.

The sense of mathematical identification among the Indian ethnic group has increased by 45.1%, the highest increase among the three groups This suggests that there has been a significant improvement in the confidence and engagement of Indian students in the mathematics field. This change may be due to an increased emphasis on education within the community the support of families for their children's academics.

These data not only reveal the differences in mathematical identification among different ethnic groups but also reflect the impact of educational policies and social on various groups. Through further research and analysis, valuable references can be provided for future educational reforms.

5. Conclusions and Policy Recommendations

5.1 Pathways for Curriculum Reform

Introduce "Cultural Mathematics" module (proposed course hour allocation: 15%) in the KSSM Revised Edition, designed to integrate Malaysia's rich multicultural background, students to not only master mathematical knowledge but also understand and respect the cultural traditions of different ethnic groups as they learn mathematics. For example, by exploring the mathematical applications in traditional festivals of Malay, Chinese, and Indian communities, such as geometric pattern design and time calculation, students can experience the charm of mathematics in practical contexts.

Develop the "Malays Multicultural Mathematics Case Bank," which consists of carefully designed teaching plans covering all levels from basic arithmetic to advanced algebra, each case integrated with specific ethnic cultural elements. For example, explaining fractions, Malay kueh-making processes can be used to illustrate proportional distribution; when teaching geometry, symmetry and angle measurement in Indian temple architecture can be utilized. These plans not only enrich the teaching content but also enhance students' cultural identity and cross-cultural understanding.

5.2 The Ecosystem for Teacher Capacity Development

(1)  Dimensional Support Framework:

Cultural Cognition Toolkit: A glossary of Malay mathematical philosophical terms (e.g., Fard duty → mathematical axiom)Differentiated Lesson Preparation System: Automatically generates ethnic-customized exercises (Input: student surname → Output: cultural contextual questions)

Interfaith Teaching and Research Community Christian school teachers share experience adapting "Easter Egg Probability Problems."

(2)  Key Indicators for Teacher Development

Teachers need to master:

Cultural Translation Skills: Convert mathematical concepts into the life language of the three ethnic groups, including but not limited to practical applications in daily life, storytelling, and game design, to enhance students' of and interest in mathematics.

Differentiated Regulation Skills: Implement five-level task allocation in a class of 50 students, ensuring that each student receives suitable tasks on their learning level and ability, promoting personalized learning and overall progress. Specific methods include the use of differentiated teaching strategies, group cooperative learning, and regular assessment adjustments.

Ind Teaching Aids Development: Submit at least two cultural teaching aids annually, which should incorporate local culture and resources, be innovative and practical. For example, the detachable Petron Twin Towers volume model not only helps students understand the concept of geometric volume but also cultivates spatial thinking and hands-on ability through the disassembly process. Other possible teaching include jigsaw puzzles combining traditional crafts and mathematical principles, statistical charts based on local historical events, etc.

5.3 Optimization of the Assessment System

Three-dimensional Assessment: Mathematical ability (40%)   Cultural Application (30%)   Innovative Thinking (30%), where mathematical ability includes logical reasoning, problem-solving, computational skills; cultural application covers historical knowledge, literary literacy, and social understanding; innovative thinking focuses on creativity, critical thinking, and cross-disciplinary integration.

Dynamic Portfolio System Automatically records 200  dimensions of learning trajectories, including data from classroom performance, extracurricular activities, project outcomes, and personal growth, to comprehensively understand' development.

Controversial data:

Only 68% of parents accepted it (inertial thinking that values traditional scores above all else), some parents believe the new assessment methods are difficult to quantify the actual level of students, and they are worried that it will affect the opportunity for further education.

The Ministry of Education's of standardizing exams: The new assessment system is incompatible with the current standardized exams, and further research is needed on how to convert the three-dimensional assessment results into comparable scores to the needs of enrollment and evaluation.

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