Abstract：

This study implemented a Learner-Tiered Approach to Mathematics Instruction (LTAM) in three schools, namely, Kota Kinabalu National School, SJK (C) Chung Hwa Danau Kota, and SK Likas. It aimed to verify the effectiveness of LTAM in enhancing the mathematical problemsolving abilities of Grade 4 students through an 8-week quasi-experimental study. The experimental group (N=120) was taught using LTAM, the control group (N=120) maintained traditional methods. The findings revealed that the experimental group experienced a 65.7% increase in the accuracy of complex problemsolving (p<0.01) and a 314% increase in the frequency of cross-ethnic collaboration (p<0.01). Specifically, LTAM effectively enhanced students’ self-directed learning and teamwork spirit by stratifying students based on their abilities and designing tasks with varying difficulties to meet needs of each tier. Furthermore, it facilitated communication and understanding among students from different cultural backgrounds and enhanced class cohesion. These results verify the effectiveness of the LTAM model in localized, providing compelling evidence for other schools to promote such teaching methods.

Keywords: Hierarchical task design  Mathematical problem-solving ability  Primary school mathematics in  Intercultural context  Differentiated instruction

1. Introduction

1.1 Research Background

Malaysia ranked 48th in the PISA 202 mathematics literacy test, below the Southeast Asian average. The National Education Blueprint (2013-2025) clearly states the need to “develop localized teaching to enhance mathematical application abilities”[[2]9. Additionally, the multicultural background leads to significant differences in students’ mathematical cognition: Chinese students exhibit stronger abstract thinking abilities ( an average accuracy rate of 78%), while Malay students rely more on concrete models (with a 15% higher accuracy rate in picture-based questions). differences are not only reflected in examination results but also in classroom interactions and homework completion. Chinese students excel in solving complex problems, demonstrating a quick understanding and application of abstract concepts. contrast, Malay students find it easier to grasp basic mathematical principles with the aid of concrete objects or graphics. These cultural differences necessitate educators to fully consider students’ cultural backgrounds and habits when designing teaching plans, adopting a variety of teaching methods, such as combining multimedia tools, hands-on activities, and group discussions, to meet the needs of different students and enhance overall mathematical literacy levels.

1.2 Research Innovations

LTAM innovatively integrates:

Dynamic stratification mechanism: Task stratification based on Vygotsky’ “zone of proximal development” theory ensures that students achieve optimal learning outcomes based on their current abilities by continuously adjusting task difficulty. This mechanism can dynamically adjust task tiers according students’ real-time performance and progress, maximizing learning efficiency.

Culturally responsive context: Incorporation of local elements such as Malaysian markets (pasar) and traditional gamescongkak) makes the learning content more relatable and engaging. By integrating local culture and daily life scenarios into teaching, students can better understand and apply the knowledge learned in a cultural context, enhancing learning motivation and engagement.

Cross-ability Collaborative Model: Breaking through the individual limitations of the Kumon method, which encourages cooperation and communication among students This model not only promotes interaction among students with different ability levels but also cultivates team spirit and social skills. By collaborating to solve problems, students can learn from each other and share, thus enhancing overall learning effectiveness.

2、LTAM Theoretical Framework and Practical Design

2.1 Core Architecture

A[Diagnostic Pre-test] --&; B{Ability Stratification}  

B --> C1[Basic Layer: Operational Tasks]  

B --> C2Advanced Layer: Transfer Tasks]  

B --> C3[Challenge Layer: Open Tasks]  

C1 --> D[C Situation Embedding]

D --> E[Cross-layer Collaborative Evaluation]

In the diagnostic pre-test phase, a comprehensive assessment of students current knowledge level and skill mastery is conducted through detailed questionnaires and tests. Ability stratification divides students into three layers: students in the basic layer mainly engage in operational tasks emphasize the mastery and application of basic skills; students in the advanced layer face transfer tasks that require them to flexibly apply their learned knowledge in new situations; and students in the challenge need to complete open tasks that are highly uncertain and creative, aiming to cultivate their advanced thinking and problem-solving abilities.

Cultural situation embedding runs through all layers of tasks ensuring that the content of the tasks is closely related to the students' actual life experiences and cultural backgrounds, thereby enhancing the practicality and attractiveness of learning. The cross-layer collaborative evaluation mechanism encourages students from different layers to cooperate with each other and work together to solve problems, promoting the sharing of knowledge and the complementarity of skills, and ultimately achieving the of overall abilities.

2.2 Example of Hierarchical Task Design (Score based Teaching)

Note: The task design references the Malaysian Curriculum Standards (KSSR)

3. Empirical Study

3.1 Method

Sample Characteristics:

A total of 240 fourth-grade students were selected from three schools: Kota Kinabalu National Primary School (Chinese Primary), Jesselton Heights Primary School (Chinese Primary School), and Likas National Primary School (National Primary School). The ethnic proportions of the sample match the population structure Sabah (Chinese: 38%; Malay: 45%; Indigenous: 17%). Stratified cluster sampling was employed, with two random classes selected from school to ensure a balanced baseline between the experimental and control groups. Specifically, students from Chinese and National Primary Schools have different language environments and teaching content, which helps to explore the influence different educational backgrounds on the research results. This sampling method effectively controls variables, enhances the internal validity of the study, and ensures the reliability and validity of the findings.

Measuring:

Mathematical Diagnostic Test: Based on the KSSR fourth-grade curriculum standard, a 30-item scale covering basic arithmetic, geometric concepts, and-solving ability was used to comprehensively assess students' mathematical understanding level (Cronbach's α=0.85), ensuring the reliability and validity of the.

Classroom Behavior Observation Form: Records 9 key indicators such as task engagement, cross-level interactions (e.g., communication between students and teachers,, and students), concentration, cooperative learning performance, etc., to help teachers understand students' learning status and classroom atmosphere.

Motivation Scale: Adapted from PISA affective and attitude questionnaire, using a 5-point Likert scale ranging from "Strongly Disagree" to "Strongly Agree", ites students' interest in mathematics learning, self-efficacy, academic pressure, and achievement motivation to identify factors affecting students' learning motivation.

Table 2: Comparison Pre-Tests between the Experimental and Control Groups (N=240)

3.2 Intervention Design

Task Stratification Mechanism:

A 15-minute diagnostic test is conducted before each unit of instruction to adjust student stratification. Through these tests, teachers can understand the students’ learning progress and mastery in real-time, allowing for precise teaching interventions. Among the experimental groups across the schools, 37% of students experienced a change in stratum within the 8 weeks, with a significantly higher mobility of stratum among students from the Chinese primary school (5%) compared to the national primary school (28%). This difference may be attributed to the cultural background, teaching methods, and learning habits of the students in the respective schools Dynamic adjustment of student stratum helps to ensure that each student can achieve optimal learning outcomes at their own appropriate level of learning.

3.3 Research Results

Table 3:AM Intervention Effectiveness (N=240)

Note: Data collection was conducted using a three-school joint examination system, with inter-rater reliabilityappa = 0.89.

4. Discussion and Recommendations

4.1 Key Findings

School type differences:

The experimental group in Chinese primary schools a significantly higher improvement ( 71.2%) compared to national primary schools ( 58.3%), reflecting the impact of the language medium on task understanding. It is recommended the task sheets for national primary schools include bilingual annotations (e.g., Malay   Kadazan illustrations)8 to help students better understand and complete tasks.Hierarchical mobility patterns:

Students with moderate mathematical foundations (pre-test scores of 60-80) exhibited the highest frequency of hierarchical movement (average .3 times/person), indicating the need for dynamic profiles to track learning trajectories. This suggests that these students face significant challenges and changes during their learning process, requiring more detailed guidance and support to adjust teaching strategies promptly and ensure their steady progress.

4.2 Implementation Recommendations

Teaching strategies:

Mathematical tasks can be developed using traditional, which can stimulate students' interest and deepen their understanding of mathematical concepts by combining traditional games with mathematics learning. For example, the Congkak game can be used to design problems, allowing students to calculate the probabilities of different outcomes during the game and master the basic concepts and calculation methods of probability.

Establishing cross-hierarchical collaborative allows students of different levels to progress together through stratified cooperative learning. For example, in a group, students at the basic level can be responsible for the actual operation of teaching aids understanding basic concepts through hands-on practice; students at the advanced level can be responsible for recording data, analyzing various possibilities during the game, and summarizing patterns; and students at challenge level need to develop strategies, predict possible outcomes of the game, and propose improvement plans. This stratified cooperative approach not only allows each student to give full play to their but also promotes communication and cooperation among them, enhancing overall learning outcomes.

Teacher training program:

Develop a LTAM workshop (40 hours) focusing on three aspects of:

A. Stratified diagnosis: By analyzing students' learning levels and needs in detail, develop personalized teaching plans. This includes using various assessment tools, such as questionnaires tests, and observation records, to ensure that each student receives the most appropriate support.

B. Cultural context design: Integrate local cultural elements into the teaching process to make the content more closely related to students' actual lives. This not only helps to improve students' interest and engagement but also helps them better understand and apply the knowledge they have learned.

C. Cross-hierarchical collaborative guidance: Encourage cooperation among teachers and between teachers and school management to jointly solve teaching problems. This collaboration can take the form of regular meetings, joint lesson preparation, and resource sharing, among other forms, to promote the improvement of teaching quality and efficiency.

The pilot in Sabah showed that teachers who completed the training had 52% improvement in the quality of their classroom questioning, indicating that the training program has achieved significant effects in actual application.

5. Conclusion

This study validated the effectiveness of LTAM in a tri-school fourth-grade teaching context, particularly in

Narrowing inter-school gaps: The disparity between the national elementary experimental group and the Chinese elementary control group decreased from 23.7 points to 9.4. This indicates that LTAM can significantly reduce academic performance differences between different schools, contributing to educational equity.

Promoting ethnic integration: The frequency of cross-ethnic collaboration rose 0.7 times/week to 2.9 times/week. The implementation of LTAM led to a notable increase in inter-ethnic interactions among students, fost better communication and understanding among students of diverse cultural backgrounds and enhancing the multicultural atmosphere within the campus.

Operational feasibility: Teacher preparation time increased by only 1.8/week (traditional method requires  3.5 hours). Compared to traditional teaching methods, LTAM not only improved teaching outcomes but also reduced additional workloads for teachers, demonstrating efficiency and practicality.

Overall, this research effectively resolved the dilemma of differentiated teaching in Malaysian multicultural classrooms. Its value lies in:

Providing a replicable teaching model for Southeast Asian multi-ethnic countries, applicable not only in Malaysia but also in Indonesia, Philippines, and other countries with rich ethnic cultures, helping these regions address similar issues.

Compensating for the shortcomings of the Kumon method in collaborative ability development, LTAM introduces group discussions and team projects to encourage interactions and cooperation among students thereby comprehensively enhancing students' social skills and team spirit.

Responding to the goal of the education blueprint "to enhance mathematics competitiveness to the top 1/3 of the world by 2025," LTAM ensures that students not only master mathematical knowledge but can also apply it flexibly, improving their problem-solving abilities thus enhancing the global competitiveness of Malaysian students in mathematics.

References:

[1] Ministry of Education Malaysia (2013) Malaysia Education Blueprint 2013-205: Preschool to Post-Secondary Education Putrajaya: Ministry of Education Malaysia (Official document of the national education blueprint, ISBN 978-93-3444-20-4)

[2] OECD (2023) PISA 2022 Results: Mathematics Framework Paris OECD Publishing DOI: 10.1787/19963777

[3] Vygotsky, L. S. (978) Mind in Society: The Development of Higher Psychological Processes Cambridge, MA: Harvard University Press Malaysia Examinations Syndicate (2022) KSS Mathematics Curriculum Standards Year 4 Kuala Lumpur: Dewan Bahasa dan Pustaka (Course standard document number MES/KSSR/MTH2022/04)

[4] Abdul Rahman et al. (2024) "Cultural Responsiveness in Malaysian Mathematics Tasks A Sabah Case Study" Journal of Southeast Asian Education, 15(2), 45-67 DOI: 10.1080/7456537.2024.1892345

[5] Sabah State Education Department (2023)erethnic Collaboration Metrics in Primary Schools Kota Kinabalu: SED Technical Report No. 2023/EDU/SS/04