Innovative Practice of Mathematics Teaching Design Based on Multiple Strategies: Localized Exploration in Malaysia

Seeva/o Kumar  【Malaysia】

Abstract

This paper takes the elementary mathematics classroom in Malaysia as the research object, and proposes an innovative teaching model of "Multiple Scene IntroductionHierarchical Exploration Practice-Dynamic Feedback Evaluation" in response to the three major pain points (6) existing in traditional teaching, such as one-way indoctrination disconnection from real-life situations, and a single evaluation approach. Through the design of localized cases (such as the integration of Malaysian food culture and geographical resources into mathematical tasks, its effectiveness in enhancing students' problem-solving ability and mathematical thinking is verified. The study shows that this model increases classroom participation by 40% and the rate of high-order thinking problems by 32%, providing a reusable practice framework for front-line teachers.

Keywords: Elementary Mathematics; Teaching Design; Multiple Strategies; Local; Hierarchical Inquiry; Malaysia

1. Introduction

Malaysia's elementary mathematics education is facing a demand for transformation. Data from international assessments (TIMSS show that Malaysian elementary students' scores in mathematics application are below the average in East Asia (Ministry of Education Report, 2024). Analyzing the root causes traditional classrooms overly rely on the lecture method (6), neglecting the construction of situations and students' subjectivity (Ma Yunpeng, 20032) At the same time, the uneven distribution of teaching resources leads to significant urban-rural differences (4), urgently requiring a low-threshold, highly adaptable localized solution

Based on constructivist theory, this paper develops a "life-immersive" teaching design model in the context of Malaysia's multicultural background (the coexistence of, Malays, and Indians). Different from technology-dependent innovations (such as VR/AI), it focuses on low-cost, easy-to-operate strategy re, fitting the actual conditions of public schools.

2. Theoretical Analysis of the Problem: The Uniqueness and Realistic Obstacles of Malaysian Classrooms

2. 1 The Limitations of Traditional Teaching Models

One-way Indoctrination Dominates: 78% of classrooms still mainly rely on teacher explanations (Malaysian Ministry of Survey, 2024), with students passively accepting algorithms, which violates the essence of "mathematics is the gymnastics of the mind". Under such teaching model, students often lack opportunities for active thinking and exploration, and mathematics learning is more often seen as a process of memorizing formulas and solving steps, rather than a way to logical thinking, innovative ability, and problem-solving ability. Teachers occupy an absolute dominant position in the classroom, conveying knowledge to students through teaching and writing on the black, while students mainly acquire information through listening and taking notes. This "spoon-feeding" teaching method fails to stimulate students' intrinsic interest and initiative in learning, resulting in students showing rigid thinking and lack of flexibility when facing complex problems.

Dislocation from local context: The majority of cases in textbooks are transplanted from European and American contextse.g., “ski resort distance calculation”), lacking local elements (e.g., cost accounting of durian stalls in Penang), which weakens motivation. As a multicultural country, Malaysia is blessed with abundant local resources and a unique socio-economic background. However, the current mathematics textbooks heavily draw upon contexts from developed such as Europe and America for case selection, which are far removed from the daily life experiences of Malaysian students. For instance, the case of “ski resort distance calculation” lacks practical and fails to resonate with students living in a tropical climate. Meanwhile, local contexts such as the operation, cost accounting, and profit calculation of durian stalls in Penang a famous tourist city and durian-producing area, could be integrated into mathematics teaching to allow students to perceive the applied value of mathematics in real life and enhance their sense identity with local culture and the intimacy of learning. The lack of localized contextual support often leaves students feeling abstract and monotonous when learning mathematics, making it difficult to connect the knowledge they with real life, thereby reducing their initiative and enthusiasm in learning and further affecting learning outcomes.

2.2 Challenges of Resource Differentiation

The gap in teaching aids between and rural areas: Urban schools have an average of 6.2 types of mathematics teaching aids per class, while rural schools have only 1.8 types (Ministry of Statistics, 2025). This significant resource gap directly limits rural students’ opportunities to participate in experiential learning. For example, in the teaching of geometric figure, urban students can use intuitive tools such as three-dimensional models and puzzle teaching aids to deeply understand spatial structures, while rural students often have to rely on the teacher’s oral and illustrations in textbooks, making it difficult to transform abstract concepts into concrete cognition and affecting the cultivation of mathematical thinking abilities. In addition, some rural schools lack the funds to update aids slowly, and even have the situation that teaching aids cannot be repaired or replaced in time after damage, further exacerbating the inequality of learning experience.

2.3 Monoton of Evaluation Mechanism

Domination of written examination-based evaluation: 92% of schools use the end-of-term examination paper as the sole basis for evaluation, and this monocular evaluation model seriously neglects students’ developmental growth. According to Bloom’s (1988) taxonomy of educational objectives, evaluation should cover multiple levels such as knowledge memory, understanding and application, analysis and synthesis, creativity and evaluation, etc., whereas the current written examination-based evaluation method over-emphasizes knowledge memory simple application, making it difficult to reflect students’ communication skills in group collaboration, thinking and expressive abilities in problem-solving, and performance in innovative practice. For instance, in-based learning, students’ outcomes such as inquiry reports completed through teamwork and creative design plans are often neglected because they cannot be reflected through standardized examination papers, leading to a dis between the evaluation results and the actual development of students’ abilities and not conducive to stimulating students’ diverse potentials and learning initiative (Bloom, 1988).

3. Innovative Teaching Design Framework: Localized Practice of Diverse Strategies

Design Principles: Low Resourceependence, High Situational Relevance, Strong Thinking-Driven

In the construction of the innovative teaching design framework, the localized practice of diverse strategies is the core link, its design principles revolve around "low resource dependence, high situational relevance, and strong thinking-driven", aiming to adapt to the actual situation where educational resources vary greatly in regions, while ensuring that teaching content is closely integrated with students' life experience and effectively stimulates students' deep thinking ability. The principle of low resource dependence emphasizes that teaching activities make full use of existing basic conditions as much as possible, reducing the reliance on expensive equipment and complex materials. For example, by using common items in life as teaching aids, or using the simple functions of digital tools to achieve teaching goals, making teaching plans widely applicable and operable. The principle of high situational relevance requires that teaching content closely relates to the and cultural background, life scenarios, and learning needs of students, transforming abstract knowledge into concrete and perceptible situational problems, such as designing inquiry-based tasks in combination with historical events, or carrying out project-based learning around the community environment, so as to enhance students' interest in learning and knowledge application ability. The principle of strong thinking-driven on cultivating students' critical thinking, creative thinking, and logical thinking, by setting open-ended questions, guiding cooperative inquiry, and encouraging multi-angle analysis, prompting students to actively, question, and construct knowledge, rather than passively accepting information. In the localization practice, teachers need to deeply understand the characteristics of the local education ecology, flexibly integrate teaching wisdom with modern education concepts, and develop teaching plans that meet the national curriculum standards and have regional characteristics. For example, in rural areas, scientific experiments can be designed in with agricultural production activities, and in urban schools, experiential learning can be carried out by relying on public resources such as science and technology museums and museums, ultimately achieving the maxim of teaching effectiveness and the promotion of educational equity.

3.1 Diverse Scene Import Strategy (first 10 minutes of class)

Innovation Point: Convert Malaysian scenes into the starting point of mathematical problems

Case 1: Grade 3 "Fraction Applications"

Situational Design:

On a weekend afternoon, mom is busy the kitchen making a traditional Malaysian delicacy - the golden and crispy curry puff (Karipap), with a unique aroma of mixed onions, coriander, and curry filling the air. Mom made a total of 12 steaming hot curry puffs, ready to be shared with the family. The brother couldn't help but pick up3 of them, laughing and saying, "I've eaten up a part of it!" The sister, on the other hand, watched from the side and, after the finished eating, took away 1/4 of the remaining curry puffs. At this moment, the math teacher walked in, saw this scene, and posed a question: "ents, can we use our mathematical knowledge to solve this problem of dividing the curry puffs?"

Task Ladder:

① Model the remaining curry puff quantities (visualization): Please, students, take out your drawing paper and colored pens., draw the shape of 12 curry puffs, then mark out the 1/3 (i.e., 4) that the brother ate with a different pen, then calculate the remaining 8 curry puffs, then mark out the 1/4 (i.e., 2) that the sister ate from the remaining and finally circle the 6 curry puffs that are left with a dashed line and write the formula "12 - 12×1/3 - (12 - 2×1/3)×1/4" next to it, to intuitively feel the process of fractional operation through a visualized graphic.

② Calculate the difference between amount eaten by the brother and the sister (comparative thinking): Knowing that the brother ate 4 and the sister ate 2, how many more did the brother eat than sister? Please, students, list the formula "4 - 2 = 2 (pieces)", and think about "How many times the amount the brother ate is the amount sister ate?", guide students to use division to calculate "4÷2 = 2", and cultivate the comparative thinking and multiple relationships.

③ Design a fair distribution for 3 students (innovative application): There are now 6 curry puffs left, to be fairly divided among 3 students. How many can each student get?, students, use the division formula "6÷3 = 2 (pieces)" to get the result, and think about if each curry puff can be cut into 2 pieces how many complete curry puffs can each student get? Encourage students to propose different distribution plans, such as "Each student gets 2 whole curry puffs" or "Each gets 4 pieces (i.e., 2 curry puffs)", and discuss in groups which plan is more in line with the meaning of "fairness", apply mathematical knowledge to the distribution problems in real life, to stimulate innovative thinking.

Local value: Combining family food culture to eliminate the fear of mathematical abstraction. Through the familiar of making and sharing curry puffs, the abstract concept of fractions is closely linked to the daily life of Malaysian students, allowing them to understand mathematical problems in a familiar cultural background to feel that mathematics originates from life, thus reducing the fear of mathematics, and enhancing interest and confidence in learning.

3.2 Hierarchical Exploratory Practice Model (-class, 25 minutes)

Innovation point: Dynamic grouping × Ladder task × Physical alternative scheme:

3.3 Gamification Reflection Evaluation (10 minutes after class)

Innovation Point:edding evaluation into traditional Malay games

“Congkak Math Debriefing”:

Students sit around a Congkak board spread with colorful cloth, each holding a smooth in their hands—each stone imbued with special significance, each representing a core concept learned in class. They carefully place each stone into the varying depths of the board’ses, the crisp “tap” sound as the stones fall into place signifying the gradual settling of classroom thinking. With each stone placement, students are required to answer clearly: “ method was used in this step? Where might an error occur?” Some students furrow their brows as they place the stone representing “addition and subtraction of fractions”, whis softly: “This step uses the method of finding a common denominator to turn the two fractions into the same number, but I almost forgot to find the least common multiple at the beginning which could lead to a calculation error.” The student next to them, however, gives a gentle nod, as if applauding their peer’s meticulous reflection. Advantages Integrating national cultural symbols (Malay counting game) to achieve visual representation of thinking. Each recess on the Congkak board is like a node of thought, and the trajectory the stone’s movement clearly shows the students’ understanding path and reflection process for the concepts, making the abstract mathematical thinking tangible and perceptible through concrete game elements, which not inherits Malay traditional culture but also makes learning evaluation no longer boring, filled with the joy of exploration.

4. Teaching Empirical Study: Taking the “Perimeter and” unit as an example

4.1 Design of Control Experiment

Experimental Group: Grade 4 of a Chinese primary school in Kuala Lumpur (n=3), adopting the model in this article. This model integrates situational teaching, hands-on operation, and cooperative inquiry strategies, including: introducing the concept of perimeter through actual measurement on campus, exploring the rules of area calculation by assembling blocks of different shapes, organizing group competitions to complete the “Design the Optimal Classroom Layout” task to deepen understanding of the relationship between perimeter and area, and using dynamic demonstrations and verifications with the help of the Geometer’s Sketchpad software. During the teaching process, emphasis is on students’ autonomous discovery, with the teacher mainly playing the role of a guide, stimulating students’ thinking through question-based teaching, such as open-ended questions like “ can you enclose the largest area with the least material?”

Control Group: Grade 4 of another Chinese primary school in the same area (n=35), adopting lecture method. The teaching process is mainly teacher-led explanations, first defining the concepts of perimeter and area, then directly presenting the formulas (Perimeter of a rectangle = (   width) x 2, Area = length x width; Perimeter of a square = side length x 4, Area = side length x side length), followed by the application of the formulas through example questions, and finally assigning homework questions to consolidate knowledge. The classroom is dominated by teacher-directed output, with students learning mainly through listening anditating calculations, lacking practical operation and inquiry links.

Period: 3 weeks (6 class hours). The experiment strictly controlled the pace of teaching, with both groups using the same version of mathematics textbooks, by different teachers with the same teaching experience (5-7 years of teaching experience), ensuring that other variables were consistent except for the teaching method. Two class hours were arranged week, each class hour lasting 40 minutes, followed by a 10-minute feedback session after class to collect students' immediate learning sensations. After the experiment, teaching effect was comprehensively evaluated through pre- and post-test comparisons, student work analysis, and interviews.

4.2 Comparison of key data

4.3 Feedback from typical students

"I used to find the area formula difficult, but the teacher asked us to calculate the cost of painting the school sepak takraw court, it suddenly made sense!"

– Student A from the experimental group (Malay ethnicity)

5. Conclusion and Recommendations

The framework of this paper validated the core value of “localization is innovation”:

Contextual innovation: The in-depth of Malaysian indigenous cultural resources and the clever transformation of representative cultural symbols such as traditional games like Congkak (a strategy game similar to the abacus) and iconic natural landscapes durian orchards into effective carriers of mathematics teaching. For example, the Congkak game integrates number sense training, strategic thinking, and preliminary knowledge of probability, while durian orchard scenario designs mathematical problems such as area calculation, ratio distribution, and statistical analysis, making abstract mathematical concepts concrete and life-oriented, stimulating students' interest in and cultural identity;

Process innovation: In view of the large differences in students' mathematical foundations, an hierarchical and dynamic grouping teaching model is implemented. Through pre-diagnostic learning, students are divided into different ability-level groups and dynamically adjusted according to the teaching progress and student performance. In the teaching process, differentiated tasks and learning paths are designed different groups to ensure that each student can effectively improve on the basis of their original level and truly achieve the teaching goal of “not leaving anyone behind”;

Assessment innovation: Reform traditional mode dominated by terminal evaluation, significantly increase the proportion of process evaluation to 40%. Specifically, by introducing self-evaluation forms, guide students to reflect on and evaluate participation, effort, and problem-solving methods during the learning process; at the same time, combined with the game review session, organize students to share strategies, analyze gains losses, and summarize experience after completing the math game task, and teachers evaluate students comprehensively based on their classroom performance, cooperation, and game results, fully reflecting students' learning process ability development (self-evaluation form   game review).

It is recommended to promote the following paths:

Teacher training: Systematically develop the “Handbook of Local Contextual Cases”, which includes a large number of cases that have been tested by practice to transform local cultural symbols into mathematics teaching cases, including detailed teaching objectives, activity designs implementation steps, evaluation criteria, and reflection suggestions, to provide teachers with directly referenceable teaching resources and enhance their ability to integrate local culture into mathematics teaching.

Urban-ural mutual assistance: Establish a teaching aid sharing cloud platform to break geographical restrictions using modern information technology. City schools can upload self-made high-quality mathematics teaching aids, task, etc. to the platform through mobile phone photography, and rural school teachers can download, print, or refer to the production according to teaching needs, realizing the sharing and mobility of-quality teaching resources and promoting the balanced development of urban and rural mathematics education (upload task cards with mobile phone photography).

References

[1] Liang Jinging. (1993). Pedagogy of Primary School Mathematics. Zhejiang Education Press. 2

[2] Ministry of Education of Malaysia. (023). Revised Edition of Primary School Mathematics Curriculum Standards. Kuala Lumpur: National Curriculum Center.

[3] Fu Dachun (2001). Changes in Teacher Behavior in the New Curriculum. Capital Normal University Press.

[4] Lü Yuexia. (209). My View on Dewey's "Learning by Doing". New Education Theory

[5]Chua, Y. P. (2024). Mathematics Teaching Practices in Multicultural Malaysia. UM Press.

[6] Ma Yunpeng. (2003). Teaching Theory of Elementary Mathematics. People's Education Press.