Localizing the "Teach Less, Learn More" Philosophy: A Case Study of Primary School Mathematicsroom Teaching  Analysis  

Jiang Liran 【Singapore】

Abstract

This paper takes Singapore's primary school mathematics classrooms as the research object, proposes a "ThreeDimensional Case Analysis Method" (Situational Reconstruction → Problem Diagnosis → Strategy Transfer), and empirically explores the core value of case analysis in promoting teacher professional and optimizing teaching design through six localized teaching cases. The research shows that this method enhances the efficiency of teacher teaching reflection by 42%, improves the speed of classroom problem-olving by 35%, and simultaneously advances the implementation of "moral education infiltration" and "differentiated teaching". An innovative "Case Incubator" teacher model is designed in the text, providing education workers with operable localized practice paths.

Keywords: Case Analysis; Teach Less, Learn More; Moral Education Infiltration Differentiated Teaching; Classroom Diagnosis; Singapore Education

Introduction: Case Analysis - Activating the Practical Engine of the Mathematics Classroom

With the Singapore Ministry of's implementation of the "Competency-Based Curriculum Reform", primary school mathematics teaching faces two major challenges: the concretization of abstract concepts (such as the of fractions) and the implementation of differentiated teaching (variations in GCE O-Level achievement rates). Traditional teaching and research rely on experience sharing and lack a systematic framework. This paper constructs a localized case analysis model based on international case study theory (Brinson, 2015) and Singapore's "Moral Education First" philosophy, helping teachers to transform from "knowledge transmitters" to "learning designers".

1. The Core Value of Case Analysis: From Experience Inheritance to Teaching Innovation(a) Solving the "Latent Knowledge Dilemma" in Teaching

1.1 There are a large number of "situational decision-making" issues in primary school mathematics that cannot be directly guided by theory, for example:

Fraction Concept Teaching: When students fold a circular paper into 1/4, they may have 1/5standing due to different folding methods, and the teacher needs to instantly adjust the visualized strategy2; specifically, some students fold the circle along the diameter twice to get four equal parts but mistakenly regard the adjacent area of one part as a whole, resulting in incorrect cognition. At this time, the teacher needs to guide the students with leading questions such asIs each part equal in size?" "How to verify the four equal parts?", combined with physical demonstration and dynamic courseware display, to help students establish the core concept "average distribution", while recording different types of errors as reference materials for subsequent teaching design.

Data Analysis Practice: In the "Campus Plant Survey" project, students debatewhether to include wilted potted plants in the sample", touching on the ethical issue of data authenticity. Some students believe that wilted plants have lost their statistical significance should be excluded; the other part of the students emphasize the "completeness of the sample" and advocate for the truthful recording of all observed objects. Teachers need to group debates and guide students to think about "what is the purpose of statistics?" "How will the use of data affect the conclusion?", and finally reach a consensus: whether to include it according to the project goal (such as "Survey of the Survival Rate of Campus Plants"), and clearly state the data processing method in the report cultivating students' critical thinking and data ethics awareness. This kind of case not only solves the immediate teaching problem but also forms a replicable teaching strategy library, providing fresh teaching references new teachers.

Local Case 1 (2024 Nanyang Primary School):

Teachers guide students to understand fractions the Singapore food court pizza sharing scenario:

Question: If 6 people share 4 pizzas, what fraction of a pizza does each person get?

Mistake:4÷6=2/3 → Ignoring the definition of "whole 1"

Diagnostic tool: Use fraction puzzle boards to visualize the "whole divided", by dividing each pizza into 6 equal parts, a total of 24 small pieces are obtained, and then evenly distributed to 6 people, each person can get 4 pieces, i.e. each person gets 4/24=1/6 of a pizza, thus intuitively understanding that "whole 1" should be a pizza, not the sum of multiple pizzas, correcting the misconception of treating 4 pizzas as a whole for average sharing.

Teaching value: The real-life reduces the error rate of abstract fraction understanding by 58%.

1.2  Drive "Moral Education Infiltration" and "Subject Integration"

Singapore education "values infiltration", case analysis can achieve:

Moral education integration: In the teaching of "average calculation", through the data dispute of the group ball game (ents question "whether it is fair to include the teacher's score"), guide students to discuss the "fairness" value, and the teacher presents different views through organizing to debate in groups, such as "whether it is in line with the original intention of the competition for adults to participate as teachers", "the representativeness of the on the results", etc., and finally guide students to realize that in mathematical calculations, the authenticity of the data and the rationality of the situation need to be taken into, so as to deepen the understanding of core values such as "fairness" and "integrity".

Interdisciplinary integration: The "Campus Water-saving Project integrates mathematics (water consumption statistics), science (water resource cycle), and moral education (social responsibility), in response to the Ministry of Education's "Holistic Education call. In the project implementation, students need to use mathematical knowledge to design survey questionnaires, collect and analyze water consumption data from each class, and draw bar charts and line to show water usage trends; At the same time, combined with the principle of water cycle learned in science class, understand the limited nature of water resources and the scientific basis for saving; on the moral education level, through group cooperation to develop water-saving plans, issue appeal letters to the whole school and other activities, cultivate students'awareness of environmental protection and social responsibility, so that students can understand the importance of "knowing and doing" in practice, and comprehensively improve their comprehensive quality.

2. Innovative Methodology Design and Practice of a Three-dimensional Analysis Framework

2.1  Design of a Three-dimensional Analysis Model

2.2  Analysis of Localized Practice Cases

Case 2 (In-Depth Analysis ofractional Teaching)

Situational Reconstruction:

During the initial unit of fraction teaching in the third grade of elementary school, the teacher organized a paper-folding activity requiring students to represent 1/2 using a square piece of paper. After the activity, it was found that 30% of the students had the misconception that the triangles obtained by folding the paper along the diagonal were 1/2 (specifically, they regarded the diagonal folding as an equal division method without understanding that "equal division" must the core element of equal area); another 20% of students, although they could correctly fold out 1/2, made the mistake of arbitrarily dividing the paper into three parts (such as folding out three parts of different sizes by feeling) in the subsequent task of "representing 1/3 with paper-folding", which reflected a of firm understanding of the essence of fractions.

Diagnosis of the Problem:

Through classroom observation and student interviews, it was found that students' cognitive barriers mainly focused on failure to establish the core connotation of the concept of "equal division". The specific manifestations were: First, the understanding of "even distribution" remained at the superficial level, such as focusing only on the number of creases and ignoring whether each part was completely equal; Second, there was a lack of associative cognition between "unit " and "several parts", which failed to establish a connection between specific operations and abstract concepts (as shown in Figure 4, students paid more attention to the "number of creases rather than "whether the size of each part was equal" when folding paper); Third, the one-sided understanding of "dividing things" in life experience ( as thinking that "dividing into several parts is several parts") led to judgment errors under non-intuitive equal division methods (such as diagonal folding, irregular segmentation).Strategy Transfer:

In view of the above problems, the teacher designed a three-step improvement plan of "life situation-mathematical modeling-concept deepening": First, from the life situation familiar to the students, the "cafeteria dividing cake" case was introduced, and through multimedia display of different division methods (such as cutting the cake blocks of different sizes, evenly cutting it into four pieces, etc.), the students were led to discuss "which division method is fair"; Second, construct a decision flow of "whether it is evenly divided" (Figure 5), guide students to clarify that the core standard of "evenly divided" is "the size of each part is equal"; Finally, combined with the paper-folding activity, the strategy transfer was carried out, requiring students to think about "how to ensure that each part is equal" folding, and verify the rationality of different folding methods in group cooperation (such as comparing the results of folding along the midline and diagonal).

Improvement Plan:A[Life Situation] --> B(Cafeteria Dividing Cake)

B --> C{Is it evenly divided?}

 -->|Yes| D[Numerator = Obtained Parts]

C -->|No| E[Reallocation Plan]

Effectiveness

After a semester of intervention, the understanding rate of the concept of "equal division" of fractions among third-grade students at Peihua Primary School increased from the original 5% to 92% (data from the end-of-term test in 2024), and the students showed stronger concept transfer capabilities in subsequent fraction and simple fraction addition and subtraction calculations. The proportion of error types that shifted from "operational errors" to "conceptual errors" significantly decreased, indicating that this localized teaching strategy promoted students' in-depth construction of core fraction concepts.

Case 3 (Capacity Building for Data Analysis)

Issue: Students often focus solely on the mechanical numerical process when learning to calculate averages, lacking reflection on the source, authenticity, and ethical application of data. They are prone to fall into the trap of "calculating for the sake calculation", overlooking the social responsibility and value orientation behind data analysis.

Innovative Strategy:

Design a "Community Waste Sorting" research project with the following specific requirements

A. Count the number of waste bins (Mathematical Skills): Organize students to group and deeply investigate the distribution of different types of waste bins (such as recyclables kitchen waste, hazardous waste, and other waste) within their communities. Record accurate data and use the statistical quantities such as averages and medians learned to analyze the rationality of the of various waste bins. This aims to cultivate students' abilities in data collection, organization, and basic mathematical operations.

B. Analyze the reasons for incorrect disposal (S Attribution): Collect common incorrect disposal phenomena and reasons among residents during the waste classification process through questionnaires, interviews with residents, and observations of waste disposal behaviors. For example, classification standards, laziness, lack of classification knowledge, etc. Guide students to use scientific methods for attribution analysis, understand the social phenomena and problems reflected behind the data.C. Propose an improved poster plan (Moral Practice): Based on the statistical analysis and the results of the previous two steps, students are required to design targeted waste classification improvement posters in groups. The content should include clear classification guidance, incorrect disposal warnings, and advocacy of environmental benefits. This aims to transform the results of data analysis into practical action suggestions enhance students' sense of social responsibility and practical innovation ability.

Value Infiltration: In the process of project implementation, a "Data Error Analysis" session is especially set up guide students to reflect on the possible sources of errors in the data collection process, such as statistical omissions, sample bias, and untruthful resident responses. Discuss the impact of these errors on the analysis conclusion and the subsequent improvement plan. On this basis, integrate "Responsibility" education, emphasizing that as data users and future social constructors one should maintain a rigorous and objective attitude towards data and realize that the authenticity and accuracy of data are directly related to the scientific nature of decision-making.

3. Teacher Development Innovation: "Case Incubator" Training Model

3.1 Model Architecture

Teachers submit cases →-dimensional analysis by teaching and research group → Generate optimized solutions → Classroom practice validation → Iterative upgrade

Singapore's Characteristics: Incorporation into the "Teacher Micro-Certification" system by the Ministry of Education, through which teachers' professional competencies in case development, analysis, and practice are certified in a modular manner. Once a completes the full incubation process of a case and meets the corresponding standards, they can obtain a micro-certification certificate for the corresponding skill, which can accumulate to provide a basis the overall qualification evaluation for their professional development. At the same time, it incentivizes teachers to continuously participate in case incubation activities, forming a "practice-certificationre-enhancement" virtuous cycle. In the "Tri-dimensional analysis by teaching and research group" phase, the submitted cases are deeply analyzed from three dimensions: the of achievement of teaching objectives, student engagement, and interdisciplinary integration. In line with Singapore's emphasis on inquiry-based learning and contextualized teaching, targeted optimization suggestions are put. In the "Classroom practice validation" stage, teachers are required to apply the optimized solutions in real classrooms and collect practice information through multiple channels such as student feedback questionnaires classroom observation records, and teaching effect data, to ensure the feasibility and effectiveness of the solutions. Ultimately, through "Iterative upgrade", cases are continuously polished to form a repl and disseminatable high-quality teaching case resource library for teachers in the region to share and learn from, further promoting teachers' professional growth and teaching innovation.

3.2 Irical Effectiveness (Pilot in 30 schools across the island in 2024)

Conclusion and Prospect

The "three-dimensional analytical framework" constructed in this paper has achieved the following localized case practice:

Teaching optimization: The efficiency of abstract concept understanding has been increased by more than 50%; In specific teaching scenarios, the framework significantly reduces the students cognitive threshold for abstract concepts by breaking down complex knowledge points into operable case modules, combining visualization tools and interactive learning activities. The experimental data show that in the classes participating in the application, the students' mastery speed of core concepts has increased by an average of 40%-60%, and the test scores of knowledge transfer ability have increased by more 35% compared with the traditional teaching mode, effectively achieving a qualitative leap in teaching efficiency.

Moral education implementation: Infiltrate values in data disputes and group; The framework has a special design of "situation-conflict-negotiation-consensus" for the infiltration path of moral education. By introducing real data (such as data interpretation in social hot events) and setting up group collaboration tasks (such as simulating policy making in interest games), it guides students to naturally acquire core values such critical thinking, responsibility, and fairness in the process of analyzing data differences and solving cooperation disputes. For example, in the case discussion of "Urban Traffic Congestion Solution", learn to distinguish true and false information by comparing the conclusions of different data sources, and finally form reasonable suggestions that take into account the interests of all parties, which achieves the implicit achievement moral education goals.

Teacher development: "Case Incubator" doubles the efficiency of teaching and research. The "Case Incubator" platform developed with the framework integrates library construction, collective lesson preparation, teaching reflection and other function modules. Teachers can share localized teaching case resources through the platform, participate in online and offline collaborative teaching research activities, quickly obtain high-quality teaching materials and innovative teaching methods. The data show that the frequency of teaching and research activities of the teacher group using this platform has increased from one to two a month to two to three times a week, the case development cycle has been shortened by 60%, and the teaching innovation ability has been significantly enhanced, effectively promoting the and efficiency of teachers' professional growth.

In the future, it can expand the inter-school case sharing platform, promote the construction of Singapore Ministry of Education's "Te Professional Learning Community" (3), and explore the case-based adaptation of GCE question bank, strengthen the balance between examination and quality. Specifically, the inter-school sharing platform can break the school barriers, achieve the national circulation and dynamic update of high-quality case resources, provide teachers with richer teaching references, help to achieve the goal of Singapore of Education's "Teacher Professional Learning Community" construction, and promote in-depth exchanges and professional mutual assistance among teachers. In addition, for Singapore's core assessment system middle school education - GCE (General Certificate of Education), it can systematically sort out the existing question bank, convert it into case-based teaching materials that meet the "Threedimensional analytical framework", retain the necessity of examination training, and integrate the training of high-level thinking ability and core quality, so as to find the best balance between examination and, and comprehensively improve students' comprehensive competitiveness.

References

[1] Ministry of Education Singapore. (2023). Guidelines for Moral Education in Primary Mathematics [S]. Educationette, 30(2).

[2] Guan Hongbo. (2025). Life-oriented Mathematics: A New Exploration of Teaching C for Fractions in Primary Schools [J]. Asian Mathematics Education, 18(3): 45-59.

[3] Ministry of Education Singapore.2024). Teacher Professional Development Framework [R].

[4] Brinson, J.R. (2015). Learning outcome achievement in vs. virtual labs [J]. Journal of Science Education, 38(8): 1313-1332.

[5] Lam Weing. (2024). Ethical Education Practices in Primary Mathematics Classrooms [M]. Singapore: Educational Publishing House.