Transformation of Life Experience: A New Path to Enhance the Effectiveness of Elementary Mathematics Teaching

Linying 【China】

Abstract：

Against the backdrop of deepening curriculum reforms, the organic integration of mathematics teaching with children's life experience has become a pivotal issue in implementing competencies. This paper, based on constructivist theory and embodied cognition theory, proposes an innovative four-stage transformation model, namely, "Experience Identification and Classification Cognitive Conflict Stimulation - Multimodal Modeling - Stratified Transfer and Application". The model systematically elaborates differentiated implementation strategies for experience transformation by integrating comparative data from six urban and rural elementary schools. The study shows that this model can improve the understanding rate of abstract concepts by 26.8% and problem-solving ability 38.5%, especially in cultivating a sense of quantity and establishing spatial concepts. At the same time, it reveals the risk of excessive development of life experience potentiallying the essence of mathematics, providing theoretical support and practical references for classroom teaching reform.

Keywords: Experience Transformation; Mathematical Thinking; Differentiated Teaching; Embodiedognition; Core Competencies

1. Problem Presentation: Multidimensional Dilemmas from Life Discontinuities to the Implementation of Competencies

(a) Spac Dislocation between Textbook Arrangement and Student Cognition

Inherent deficiency in cultivating a sense of quantity: In the People's Education Press textbooks, the units ofhectare" and "square kilometer" are set in an urban context, while rural students are more familiar with land units such as "mu" and "fen". survey in a certain county shows that 83% of rural students are unable to establish a spatial representation of 1 hectare, but can accurately describe the actual scope of1 mu of land, which reflects the significant differences in educational resources and living environment between urban and rural areas, resulting in students struggling to connect abstract concepts with actual experience during the process.

Abstract dilemma of geometric concepts: The derivation of the formula for the volume of a cuboid relies on the dimensional superposition of "length × width × height", but can more easily understand the essence of volume from concrete experiences such as "brick stacking" and "water tank filling". An experiment in a Guangzhou school shows that the that adopted the method of layered accumulation of physical objects had a formula mastery rate of 92%, significantly higher than the 67% of the traditional teaching group, which that through concrete operation and intuitive experience, students can better understand and remember abstract mathematical concepts, thus improving learning outcomes.

Typical contradiction: The "Data Statistics" unit of the Normal University Edition uses urban traffic surveys as a scenario, but rural students are more adept at statistics such as the number of poultry and the yield of crops. In urban traffic, students need to analyze complex traffic flows, bus routes, and pedestrian mobility, which may be relatively unfamiliar to students living in rural areas. In contrast, rural students are often exposed poultry farming and crop planting in their daily lives. They can skillfully record the number of chickens and ducks, calculate the grain yield per mu of land, and have a profound understanding agricultural production that changes with the seasons and is affected by the weather. This difference makes them more adept at dealing with statistical data related to agriculture, while they may feel challenged when urban traffic data.

(b) The Risk of Alienation in Situational Creation

Entertainment Tendencies Weaken the Depth of Thought: In a high-quality lesson competition, 62% of teachers designed "Preliminary Understanding of Fractions" as a birthday cake division game, with the colorful cake and festive atmosphere attracting' attention. However, 83% of the classes remained at the "Average Division" operation, failing to delve into the essential connotation of the fraction unit, such as relationship between the numerator and denominator of a fraction and its practical application, resulting in a superficial understanding of the concept of fractions among students.

False Situations Cause Cognitiveusion: A teacher designed "Alien Supermarket Shopping" to help students understand decimals, attempting to stimulate students' interest through a fictitious currency system and bizarre commodity prices However, this situation, which deviates from reality, actually interferes with students' understanding of the real meaning of 0.5 yuan, 1.2 meters etc., causing confusion and confusion when they face decimal problems in real life.

(c) Structural Differences in Urban and Rural Experience

2. Construction of transformative models: innovative design of fourth-order progressive systems

(a) Emp identification: three-dimensional classification and dynamic evaluation

Experience source matrix

Direct experience ---------> Indirect experience

Household labor ---------> Media informatione.g., comparing prices on shopping apps)

Community practice ---------> Cultural heritage (e.g., traditional measuring tools)

A school in Shenhen has developed a "Family Math Day" project, guiding students to accumulate experience in scenarios such as the kitchen (by measuring the volume of ingredients and cooking time, accumulating experience volume measurement) and the balcony (recording plant growth data, conducting statistical analysis, and understanding the growth patterns of plants).

Experience quality evaluation tools

Effectiveness: it contains the essence of mathematics (for example, the mooncake sharing activity not only allows students to experience the joy of sharing but also contains the meaning of fractions, helping them the concept of fractions)

Transferability: whether it can support subsequent learning (for example, through shopping experience, students can master the basics of decimal operations, laying a solid foundation more complex mathematical problems in the future)

Difference: group characteristics such as urban-rural, gender, etc. (boys may be better at analyzing motion trajectories, while tend to understand and apply mathematical knowledge through hand-made and measurement activities).

(b) Cognitive conflict: design strategies for three types of contradictions

Experience- conflicts

Case: teaching "the area of a circle"

Pre-task: use a rope to enclose land, compare the planting area of circular and square plots (r) / compare the seating capacity of round and square dining tables (urban). In rural areas, students can personally experience enclosing different shapes of land with a rope and observe which can accommodate more crops. In urban areas, students can simulate round and square dining tables in the classroom, comparing which shape can accommodate more people by placing chairs.

Conflict stimulation provide circles and squares with the same circumference, and measure the actual area difference. Students will find that, although the circumference of the circle and square are equal, the of the circle is always greater than that of the square. This intuitive comparison can stimulate their in-depth thinking about the characteristics of geometric shapes.

Thought progression: "Why herdsmen always make sheep pens round?" This sparks exploration of the optimal area solution. Through this question, students can further explore the advantages of circles in maximizing the use space and how to apply this principle in real life.

Experience-misleading conflicts

Students believe that 3/4 = 75%, i.e, 75% off, based on the experience of "buy three get one free," but in fact, the discount rate calculation needs to consider the ratio of the actual price to the total original price.3 For example, if an item's original price is 100 yuan, buy three get one free means purchasing three items for 200 yuan, not 300 yuan. Therefore, the actual payment price is 200 yuan, and the total original price is 40 yuan, the discount rate is 200/400 = 50%, i.e., 50% off, not 7% off.

Experiential gap-type conflicts

For rural students who have never seen escalators, use "car grain up the hillside" as an analogy to understand "speed relativity" and solve the difficulty of the encounter problem. In rural areas, students may be more familiar with the scene carrying grain up the mountain. By likening the speed of the escalator to the speed of carrying grain, they can better understand the encounter problem when two objects travel in opposite directions different speeds. For example, assume that one person carries grain up at a speed of 5 meters per minute, and another person carries grain down at a speed of 3 meters minute, then they approach each other at a relative speed of 8 meters per minute. In this way, students can more intuitively understand the speed relativity and the solution to the problem.

(c) Multimodal Modeling: Five-level Abstract Ladder

A[Embodied Operation] --> B(Physical Model)

    B --> C(Diagrammatic Model)

    C --> D(Linguistic Model)

    D --> E(ic Model)

    E --> F(Mathematical Model)  

Practice Case: "Cylinder Volume" Teaching Reconstruction

Physical Level Compare the water-holding capacity of different thickness bamboo tubes (rural) / Observe the volume change of a thermos flask (urban)

Diagrammatic Level: the cylindrical development diagram, understand the relationship between the lateral area and volume.

Symbolic Level: Derive V=πr²h, compare the difference in formula representation between and modern China and foreign countries.

Application Level: Calculate the storage capacity of grain stacks (rural) / Design a minimum material consumption beverage can (urban).

(d) Hierarchical Transfer: Three-level Task System

Basic Transfer: Direct application of formulas to solve problems (such as calculating the area of a flower bed, by measuring the and width and substituting into the formula, to feel the practical application of geometric figures)

Integrated Transfer:

Urban Project: Analyze metro passenger flow data, optimize bus (statistical and optimization ideas, by collecting passenger flow data at different times, drawing charts, finding peak and low periods, and thus adjusting the number of buses and routes to improve efficiency of public transport).

Rural Project: Plan a vegetable garden planting scheme to maximize land utilization (area and ratio, according to soil type, sunshine time and water source, rationally arrange vegetable varieties and planting density, to ensure that every piece of land can be used efficiently).

Creative Transfer:

Make "Community Garbage Classification Survey Report" (data collection and analysis, through questionnaire surveys and field observations, record the community garbage classification situation, use statistical methods to analyze data, put forward improvement suggestions, and community environmental awareness).

Design "Family Water-saving Renovation Plan" (measurement and operation practice, measure the water consumption of household water-using equipment, calculate water-saving potential, design specific water-saving measures, such as installing water-saving faucets and improving irrigation systems, and experience the application of mathematics in daily life through actual).

3. Practice Verification and Reflection Iteration

(I) Four-dimensional Effectiveness Evaluation System

Conduct comparative experiments in 12 classes (=580)：

(II) Reflection on Typical Issues

Overly Lifestyle-oriented Negative Transfer

 teacher adapted the "Chicken-Rabbit Cage" problem into "Shared Bicycle and Private Bicycle Parking Fee Calculation," which enhanced the connection to real life However, this adaptation weakened the value of hypothesis-based thinking training for students. In actual teaching, students might focus more on the specific fee calculations and overlook the cultivation of abstract thinking logical reasoning abilities.

Cognitively Shallow due to Technological Dependency

Overreliance on AR technology to display three-dimensional graphics led to 28% of developing "screen dependency syndrome," reducing their spatial imagination. Additionally, the frequent use of digital tools may cause students to lose interest in physical operation, further affecting their hands- ability and intuitive perception.

Bottleneck of Differentiated Implementation

Lack of rural teacher resources: 76% of rural schools lack sufficient teaching staff to effectively carry customized experience collection, resulting in students struggling to receive personalized learning guidance. Single evaluation criteria: Standardized test questions are still dominated by the experiences and knowledge background of urban students, ignoring actual life and learning needs of rural students, which makes the evaluation results unable to fully reflect the true level of all students.

(III) Suggestions for Improvement Paths

 a Rural-Urban Experience Resource Database

Rural Version: Integrate the measurement of farming activities in the twenty-four solar terms, detailing the climate change, crop growth cycle and the best farming time for each solar term; traditional architectural geometric analysis, in-depth discussion of the structural characteristics, material selection, and feng shui layout of ancient.

Urban Version: Focus on smart home data statistics, fully collecting the usage of smart devices, energy consumption analysis, and user feedback; community planning optimization, detailed research on' living needs, distribution of public facilities, and traffic flow, to improve the comfort and convenience of living environments.

Build a Dual-track Evaluation System

Basic Standard Layer ——→ Quality Development Layer

Concept and formula mastery degree————→ Real-life problem modeling ability

Calculation speed and accuracy————→ Cross-disciplinary integrated application level

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