Innovative Practice Research on Inquiry-based Teaching of Junior High School Mathematics in an Interdisciplinary Perspective                

 Liu Fangli【China】       

Abstract:

This paper addresses the issues of fragmented knowledge and insufficient student engagement in traditional junior high school mathematics education, proposing three-dimensional teaching model of "Situation Chain-Inquiry Field-Practice Cycle". This model creates authentic situations to guide students in understanding mathematical concepts within specific scenarios enhancing the coherence and practicality of knowledge. At the same time, through inquiry-based learning activities, it stimulates students' initiative to explore and cultivates their critical thinking and-solving abilities. In addition, through practical activities, theoretical knowledge is applied to real problems, improving students' hands-on and innovative abilities.

By integrating inter themes, mathematics is organically combined with other subjects such as physics, chemistry, biology, etc., enabling students to understand and apply mathematical knowledge in multiple dimensions. In terms of infiltration, elements of Chinese excellent traditional culture are integrated to allow students to feel the charm of culture while learning mathematics, enhancing their national pride. The construction of an ecological classroom emphasizes-student interaction and cooperative learning, creating a positive learning atmosphere and promoting the all-round development of students.

Combining empirical data to verify its effect on abstract thinking and application ability improvement. The research shows that the problem-solving ability of the experimental class has increased by 12.3% compared to the control class, and the proportion innovative practice papers winning municipal awards has reached 35%, indicating that this teaching mode has significant effects in improving students' comprehensive quality.

Keywords: Junior High School  Interdisciplinary Teaching

Inquiry-based Learning  Situation Chain Design   Ecological Classroom

I. Introduction

Currently, there are three major pain points in high school mathematics education:

Knowledge fragmentation: 71% of classrooms still use the single-point knowledge indoctrination model, resulting in students struggling to connect scattered points into a systematic understanding, greatly reducing learning effectiveness.

Cultural absence: Insufficient infiltration of the history of mathematics and thinking methods leads to a lack of deep understanding of culture and comprehensive mastery of mathematical thinking methods in the learning process, affecting their comprehensive quality improvement.

Practice disconnection: Over 60% of students are unable to mathematical models to solve life problems, indicating a clear gap between theory and practical application, making it difficult for students to flexibly apply their knowledge in real situations.

This paper innov introduces the concept of "interdisciplinary inquiry", constructs a three-dimensional teaching model with mathematics as the core, integrating physics, art, history, etc., and stimulates' interest and creativity through in-depth interdisciplinary inquiry, promoting the reconfiguration of the subject's educational value and enabling students not only to master mathematical knowledge but also to understand apply mathematics in a multidimensional cultural context, thus comprehensively improving their quality.

Ⅱ. Theoretical Framework: Three Dimensions of Inquiry-Based Teaching.

(a) Situational Chain Design A Multidisciplinary Integration of Cognitive Scaffolding

Living Anchor Points Reinforce Concrete Transformation

Physical Situational Case Expansion: In the teaching "Quadratic Functions," the "Basketball Parabolic Motion" is used as a starting point to guide students to collect data on the height and angle of shooting using motion. By fitting the function curve with the TI-Nspire graphing calculator, students independently discover the significance of the vertex form parameters, including the vertex coordinates representing the position and when the basketball reaches its highest point, the symmetry axis representing the symmetry of the basketball's trajectory, and the opening direction reflecting the influence of the acceleration of gravity. Experimental data that 83% of students can independently derive the maximum value formula, which is an improvement of 37% compared to traditional teaching.

Cultural Immersion Realizes Dialogue

Reconstruction of the History of Mathematics Across Civilizations: In the "Pi" unit, the ideological differences between Liu Hui's "Exhaustion Method and Archimedes' squeezing method are compared. Liu Hui's method of approximating pi by repeatedly dividing the inscribed regular polygons in a circle reflects the characteristics ancient Chinese mathematics that emphasized practical operation and graphical analysis. Archimedes, on the other hand, used the method of circumscribing and inscribing polygons with circles gradually approximate pi through the concept of limits, demonstrating the ancient Greek mathematics' emphasis on logical reasoning and theoretical proof. Students use GeoGebra software to iteratively calculate the perimeter of polygons to recreate the process of approximating pi by the ancients and write a comparative report titled "The Thinking Behind the Algorithms of East and West."

Novation of Intangible Cultural Heritage Carriers: The introduction of the mortise and tenon structure of the Dong drum tower into "Solid Geometry" and the use three-dimensional modeling software to analyze the stability principle of oblique prisms (, demonstrate the combination of Dong architectural wisdom and modern mathematical theory. Through this project, students not only the geometric properties of oblique prisms but also gain an in-depth understanding of the unique charm of Dong culture. The derivative "Mathematical Heritage Protection" interdisciplinary won the first prize in the provincial youth science and technology innovation competition, further stimulating students' interest in the protection of cultural heritage and the application of mathematics.

(b) Construction the Inquiry Field: A Three-Stage Model for the Advancement of Thinking

Implementation Points: Set up "challenge thresholds" at each level, such as requiring development layer tasks to include ≥2 variable constraints, avoid mental inertia.

(C) Practice Closed Loop: Dynamic Feedback and Social Extension

Metaverse Learning Community Construction

A "Math Emergency Room" is established on Discord platform, where students, disguised as "subject doctors," diagnose wrong question cases (see Figure 2.4). This virtual space is filled with an academic atmosphere, with students wearing virtual white coats and holding electronic medical records, earnestly analyzing every difficult problem, as if they were in a real hospital environment. In May 204, data showed that an average of 47 difficult questions were solved daily, with a response time of <30 minutes. Whenever a question is answered, a green confirmation pops up on the screen, symbolizing the resolution of the problem and the transmission of knowledge.

Public Issue Mathematical Modeling

Combining with the "Statistical Survey", the "Prediction of Community Elderly Meal Delivery Demand" project was carried out. In this project, students went deep into the community, had face-to-face with the elderly, and collected first-hand data. They established a Logistic regression model through the open data of the Health and Health Commission, with an accuracy rate of 8.2% in demand prediction. This detailed report not only showcases their research results but is also adopted by the street as a basis for aging transformation. The charts and data analysis in report clearly show the demand trend of the elderly for meal delivery services, providing the community with valuable references.

III. Empirical Analysis

(I) Innovative Points of Experimental Design

1. Double-Blind Controlism

240 students were selected from three junior high schools in City X, randomly divided into the experimental group (three-dimensional teaching model) and the control grouptraditional model), with neither teachers nor students knowing the purpose of grouping to avoid the Hawthorne effect.

2. Multidimensional Evaluation Tools

The "Mathematics Core Literacy Scale" (Cronbach's α=0.87), adapted by the research, was used, covering 6 dimensions:

A[Abstract Thinking] --> B[Modeling Ability]  

A --> C[Critical]  

D[Cultural Identity] --> E[Transfer and Innovation]  

D --> F[Cooperation and Communication]  

(2)In-Depth Data Mining

Latent Capabilities Made Explicit

Student inquiry notes were analyzed using NVivo, and the experimental group had a significantly higher frequency ofproposing conjectures" (5.7 times/person) than the control group (1.3 times/person) (p<0.01). conjectures covered a wide range of scientific fields, including physics, chemistry, and biology, showing the enthusiasm and creativity of the experimental group students in exploring unknown territories. In addition, in the experimental group detailed their thinking process and reasoning steps in their notes, reflecting their deep understanding of knowledge and demonstrating their logical thinking ability in solving problems.

Anxiety measured using the "Learning Status Scale" showed that the anxiety value of the experimental group dropped from 38.2 to 19.3, a decrease of 4.5%. This significant decrease indicates that the psychological state of the students in the experimental group has improved significantly, and they show higher confidence and less sense of pressure. This change stem from the experimental group's more flexible and interactive teaching methods, making students feel more relaxed and pleasant during the learning process.

Comparative Analysis of County Differences

The experimental group in rural schools had a higher improvement rate in the "cultural identity" dimension (21.7%) than urban schools (12.3%), verifying compensatory effect of the cultural response model on schools with weaker resources. In rural schools, students enhance their cultural identity and sense of pride by participating in projects and activities related to local. This cultural identity not only boosts students' self-worth but also promotes their performance in academics. In contrast, urban school students, while they may have more resources in other aspects have a smaller improvement in cultural identity, possibly because they are exposed to higher cultural diversity, leading to a relatively weaker sense of single cultural identity.

IV. Innovative features

(1) TARGETED DEVELOPMENT OF INTERDISCLINARY THEME DATABASES

"Mathematics   Military History" New Module

Development of "Ballistic Equation and Range of the Red Cannon" theme: recreating the data of the point of impact in the Ming and Qing war cases (Volume 208 of "Wu Bei Zhi"), a for the correction of the coefficient of air resistance is derived. Students discover the formula for the range of solid projectiles in the 17th century:

where k is the coefficient of wind resistance for the projectile (Innovation point: The historical weapon parameters are for the first time to optimize teaching).

Deconstruction of Artistic Perspective Algorithm

Analyze the algorithm of the vanishing point of the ship body in "Riverside at Qingming Festival", and combine the perspective matrix to derive the formula for the digital painting.

(2) OPERATIONALIZATION PATHS OF CULTUR RESPONSE TEACHING METHODS

flowchart TB

A[Original Text of Ancient Books] --> B{Question Transformation}

B --&;|Such as "Shu Xue Jiu Zhang" Surplus and Deficiency| C[Modern Business Decision Model]

B -->|"Siuan Yu Jian" Pile Storage Method| D[Combinatorial Mathematics Problem]

C --> E[Students design "Bookstore Inventory Optimization"]

D --> F[Establish a courier stacking load-bearing model]

(3 )Innovation of ecological evaluation system

Introduction of "Photosynthesis Index of Thought":

With this innovative indicator, we can more comprehensively assess a team's creativity and collaborative efficiency within ecosystem. The formula for this index is:

P=number of proposed plans×interdisciplinary relevance ÷completion time

where "Number of Proposed Schemes" refers to the number of innovative schemes proposed by the team within a specific period; "Interdisciplinary Cor" measures the breadth and depth of the different disciplines involved in these schemes; "Completion Duration" refers to the time taken to complete these schemes from start to finish.

Through this formula, we can intuitively see that a high P value means that the team has not only proposed a large number of innovative schemes, but also that these schemes have a degree of interdisciplinary correlation and the time to complete these schemes is relatively short.

The average P value of the experimental group reached 8.7, an increase of 72% over the control group. This shows that after the introduction of the "Photosynthesis Index of Thought", the experimental group's creativity and collaborative efficiency within the have significantly improved, as shown by the increase in the number of innovative schemes, the enhancement of interdisciplinary correlation, and the shortening of completion time.

Ⅴ. Conclusionary Remarks

(a) Threefold Breakthroughs in Paradigm Shifts

1 Reconstruction of the Knowledge Chain: By cross-disciplinary context chains, fragmented knowledge points are transformed into "cognitive toolboxes" for solving complex problems (e.g. students optimize community greening spacing using the Fibonacci sequence1).

2. Activation of Cultural Genes: Mathematical historical facts are upgraded from "additional materials" carriers of thinking methods (e.g., Shang Gao's proof method inspires students to discover variations of chord diagrams).

3. Expansion of Social Inter: 35% of student research proposals are adopted by government/enterprises.

(b) Patterns for Solving Practical Difficulties

1. Bottlene of Localized Curriculum in Counties

Establishing "Cloud Exploration Workshop": Through VR virtual laboratories (e.g., simulating celestial orbit), addressing shortage of experimental equipment in county schools (referring to the Ministry of Education's "5G  Smart Education" pilot7).

2. Conflict of Evaluation Standards· Formulating the "Polyhedral Lens Scale for Inquiry Ability," reducing the weight of traditional knowledge scores to 60%, and adding new dimensions of "inality of Conception" (20%) and "Cross-Domain Integration" (20%).

(c) Future Research Axes

1. Ethical Boundaries ofological Intervention

 Beware of AI teaching tools oversimplifying the thinking process (e.g., automatic graphing software weakening spatial imagination), and setNo Technology Support Inquiry Day" (referring to Lin Chongde's cognitive development theory).

2. Mining of Agricultural Civilization Mathematical Resources

Launch the "Cultivator's Legacy 2.0 Plan": Systematically converting proportions algorithms, field measurement techniques, etc., in "Tiangong Kaiwu" into teaching modules.

When mathematics classrooms become a bridge of thinking connecting past and present, and a breeding ground for cross-disciplinary innovation, we cultivate not only problem solvers but also bearers of civilization's advancement – this could be the ultimate scenario for core competencies to take root.

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