06 Spring Divergent Thinking, Senior 2 Mathematics

Author: Xi Yang, Chief Editor / Editor-in-Chief of Source and Flow / Co-editor of Source and Flow
Publisher:
Publishing Date: 2005-11-01
Features: Divergent thinking, also known as divergent thinking, moves from a single point along multiple directions to reach a thinking goal. Illustrated graphically, it is a beam of rays emitted from a point toward the knowledge network space, forming connections between two or more knowledge points. It includes horizontal thinking, reverse thinking, and multi-directional thinking. Divergent thinking is characterized by multi-directionality, flexibility, fluency, and uniqueness, focusing on multiple approaches and solutions when thinking about problems, and multiple methods when solving problems. It explores the same problem from different directions, perspectives, and levels, horizontally expanding and deeply delving into reverse thinking, employing techniques such as exploration, transformation, variation, transfer, construction, deformation, combination, and decomposition. This opens students' minds, stimulates their potential, and enhances their quality, which is crucial for cultivating creative talents. This series of books strives to align closely with the entire teaching process, focusing on cultivating students' creative thinking abilities, enhancing their flexibility and expansiveness of thought, and improving their problem-solving skills. To this end, we closely connect with students' learning realities and comprehensively reflect the questions from recent years' national college entrance exams and provincial/municipal middle school entrance exams. Aligned with the teaching syllabus and current textbooks, it covers from the first to the second year of high school, synchronizing with each chapter and unit of the current textbooks. The basic objective is to enable students to use goal management methods, grasp key learning points and directions, and achieve targeted learning goals and outcomes for each chapter (or unit). The "Basic Knowledge Guide" provides a concise overview of the intrinsic knowledge system of each chapter (or unit) and offers insightful analysis of key knowledge points for the middle school and college entrance exams. The "Key and Difficult Points Illumination" highlights key and challenging areas as the main thread for developing divergent thinking. The "Divergent Thinking Analysis and Practice" is the core structure of this series, divided into the following two parts:
- Divergent Thinking Analysis: Starting from knowledge points, key points, and difficult points, it analyzes the content and interrelationships of the chapter (or unit) and reveals thinking patterns and problem-solving rules through divergent thinking methods, aiming for comprehensive understanding.
- Divergent Thinking Application: Selecting typical examples, it employs multi-angle, multi-perspective, and multi-level divergent thinking for key problems to cultivate students' comprehensive abilities, including conceptual differentiation, synthesis, transformation, thinking transfer, reverse application, experimental design, writing expression, and multi-solution flexibility.
The "Basic Knowledge Consolidation and Ability Testing" helps students assess their classroom learning outcomes, while parents can use it to evaluate students' mastery of knowledge in each chapter of the textbook. This book employs various forms of divergent thinking, including:
- Type Divergence: Transforming typical problems into different forms.
- Solution Divergence: Using multiple methods for a single problem or a single method for multiple problems to train flexible thinking.
- Vertical and Horizontal Divergence: Establishing connections between two or more divergent points and between divergent points and other knowledge points through examples.
- Transformation Divergence: Changing the form while preserving the essence of the proposition.
- Combination Divergence: Combining multiple divergent points into a cohesive structure.
- Transfer Divergence: Solving new situational problems through information or method transfer.
- Decomposition Divergence: Breaking down complex propositions into simpler ones and analyzing them individually.
- Reverse Divergence: Thinking from the goal back to the conditions.
- Creative Divergence: Overcoming cognitive rigidity and solving problems unconventionally.
- Comprehensive Divergence: Integrating connections between divergent points across chapters (or units) and between different disciplines.
In summary, this series of books progresses from simple to complex, with in-depth analysis and extensive practice, bringing students' review and exam preparation closer to reality, thereby enhancing their flexible knowledge application, transferable adaptability, and creative thinking abilities.