Once a skill or a body of knowledge enters the advanced stage, the practitioner has two primary tasks: first, to achieve flexible application of that knowledge; and second, to further enhance the proficiency, accuracy, and reaction speed of already mastered skills.
If, at this stage, one continues to use the learning methods of the beginner and intermediate stages, such as mere repetitive training and “intense drilling,” progress will often stagnate. For example, when a learner’s skill was at an intermediate level, they successfully built a complete knowledge system and entered the advanced stage by filling knowledge gaps, repeatedly practicing typical problems, and intensely tackling difficult challenges. However, if they continue to rely on repetitive training as their primary method thereafter, their improvement will hit a bottleneck. They must shift their approach, exploring how to integrate knowledge through methods like “deep thinking” and “one problem, multiple solutions vs. multiple problems, one solution,” in order to achieve another breakthrough.
The Foundation of Flexible Application: Precise Knowledge Mastery
To achieve flexible application, the prerequisite is the precise and firm mastery of knowledge points. If the foundational knowledge itself is vague, flexible application is impossible. Therefore, in the beginner stage, one should not over-analyze the nuanced variations of techniques when solving problems. Instead, more energy should be devoted to understanding and memorizing foundational knowledge points and core methods. In fact, for many basic problems, so-called flexible application is merely the forceful application of a precisely mastered principle to a new scenario.
Distilling Practical Techniques Regardless of the stage, practitioners must face real-world challenges. Therefore, it is crucial to analyze past case studies and problems from high-stakes assessments. One must have the courage to summarize and trust the practical techniques they have distilled, even if they seem unconventional. Only through personal summation can one truly internalize the wisdom of others into their own capability. In this process, you not only acquire techniques but also learn how to apply knowledge flexibly.
Building a System is Key to Flexible Application Once a complete and clear knowledge system and methodological framework are established, flexible application becomes a natural outcome.
With a knowledge system in place, different modules of knowledge become interconnected, forming an organic whole. When faced with a specific problem, you can quickly search all relevant knowledge modules in your mind and automatically filter out irrelevant information.
With a methodological framework in place, when faced with a difficult problem, you can not only call upon various relevant techniques but also draw analogies and transfer techniques from other seemingly unrelated fields. In this way, given enough time, you can always find a path to a solution.
Practice is the Essential Path To achieve flexible application, deliberate practice is the most fundamental and effective method. It is unrealistic to talk about flexible application without a sufficient volume of practice. For the vast majority of knowledge, no matter how thoroughly you understand it or how accurately you memorize it, a certain amount of practice is necessary to solidify it. Conversely, once you can apply it with ease, excessive repetitive practice loses its meaning.
Definition: “Forming a Circuit” For certain knowledge points, even without fully understanding their deep principles, you can still achieve effective application by covering all related problem types through extensive practice. This is a method of forcibly establishing a direct mapping between a “problem pattern” and a “solution” through “intense drilling” before a complete knowledge system is built. In application, once a problem type is identified, it can be solved by imitating and invoking a well-practiced technique. This is “forming a circuit,” akin to procedural memory.
However, practitioners who rely solely on these “circuits” will expose their weak foundations when faced with complex or innovative problems that require deep understanding. Therefore, the essential path to building a truly robust knowledge system is through “deep thinking” to uncover the profound connections between different knowledge points.
Learning Methods for the Advanced Stage
For practitioners who have entered the advanced stage, the following methods are conducive to the integrated application of knowledge:
One Problem, Multiple Solutions & Multiple Problems, One Solution: The more cases of “one problem, multiple solutions” you master, the broader your thinking becomes. The more cases of “multiple problems, one solution” you master, the more you understand the essence of the issue.
Posing Problems for Yourself: This method allows you to stand from the perspective of a designer or examiner, leading to a deeper understanding of a problem’s structure and intent.
Making a Small Problem Big: Deeply analyzing a simple problem to explore all the core principles it connects to is an effective way to grasp the essence of a discipline.
Deep Thinking: The bottleneck at the advanced stage is often not a lack of knowledge, but a deficiency in application. You need to bridge the gap between “knowing” and “doing” through deep reflection. Accustom yourself to examining a problem from multiple angles, seeking the deep connections and application boundaries of knowledge. The depth, breadth, and freedom of your thought directly determine your ability to apply knowledge flexibly.
Selective Recitation to Form “Intuition”: For humanities like language and design, repeatedly reading and reciting top-tier classic examples and carefully savoring their subtleties is an excellent way to cultivate “feel” or “intuition.” With sufficient accumulation, you can make high-quality judgments and creations directly from this internalized sense.
Seeking Cross-Domain Patterns: Become adept at thinking about whether the same underlying patterns exist in different problems. For instance, clear and standardized documentation is a common factor for success in any task. Recognizing this, you will prioritize quality record-keeping in all your work.
Establishing a Decision-Making Framework For a certain class of problems, you must not only summarize the methods that must be used and those that can be used, but also clearly identify the methods that must never be used. This drastically improves your decision-making efficiency in unknown situations. When facing a new problem, first try the mandatory methods; if they fail, try the optional ones. But under all circumstances, avoid the “dead ends” that have been proven ineffective, thereby saving precious time and energy.
Cross-Disciplinary Integration and Application
Transfer of Knowledge and Methods: While different disciplines have distinct knowledge systems, their underlying thought processes and analytical tools are often similar. Become skilled at applying knowledge from one field (e.g., history) to another (e.g., political analysis), or using tools from one domain (e.g., mathematical models) to solve problems in others (e.g., physics, biology). Likewise, effective learning methods you summarize in one discipline can often be transferred to others.
Solving Real-World Problems Holistically: Real-world problems are often complex and interdisciplinary. The ultimate purpose of learning is to use knowledge to solve them. Train yourself to synthesize knowledge from different disciplines to analyze and address a complex real-world issue, such as environmental problems, which requires drawing upon knowledge from physics, chemistry, geography, history, and more.
Breaking Through Cognitive Fixedness The greatest danger for advanced learners is being constrained by past successful experiences. One must become adept at extracting more universally applicable laws and principles from specific case studies. A master of physics can see the unifying Newtonian laws behind countless seemingly different problems; an expert historian can summarize universal patterns of human behavior from events in different eras and countries. When they think, specific cases are replaceable variables, while the underlying principles are the eternal constants.
The Mindset and State for Flexible Application To truly achieve flexible application, techniques and methods are only one part of the equation; the practitioner’s internal state is even more critical.
Maintain a Relaxed, Joyful, and Inspired Mindset: Flexible, creative thinking is born from a positive and open state of mind. In advanced learning, if the “intense drive” for efficiency conflicts with maintaining a positive mindset, the latter should be prioritized.
Ensure High Mental Clarity: Applying knowledge flexibly requires the brain to be exceptionally clear and sharp. If high-intensity learning leads to mental fog, that “effort” is ineffective. You must prioritize your mental state, even if it means reducing study time. A key reason many diligent learners fail to reach the advanced stage is that they spend too much time accumulating knowledge in a state of low mental clarity.