In the process of summarizing the knowledge of the "comprehensive recall" learning method, we tend to summarize and consolidate knowledge according to the order of course teaching, which is also very effective, but there is also a disadvantage, that is, the way is relatively single, and it is impossible to efficiently build a wall of knowledge.
Today we introduce how to deduce more knowledge through logic and enrich your own knowledge system.
For example, when you are studying, you learn the solution of a specific problem type, if you just stop here, then the same problem type to change the conditions, you may have to spend your brain to rethink the solution. However, if you can summarize the general rules on the basis of specific question types, then such problem types can be solved in the future. This is the use of logic to improve their learning ability.
This world is a world that pays attention to the "causal logic" thinking, deriving the result from the cause and deducing the cause from the result, as long as it conforms to such causal logic, it will have strong persuasiveness and facilitate memory and application.
Logic is meticulousness
<h1 class="pgc-h-arrow-right" > logical method</h1>
Logic is a way of thinking, this term comes from the transliteration of the word logic, mainly including inductive logic, deductive logic, but there is also a logic in learning, that is, symmetric logic.
1. Inductive logic
Inductive logic is to find a common law from many phenomena, such as long-term observation of the weather, you can summarize the law of the weather, predict the weather conditions in recent days, or extract a unified solution idea from many similar problem types.
This inductive method can sometimes refine precise methods or routines, and sometimes it can enhance your "intuition" and let you see a phenomenon and give an answer in an instant.
After the reform of a steel factory, it was bought by a boss in Guangzhou, and the boss saw a teacher who made a cup of strong tea every time he went to work, lay on a recliner, and occasionally shouted a voice "out of steel", and then it was fine, and he left at the point when he left work. The boss in Guangzhou fired him because he felt that the teacher had no value, and as a result, it was difficult for the steel factory to produce high-quality steel from then on. Later, after being pointed out by others, he re-invited the teacher Fu with double salary, and the high-quality steel was guaranteed. Because the teacher Fu has been making steel for more than 30 years, he has also "summarized" a set of laws for the temperature of steel, and has an "intuitive" feeling of the fire control of steel, which is more accurate and reliable than the thermometer.
Summarize the general laws
Similarly, in the process of summarizing the body of knowledge, this method is also very practical, for example, if you do a lot of topics about the ship sailing in the upstream and downstream two docks, you will find a common problem:
The speed of the water flow = (down-water speed - counter-water speed) ÷2
Boat speed in still water = (down-water speed + counter-water speed) ÷2
As long as these two laws are summarized, in the future, when encountering this type of problem, you can directly calculate the speed of the water flow and the speed of the boat, and there is no need to list equations to solve the problem.
However, inductive logic has a point of attention, that is, do not generalize the whole, that is, after deriving the general law according to several similar phenomena, we must use this law to verify it to see if we can explain all the phenomena of the same kind.
The same is true in learning, whether the general rules summarized can really solve all the problems of this type of problem, after passing the verification, it can be determined that they are really general rules.
2. Deductive logic
Deductive logic is the decomposition of countless specific cases and scenarios according to a general rule.
For example, according to the law of "fish scale day is either windy or rainy", as long as the fish scale day appears, we can "deduce" the specific weather for the next three days.
Deductive logic is very common in the learning process, textbooks will generally give theorems or formulas, we solve countless specific application problems according to theorems and formulas.
For example, for the formula of "profit margin = (selling price - cost) / cost", you can design a variety of economic application questions, and the application questions of different discounts in the promotion of Double Eleven are very typical question types and common examination questions.
Some students have fewer opportunities to participate in shopping, and they will be frustrated when they encounter this type of problem, but once they master this deduction method, they will find that this kind of topic is actually very simple, and they will take fewer detours and pay less tuition when shopping online in the future.
Play out all the scenes
3. Symmetric logic
This logical approach is a routine that often occurs in debate competitions, which is to use the opposite line of thinking like a mirror to refute the other party.
There was a musician who was very dissatisfied with the current music, and a friend said, "This is pop music, everyone likes it." ”
"Does everyone who is popular like it?"
"Of course, if you don't like it, how can it be popular?"
"So everyone likes the flu too?"
"Uh..."
In learning, this logical approach is also very practical, such as the method of counter-evidence and the law of reduction, that is, to find the opposite content. When building a body of knowledge, symmetric logic can fill in the blind spots and loopholes in our thinking.
For example, you've found the "universal rule for chasing problems in the same direction on the runway": every extra lap you run, you catch up.
At this point, you can think about the opposite, that is, whether this general rule can also be used in the "opposite" chase problem, and finally you will find another general rule: every time you meet, the two sides go together in a complete circle.
Find blind spots in your thinking from the perspective of symmetry
<h1 class="pgc-h-arrow-right" > apply logical methods to build a more sophisticated body of knowledge</h1>
Many students like to summarize knowledge, form their own knowledge system, this is a good habit, if you use logical methods to assist yourself, then the content of the knowledge system will be more comprehensive, accurate, easy to remember, while further improving their logical thinking ability.
Because the process of applying logic is a rigorous deduction process, involving more content, in the reasoning process, you can use paper and pencil or mind mapping tools to assist the recording.
1. Deduce the application question type without omission
Deductive logic deduces the theorems, rules, and formulas in textbooks to determine all application scenarios and question types.
For example, the definition of the number axis, "a straight line that specifies the origin, positive direction, and unit length is called the number axis", which can deduce many judgment questions:
The number on the right side of the axis must be larger than the number on the left.
As long as the origin and unit length are determined, this line is a number axis.
Positive integers, 0s, and negative integers are all numbers on the number axis.
The unit length on the number axis can be 0.5.
A ray extending to the right at the origin is a number axis if the unit length is added
….
These conceptual judgment questions about the number axis cover the four key elements of the definition of the number axis: origin, positive direction, unit length, and straight line. If you understand these four key elements correctly (which is also the trap of the question), you can give the correct structure when encountering similar question types.
When deriving scenes through deductive logic, there is a point of attention: to cover the scenes corresponding to all the points, do not overlap, do not omit, that is, these scenes are "vertical orthogonal".
2. Summarize the common laws and verify the correctness
Whether it is the questions that the teacher takes or brushes the questions himself, he will encounter a large number of similar questions, and if you do more of these questions, you will find similar ideas.
However, if you first encounter these problems and summarize the general solution methods, then you can jump over when you encounter such problems in the future, save time to do other problems, and improve learning efficiency.
Here is the process of summarizing the common laws:
For example, the previously mentioned number reporting game needs to further summarize the general rules on the basis of specific problem solving ideas, and no matter how to modify the conditions and change the problem type in the future, it can be applied.
Starting from 1, the two children take turns to report the number sequentially on the basis of each other's number, each time can report 1 to 2 consecutive numbers, and whoever reports 30 first wins.
The solution to this problem has a few small bends to understand, after the teacher gives you the solution, you may be clear, but at this time if you are only satisfied with the problem itself is too pity, because the problem can be changed to a variety of ways to play, such as "who first reports to 30 to count losses", "who reports to 31 first to count win", "each time can report 1 to 3 numbers, who reports 30 first to count win" and so on.
In this case, you need to discuss the solution ideas of the above problems with the teacher, and you will find that they have a commonality: the number of reported numbers is added to one is the control length of a winning chance, and then the final 30 minus the multiple of the control length can be calculated to calculate the first number of stable wins.
3. Through symmetrical logic, find the blind spot of thinking
This logical approach is to ask three questions:
(1) "What is the opposite?" Are the current general laws also used? ”
(2) "In addition to the current general approach, are there any special cases?" ”
(3) "At the critical value, what special situation will there be?" ”
Teachers especially like to use this symmetrical logic method to design traps when asking questions to check whether the students' knowledge is comprehensive.
Opposite: For example, the opposite of the law " For natural numbers , the closer to the origin , the smaller " ( " On the axis of numbers , the closer the number is to the origin , the smaller the number ) does not hold.
Exception: For example, the phrase "rational numbers are either integers or negative" misses a special case: 0.
Critical value: For example, "the maximum value of y is found to be | y=|2x+6|+|1-x|-4||x-1", which uses the idea of taking the maximum value on the critical value.
Symmetric logic will play a huge role in logical reasoning, please use the above three questions when learning each knowledge point to ask questions from me, find blind spots and possible pitfalls.
<h1 class="pgc-h-arrow-right" > one-sentence summary</h1>
The process of learning is the process of establishing a complete knowledge system, and the rational use of logical methods can establish this knowledge system more efficiently and rigorously: deduce all possible scenarios through deductive logic, find general laws through inductive logic, and find blind spots in thinking through symmetrical logic.
Master the logic, become a big tool early.
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