1, at the request of the school, set up a math club class, which requires not only the content of learning now, but also a higher dimension to examine the internal relations and core ideas of mathematics and related disciplines;
After careful consideration, I finally chose logic. Because in mathematics and other sciences, a lot of knowledge is closely related to this, such as: definition and classification, what is a proposition (true and false proposition, inverse proposition, negative proposition …), reasoning and argumentation (geometric deduction, deductive reasoning, inductive reasoning in junior high school …), confirmation and falsification, axiomatic system, reduction to absurdity, and set and logic terms in senior high school.
3. Another reason is that, based on practical teaching experience, some students with weak thinking will encounter a great cognitive conflict when they first learn geometric proof: what is proof? Why "prove"? How can I count as "proof"? These very strange contents, the result of forced entry is great inadaptability.
In order to increase the interest, I quoted a large number of non-mathematical cases in class, and the results were very popular with students. With the progress of the course, I found that the content can be richer and more closely related to mathematics, mainly thinking, which will naturally be more meaningful. After that, we can also discuss with students how to study more effectively ... In short, the more significant this course is, the more carefully polished it is, and it can be made into a course connecting primary school and junior high school.
1, after junior high school, students gradually enter the formal operation stage, and have the basis of thinking mode in the general scientific sense;
2. Matching with this physiological feature, the setting of mathematics in junior middle school is more formal and abstract than that in primary school, which also puts forward higher requirements for students.
3. It is said that junior high school is more difficult than primary school in knowledge, but in fact it is difficult to change the way of thinking, which is the deeper reason why many students can't keep up with the rhythm.
Although junior high school students have entered the formal operation stage, they can only be regarded as the theoretical basis. From theory to practice, it needs a gradual transformation process, and there are differences among students;
5. Compared with junior high school and senior high school, there is not much difference in thinking mode. Most of the mathematics thoughts in senior high school have actually been reflected in junior high school. The biggest difference is the difficulty of knowledge.
6. After all, junior high school knowledge is not too much, and most of them can be dealt with by rote memorization and mechanical training. However, if you don't master the correct core literacy of the subject, the disadvantage will be revealed in high school.
7. In a word, the connection between primary school and junior high school, especially the change of thinking mode, is a big problem worthy of teachers' thinking.
1, having said so much, what should I do? Since it is a question of thinking, who else can be the most primitive thinking logic besides the basic "logic philosophy"? Of course, "logical philosophy" covers a wide range, but we should focus on mathematics (philosophy) and science (philosophy)-this is the core of the content;
2. Since it is to help students change their thinking, we should develop according to the current situation of students. Combined with students' cognitive psychology, these formal logic systems are brought to students in a way that students can accept. Let's start with examples and emphasize concepts as little as possible. -This is the boot mode.
1. 1? The origin of logic: language is the root of misunderstanding-the imperfection of human thinking and language-logic comes from human rational self-reflection;
(1) Quote: A common paradox in life-the liar paradox;
Through a simple example, the concept of "paradox" is introduced: on the surface, the same proposition or reasoning implies two opposite conclusions. However, more expansion only gives students a general understanding.
At the beginning, students will be curious, try to think about the reasons and give some time appropriately.
There are more interesting "paradoxes" in the follow-up.
(2) Zeno paradox-summation of geometric series, simple explanation;
This problem will not exist forever. According to the argument, it is actually a geometric series, and its sum has a limit value. The students can't understand the specific calculation, but the general idea is acceptable. The students will be very excited after the results are announced. It turns out that mathematics is so powerful.
(3) Half-fee litigation.
……
Objective: Through some interesting cases, guide students to get the understanding that the language we communicate is actually imperfect, and many times, misunderstanding is only caused by language.
First of all, it needs to be clear that the above problems are not grammatical errors, so what should be done? -In order to use language and thinking correctly and make rational communication go smoothly, should people abide by some universal principles, assumptions or laws?
Lead to the following contents: identity, law of contradiction, law of excluded middle.
1.2? Equality: Are you talking about the same thing?
(1) Example-Problems in Mathematics.
(2) the scarecrow fallacy;
(3) Several possibilities of violating the law of identity-connecting the preceding with the following, leading to the concept;
(4) Mathematical case-what is a "point"? -leading to unclear meanings of concepts and definitions;
(5) The concept in life is unknown.
In fact, the "unclear concept" in life has little to do with mathematics. From this perspective, there is absolutely no need to mention it. The reason why I want to mention this is to expand the number of students. After all, education is holistic.
1.3? Law of contradiction: I am not proud of you!
(1) Quote: The story of spear and shield;
(2) Case: Is God omnipotent?
(3) Who broke the glass-are they really contradictory?
(4) What is contradiction? Is contradiction necessarily derogatory? "contradiction" in mathematics? Binary, ternary and quaternary opposites, Wayne diagram;
(5) the relationship between fractions and integers-mutual exclusion and classification
1.4? Law of excluded middle: Refuse to be two-faced.
(1) citation: directly given;
(2) reduction to absurdity-how many straight lines are perpendicular to the known straight lines in the same plane and beyond the straight lines?
(3) Exclusion method-what is the side length of a square with an area of 2?
Classification of rational numbers.
1.5 Does this logic make sense?
(1) Quote-Don't complain doesn't mean you like it?
(2) The contradictions caused by one-to-one correspondence-endless-seemingly "contradictions" are actually the limitations of human cognition;
(3) Higher education does not mean higher ability? Why do big companies like to recruit graduates from famous schools?
(4) The logic in life and mathematics is reasonable.
(5)……
2. 1 What is "reasoning and proof"? -second, talk about romance.
(1) Quote: Is Christianity allowed to discuss the existence of God? !
(2) What is reasoning? What is proof? Are they the same?
Subsequent general content can be more closely related to mathematics. ...
(1) What is a proposition? How to judge true and false?
(2) Only fools do that-syllogism and proposition, condition and conclusion, original proposition and inverse proposition;
(3) Axioms and theorems;
(4) Axiomatic system;
(5) Deductive reasoning and inductive reasoning;
(6) Verification and falsification, philosophy of mathematics and philosophy of science;
(7)……
1, "What is logic?" Fifteen lectures on logic ";
2. Ten lectures on philosophy of science and fifteen lectures on philosophy of science and technology;
3. Basic concepts and algorithms, lectures on basic mathematical thoughts 18, probability of mathematical thoughts, and various books on the history of mathematics;
4. The purpose of children's psychology and education
5. Others