Mathematics College Entrance Examination and Solving Problems in College Entrance Examination
Luo Zengru (
1945
—)
, male, from Huizhou, Guangdong,
1962
I studied in Sun Yat-sen University in 2000 and worked as a miner for a long time after graduation.
Teachers in children's schools. At present, he is a professor in the Department of Mathematics of Shaanxi Normal University, a doctoral supervisor of curriculum and teaching theory (mathematics), and enjoys the country.
Author of Special Government Allowance of the State Council: Introduction to Solving Mathematical Problems.
、
Introduction to Mathematics Competition
、
Analysis on Middle School Mathematics Class
、
How to solve math problems in college entrance examination
、
How to solve math problems in senior high school entrance examination
、
Mathematical understanding
、
Intuitive exploration method
、
zero distance
From mathematical communication
、
Theory and practice of solving mathematical problems in middle schools.
300
Ten thousand words, published articles.
300
Many articles. from
1980
Since then, I have studied the problem-solving and proposition of college entrance examination and competition for decades, as well as the project of "focusing on mathematical quality"
Serve basic education.
-The theoretical construction of solving problems in the college entrance examination of mathematics won the provincial outstanding teaching achievement award, and the project "Construction of Olympic Mathematics Discipline"
He has won the National Excellent Teaching Achievement Award.
Mathematics college entrance examination
0. 1
The whole process of mathematics college entrance examination
from
1977
Resume the college entrance examination in,
History has experienced brilliant
30
Many spring and autumn seasons,
Cultural accumulation around the college entrance examination work
Studying in the exam,
Talent science and mathematics form academic achievements.
I am looking forward to the birth of the math college entrance examination.
Mathematics college entrance examination
The whole work includes
four
A basic question
：
(
1
) the problem of mastering mathematical knowledge
——
How to review.
(pedagogy)
(
2
) improve the ability to solve problems
——
How to solve the problem.
(Mathematics)
(
three
) the application of examination skills
——
How to answer questions?
(Examination Science)
(
four
) fill in the volunteer questions scientifically.
——
How to choose.
(operational research)
Among them,
The core is to solve the problem.
Doing a good review is to accumulate strength for solving problems.
The application of examination technology is enough to solve the problem.
Giving full play to subsection grading technology is the application of problem-solving strategy, and problem-solving ability is the core competitiveness of mathematics college entrance examination.
0.2
The Style of Mathematics College Entrance Examination Proposition
The proposition of college entrance examination has always been "striving for progress in stability, seeking change in stability and seeking innovation in stability"
, explore
Fair selection, service quality education
The service road has formed some stable styles and noteworthy orientations.
.
(
1
) On the basis of a comprehensive examination of "basic knowledge, basic skills and basic methods", the mathematical thinking method is more prominent.
Examination highlights the connection between mathematics and real life.
.
Comprehensive coverage of science in middle school mathematics textbooks.
15
Personal and liberal arts
13
A knowledge module, the coverage of knowledge points.
60%
(About
70
~
80
A knowledge point)
; At the same time, the test paper highlights the core content of this question, set and function, solid geometry and solution.
The analysis of key contents such as geometry, sequence, inequality and derivative application occupies a high proportion in the test paper, and the overall structure is reasonable.
It also reached the necessary depth of investigation;
In addition,
On the basis of taking the single type of test questions in the module as the main body, the knowledge is handed over.
Bifurcation, permeation and synthesis.
Although the examination paper covers the basic knowledge comprehensively,
Will pay attention to the examination of ability,
Especially logical thinking ability,
service ability
And spatial imagination. As for practical ability and innovative consciousness, it is difficult to reflect.
(five abilities)
In terms of mathematical thinking methods,
Seven basic mathematical ideas will be involved in the test paper.
Among them,
Mathematics of functions and equations
Thinking method,
The mathematical thinking method of combining numbers and shapes,
The mathematical thinking method of transformation and transformation will be more prominent.
middle school
The basic mathematical thinking method of the stage mainly
"Basic thinking method of using letters to represent numbers"
"Set and the corresponding basic ideas.
Law "
, and
● Basic mathematical ideas of functions and equations.
(Through function questions and comprehensive questions)
● The basic mathematical idea of the combination of numbers and shapes.
(Through function problems, analytic geometry synthesis problems, constructing graphs, etc. )
● Basic mathematical ideas of classification and integration.
(Through the arrangement of comprehensive questions, combined questions and parameter discussion questions)
The basic mathematical thought of transformation and transformation.
(through comprehensive questions)
2
Special and general basic mathematical ideas.
(through comprehensive questions)
The basic mathematical thought of finiteness and infinity.
(Through Limit and Calculus Function Problems)
● Basic mathematical ideas of possibility and necessity.
(Through Probabilistic and Statistical Questions)
Main problem solving methods
(undetermined coefficient method,
Alternative methods,
Matching method,
Reduction to absurdity,
Alternative method,
Exclusion method,
Mathematical induction)
There will be different degrees of reflection.
(
2
)
When examining the subject of middle school mathematics,
It will reflect the demand for further study of advanced mathematics.
.
Especially some people.
A challenging ending,
Especially after the idea of provincial independence was put forward,
More
"Pay attention to pure mathematics,
Test candidates' potential for further study. "
(Someone saw the mutual penetration of the college entrance examination and the competition)
.
(
three
) Infiltration of new curriculum ideas
.
Although the curriculum reform in the new century has just begun (high school textbooks have just begun to be tried out)
, but it
Three-dimensional goals and ten basic concepts will begin to penetrate (where the curriculum reform is changed, the college entrance examination reform will also be changed)
.
Like fate
The scope of the topic has been expanded, and humanistic care has emerged, which embodies the curriculum goal of "emotion, attitude and values"
.
(
four
) on the proposition technology, you can see:
(1) is based on the textbook, and is not limited to the textbook.
.
(2) Designing propositions at the intersection of knowledge.
.
③ Ability and concept
.
Changed the past understanding.
.
④ Reduce the number of questions, reduce the difficulty and increase the time for students to analyze and think.
.
⑤ Two small climaxes from easy to difficult are designed for three types of questions.
.
⑥ Turn a small problem into a full volume.
.
⑦ It is easier to cut into the problem than to go deep into it (step problem).
.
(8) Avoid rote memorization and cumbersome operations (the test paper provides formulas that are difficult to remember and easy to forget).
.
Pet-name ruby liberal arts papers, the difficulty is not the same (sister)
.
0.3
The Organization of Mathematics College Entrance Examination Review
(
1
) guiding ideology
(
2
) resume the stage arrangement of the college entrance examination.
(
three
) Compilation of Mathematics Review Questions
(
four
) the organization and evaluation of mathematical simulation examination
(
five
) On-the-spot Strategies for Mathematics College Entrance Examination
0.4
Research work of mathematics college entrance examination
(
1
) the characteristics of college entrance examination mathematics
(
2
) the characteristics of solving problems in mathematics college entrance examination
(
three
Solution of multiple-choice questions in mathematics college entrance examination
(
four
) Solve the Fill-in-the-Blank Problem in Mathematics College Entrance Examination
(
five
) the solution of mathematics college entrance examination questions
(
six
) Error analysis of solving problems in mathematics college entrance examination (there will be strategic errors if the solution is correct)
(
seven
) Research on Mathematics Proposition of College Entrance Examination
(
eight
) Mathematics College Entrance Examination Paper Composition
(
nine
) Mathematics college entrance examination questions
(
10
) Research on Mathematics College Entrance Examination Proposition
(
1 1
) Research on the Difficulty of Mathematics College Entrance Examination
(
12
) Research on Mathematics College Entrance Examination Score
(
13
)
three
0.5
Basic suggestions on the scene of college entrance examination
(
1
) keep tight inside and loose outside in a state of war.
.
(
2
) use the answering strategy that adapts to the college entrance examination.
.
(
three
) use test skills to deal with the selection.
.
College entrance examination answering technology
● Enter the role in advance.
.
● Quickly find out the "topic"
.
● Perform "three cycles"
.
● Do "four first and four later"
.
● Answer "One Slow and One Fast"
.
● Strive for a higher level based on the middle and lower levels.
.
● Based on success, pay attention to review.
.
● Tight inside and loose outside
.
0.6
Fill in the college entrance examination volunteers
.
● Priorities for further research.
.
● Employment priority
.
● Professional priority
.
● Cost priority
.
● Regional priorities
.
● Some considerations
.
● Parents decide
.
1
Necessary basis for solving math problems in college entrance examination
1- 1
Clear problem solving process
1- 1- 1
General procedures for solving mathematical problems
(Paulia:
How to solve the problem
)
Find out the meaning of the question
The most important thing is to find out what the conditions are.
What is the conclusion?
How many are there in each?
How to establish the logical connection between conditions and conclusions
example
1
Three equations are known.
2
2
2
four
0,
2
1
16
0,
2
three
10
x
Title used by people who don't want to specify their gender.
x
m
x
x
Title used by people who don't want to specify their gender.
m
At least one equation has real roots and real numbers.
m
The value range of.
solution
1
If the solution is positive and at least one of the three equations has a real root, it will appear.
seven
There are two possibilities, and the situation is more complicated.
But the opposite is only one case: the three equations have no real roots, and the problem becomes extremely simple.
2
1
2
2
2
three
four
four
four
four
0,
four
1
four
16
four
five
three
0,
four
four
three
10
four
five
2
0,
m
m
m
m
m
m
m
m
m
m