How to improve the thinking ability of first-year students

The establishment and cultivation of mathematical thinking is the establishment and development of the core of students' abstract thinking, the first year students already have a preliminary abstract thinking ability, from the first year, the establishment and cultivation of students' good mathematical thinking ability, it is very important for students to learn math well, improve their performance, expanding their thinking, and improve the level of intelligence and so on.

Keywords: first year students, mathematical thinking ability, stimulation, cultivation

Mathematical thinking ability belongs to a kind of logical thinking ability, which is to think about the problem, analyze the problem, and solve the problem with mathematical point of view. The new syllabus puts forward the requirements of mathematical ability is "to cultivate students' arithmetic ability, logical thinking ability and spatial imagination ability, in order to gradually develop the ability to analyze and solve problems by using mathematical knowledge". Among the mathematical abilities, the cultivation of thinking ability is the core . [1]

So, how to stimulate and cultivate students' good mathematical thinking ability? According to the author's own nearly 30 years of teaching experience and experience, fully integrated with the research results of some education experts at home and abroad, that should be carried out from the following four major aspects:

I. Cultivate students' interest in mathematics as an inducement to stimulate and cultivate students' mathematical intuitive thinking ability

1. The method is to introduce interesting stories of math into the classroom to stimulate students' interest in math.

The author mostly takes those very interesting math problems in life as the introduction to stimulate students' curiosity and love for math. Examples are as follows:

"The epitaph of the great ancient Greek mathematician Dufantu is different, not an inscription, but a math problem, which reads: Here is a stone monument in which Dufantu is buried. How long he lived, the following words can tell you: his childhood was 1/6 of his life, then 1/12 of his adolescence, and after 1/7 of his life, he found his life partner. 5 years later, the god of marriage gave him a son, but the son's fate was not good, and only lived half of his father's life span, and then left in a hurry. This was a heavy blow to him, and four years later, saddened by the loss of his beloved son, Dupantu finally bade farewell to science and departed this life."

As soon as the example was shown, the students were immediately interested, talking, discussing, analyzing and calculating. This problem is not difficult, students can solve it with sixth-grade knowledge, but of course, it is easier to solve it with first-year one-variable equations. This kind of problem can fully stimulate students' interest in math. [2]

There are countless interesting math problems such as these, as long as you pay attention to the accumulation of the usual, the class cited one or two, the student's interest will be stimulated, but also on the cultivation of intuitive thinking is also very favorable.

2. Cultivate students' mathematical intuitive thinking

The essence of mathematical intuitive thinking is the mathematical object and its structure, the relationship between the imagination and judgment, which is similar to the conjecture, but also manifested as inspiration, epiphany. [3]

Looking at the history of the development of mathematics and science, many major discoveries are produced under the intuitive thinking: Hamilton on the way to a walk, inadvertently sparked the construction of the four elements; Archimedes discovered the law of buoyancy when he took a bath. Newton discovered Earth's gravity from an apple falling to the ground.

Teachers in teaching as long as they continue to activate the students' inner potential, the students' thinking in the breadth, depth, independence, flexibility and other aspects can be developed.

3. Cultivation Methods

The teaching fully mobilized all the problems related to the apparent consciousness and subconsciousness, with the help of students' keen imagination and rapid judgment, to understand the essence of knowledge, grasp the relationship between mathematics and real life.

(1) Contact with real life, cultivate students' intuitive sense of mathematics in life;

(2) Cultivate the simplicity and conciseness of students' thinking in the process of solving problems;

(3) Guide students to read more questions and understand the problem from multiple perspectives.

Two, expand the depth and breadth of students' thinking, stimulate and cultivate creative thinking

Modern society needs people who are rich in creative consciousness and have innovative qualities, which is exactly what our students lack.

Many students have difficulty in understanding and answering math problems, the reason for which is due to the narrowness of divergent thinking, that is, the depth and breadth of thinking is not enough. Therefore, in teaching, teachers should focus on the cultivation of students' depth and breadth of thinking. A problem is the most effective way to expand the thinking space of students.

1. Training divergent thinking. Encourage students to boldly explore new relationships between knowledge, looking for new answers to questions, and strive to use comparison, imagination and other methods to think about the problem.

Quite a few exercises have a variety of solutions, and therefore after solving, to guide students to think: whether there is a better, more concise way to inspire them to think from multiple perspectives. After a problem, we should analyze the rationality of various solutions, and select the best solution by comparison. This not only strengthens the connection between knowledge and expands the students' ideas of solving problems, but also develops the ability to think carefully, flexibly and diffusively. It can also cultivate innovative thinking and open up the space of divergent thinking.

2. Expand knowledge. This aspect of the practice is very simple, do more and more accumulation of type questions.

3. Classroom teaching teachers should encourage students to boldly put forward different opinions.

Three, math problems into life, learning math in life

Many teachers have a fatal problem in math teaching, that is, on the knowledge of knowledge, rigid, boring classroom, students lack of interest, do not like to listen. So, how can we integrate math problems into students' lives, I think: put them in their existing life experience to understand better.

1. Examples of more life phenomena and examples

The author in teaching "rational numbers", the students of the concept of negative numbers to establish and understand the difficulties, then life such as "sub-zero temperatures", shopping malls, "basement", "owe others money" as an example, so that they first realize that negative numbers are around, negative numbers exist everywhere in life, students combined with the reality of life, it is much easier to understand.

2. Carry out classroom activities to cultivate and improve students' hands-on ability

Discussing and solving some math-intelligence-type operation problems can not only cultivate students' hobbies and interests and develop their intelligence, but also improve students' hands-on ability.

In the "Preliminary Geometry" chapter, "Angle" section of the teaching, I let the students use the hands of a pair of right-angled triangle board, hand spelled out 15 °, 75 °, 105 °, 120 °, 135 °, 150 ° of the Angle, a lot of students holding the triangle board can not begin, will not spell, spell out. It was only after the author's guidance, inspiration and demonstration that students learned to use the triangle board to spell out different angles. This kind of math activities can intuitively use mathematical knowledge and measuring tools to solve practical problems, and improve students' hands-on ability.

Four, cultivate good study habits and scientific learning, teaching methods

Study habits and methods seem to have nothing to do with the development of thinking, but I think, do a good job in the cultivation of students' non-intellectual factors, but also on the thinking of the stimulation and cultivation of a huge role in promoting.

1. Several good habits necessary for learning mathematics

(1) listen carefully; (2) think positively; (3) good at asking questions; (4) good at reflecting and summarizing.

2. Several scientific learning methods necessary for math learning

(1) advance study;

(2) correction of mistakes and accumulation of key questions;

(3) teacher-student and student-student exchanges, discussions, and cooperation;

(4) the role of the instructor to change: from the dominant player in teaching to the leader of the students' learning, the inspirer, the collaborator, and the questioner. The teacher's role is changed: from the leading teacher to the student learning guide, inspirer, collaborator and questioner. In the process of student learning, timely guidance, enlightenment, doubt and expansion.

To stimulate and develop students' mathematical thinking ability is not an easy task overnight, as long as from the beginning, the establishment of a harmonious relationship between teachers and students, to create an active classroom atmosphere, students develop good student habits, master the scientific learning methods, teachers strict requirements and guidance, students' mathematical thinking can be stimulated and cultivated up.