北美作业代写：The cultivation of mathematical thinking

下面为大家整理一篇优秀的essay代写范文- The cultivation of mathematical thinking，供大家参考学习，这篇论文讨论了数学思维的培养。数学是严密的科学，拥有独特的概念和公式等，按照一定的逻辑规则组成的严密的科学体系，具有很强的系统性。而数学思维就是围绕这些概念和公式等的思维活动。对数学概念和公式等的教学可以让学生从一般现象中通过总结和计算，最后得出结论，以此培养学生的数学思维能力。

Is mathematical thinking logical? If mathematical thinking is logical thinking, can mathematics be called logic? But logic is really a separate science. To this end, we can concluded that there is a difference between mathematics and logic, we train and develop students' mathematical thinking, is based on mathematical problems and mathematical thinking, but it is not only a simple logical thinking training. The purpose of this paper is to distinguish mathematical thinking from logical thinking, not to confuse it, and to examine its unique thinking cultivation from a mathematical perspective.

When it comes to thinking, first of all, let us think of psychology, indeed, the phenomenon of thinking is one of the studies of psychology, the psychological thinking is the process of the human brain work to reflect the objective reality, is the human mind in the process of understanding the world to compare, analysis, comprehensive ability, and is a function of the human brain. There are many and many categories of thinking. Some divide thinking into image thinking, abstract thinking, calculus thinking, analogy thinking, imagination thinking, integration thinking, divergent thinking, logical thinking, judgment thinking and practical thinking. Some divide thinking into logical thinking, divergent thinking, intuitive thinking, integrated thinking, image thinking and creative thinking. These are all forms of thinking. No matter how they are classified, logical thinking is an independent form of thinking, which is not the same as mathematical thinking, but requires strict logic. So what is mathematical thinking? Let's first see what math is. Mathematics is a rigorous science, which has concepts, properties, theorems, formulas and so on. It is a strict scientific system composed of certain logical rules and has a strong system. Mathematical thinking is thinking around these concepts, properties, theorems, formulas and so on. Below we carry on the simple elaboration from these four aspects to its mathematics thought training.

Concept is an essential element of any subject. Every subject has its own unique concept. How can students understand, remember and apply concepts? The general practice is to teach, students remember, and finally do the questions. However, this approach is a concept, the teacher taught students remember a concept, teachers don't teach, students have the ability to summarize the concept of, so, we should teach students to learn to define concepts. For example, we want to the triangle next to define, can draw on the blackboard many different size and different angles of a triangle, or in real life to find out students' daily can see triangle, let the student through the observation of the triangle, summarizes the commonness of the triangle, triangle has three sides and three corners, in the same plane, the three sides end to end, the concept of the triangle nature is: in the same plane, composed of three edge end to end. So, through our observation and summary process, let the students to learn a kind of summary of the concept of method, if we mastered the concept of triangle, then we can summarize the concept of quadrilateral, pentagon and N deformation.

A property in mathematics is a description of a concept, a description of the object in question. Concepts tend to use "what's what" format, and nature is what format, in the concept of triangle, describe the nature of the triangle is: there are three sides and three angles, the same plane, end to end, and so on. When we summarize the nature, can't say it out directly by the teacher, but to allow students to summarize, if the results directly by the teacher to the student, killed the enthusiasm and initiative of students' autonomous learning, eliminated the students learn the opportunity to learn.

Theorem is after numerous logic reasoning judgement for the description of the "true", such as additive commutative law of teaching, we can't without understanding the students told students directly additive commutative law is the addition of two addend, exchanging the positions of the addend, and remains the same. Let students calculate many addition problem, and then in the process of calculation of each other by exchanging the positions of the addend, let the student see if concluded and equal, so, lets the student in practice to go through their own calculus additive commutative law are obtained. In the same way, such as the addition of associative law, associative law, multiplication commutative law, such as theorem, can use the same pattern for teaching, let the student through his own calculation summary conclusion.

Above all, can only say that the mathematical thinking ability of individual case, also can only say that some Suggestions, in mathematics teaching in the classroom, real situation is much more complex, because mathematics or other subjects, the object of education is people, people's thinking activity differ in thousands ways, to be able to do the thinking ability of students of differ in thousands ways according to their aptitude, targeted training, classroom teaching can not do that, we are talking about is only in view of the universal phenomenon of classroom teaching discourse on the topic. As for the cultivation of mathematical thinking, we dare not elaborate too much here. The above mentioned mathematical classroom teaching only sticks to the principle from practice to practice. Of mathematical concept, nature, theorem, formula of teaching makes students from the general phenomenon through induction, summary, calculation, finally came to the conclusion that in order to better develop the students' ability of mathematical thinking.

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