1. The connection between numbers and algebra
Number and algebra are the basic contents of mathematics in primary and secondary schools.
The primary school stage is mainly the operation of exponent and number (the number here mainly refers to non-negative rational number, the so-called arithmetic number).
In middle school, in addition to the concept of number extended to real numbers, it is more important to have formula operations. From primary school to middle school, we learn the operation of numbers and letters, which is algebra. On this basis, we study the operations and relations of algebra, and the resulting equations, inequalities, functions and so on. It constitutes the basic part of number and algebra in junior high school mathematics.
Therefore, from primary school to middle school, the main change in the field of numbers and algebra is from the concrete operation of numbers to the formal operation of algebraic expressions. In order to successfully complete this transformation, we should accumulate some "semi-formal operation" experience in junior high school and junior high school.
In addition, in the field of number and algebra, another important connection point between elementary and secondary mathematics is to list simple equations.
Simple equations are common in primary and secondary schools, but in primary schools, due to the influence of students' arithmetic thinking, the listed equations often cannot reflect the core idea of equations. From the perspective of connecting primary and secondary schools, we should guide students to understand the importance of unknown quantities participating in the operation in the process of formulating equations. The equation 1200+ 100=x is listed, which shows that students' thinking mode is arithmetic in essence, not algebra. Guiding students' thinking mode to gradually change from arithmetic thinking to algebraic thinking is undoubtedly an important link in the connection of mathematics education in primary and secondary schools.
The transformation of thinking mode depends on the carrier, and this kind of graph order equation is an important carrier to cultivate students' algebraic thinking mode, which should be paid attention to by mathematics teachers.
In the face of solving equations mentioned in primary school mathematics, most of them depend on students' understanding and proficiency in four operations. Inverse operation is dominant and plays a decisive role in solving simple equations. But this solution is not the main idea of equation thought. Therefore, when we teach relevant content, we should be fully prepared. When students are still using arithmetic to consider equations, we should leave enough space for them to explore the advantages of algebraic thought by themselves through multi-angle and multi-dimensional thinking.
2. The connection between space and graphics.
In primary school, the field of space and graphics mainly includes the preliminary knowledge of graphics, such as cognition, measurement, graphics and transformation, graphics and position. The main means of cognition is intuitive perception. On this basis, junior high school has added graphics and coordinates, graphics and proof. The way of cognition has also changed from intuitive perception to "telling a little truth" and "reasoning", that is, from intuitive perception to logical argument. In order to successfully achieve integration in this field, it is important to
First of all, in mathematics teaching, students should gradually develop well-founded habits. For example, "Because these two triangles have equal bases and equal heights, their areas are equal", "Because this triangle is a right triangle, the sum of its two acute angles is 90 degrees", and so on. Reasoning can be less strict, but we must pay attention to the basic scientific nature.
Secondly, try to make students understand the necessity of reasoning, such as the interior angle of triangle, theorem and so on. In primary school, students have learned that the sum of the internal angles of a triangle is 180 degrees through operations such as measuring, cutting and spelling. The teaching in this part of junior high school is mainly to render a triangle, no matter its shape or size, it has internal angles, without exception. And ask the students the following questions: in primary school, we measured the internal angles of some triangles and found that the sum of the internal angles was 180 degrees, but we could not test all triangles one by one. Is there any way for us to confirm that the sum of the internal angles of all triangles (including those we have not tested) is 180 degrees? By thinking about these two questions, I realized the necessity of argumentation.
Third, junior high school geometry teaching should attach importance to students' existing knowledge base. In fact, there are many contents of "space and graphics" in junior high school mathematics, which have already had a preliminary infiltration in primary schools. For example, "the two base angles of an isosceles triangle are equal". In primary school, students have understood this conclusion through calculation. Therefore, when teaching this content in junior high school, they should proceed from this point without spending too much time and energy to organize students to measure and guess.
3. The connection between statistics and probability.
Everyone thinks that there are many convergence problems in the fields of statistics and probability. Especially in the field of probability, because it is a new thing, the textbook itself is not as mature as other contents. We believe that in order to do a good job in this field, we should pay attention to the following points.
First of all, we should pay attention to the teaching objectives of each stage, and the starting point of junior high school should not be too low to avoid duplication with primary school. In fact, due to the limited content in the field of statistics and probability, writing in all stages and grades is in a spiral way, and the lack of mature writing schemes makes it difficult to connect the relevant contents between grades, so the difference in teaching requirements is relatively small. If you don't understand it carefully, it is easy to have unclear or even repeated requirements.
Secondly, when teaching some statistics, such as average, median and mode, we should pay attention to science, that is, on the one hand, we should reveal the rationality and advantages of using these statistics to represent a group of data; On the other hand, we should also reveal its limitations. Students may appreciate the advantages of these statistics more. In junior high school, due to the gradual development of students' critical thinking, they should be guided to consider the limitations of these statistics more.
Second, the convergence of mathematical thinking methods
Mathematics teaching should be the unity of "two basics" (basic knowledge and skills) and basic mathematical thinking methods, which are intertwined and form the rich connotation of mathematics. For mathematical thinking methods, the primary stage is mainly infiltration. This requirement accords with the characteristics of primary school mathematics content and the level of primary school students' thinking development. In middle school, there are more specific requirements, such as the idea of function, the idea of sample estimation and so on. So, how to improve teaching?
Take trapezoidal area teaching as an example. In primary school mathematics teaching, two identical trapezoids are usually combined into a parallelogram, that is, the calculation of trapezoid area is converted into parallelogram area to deal with. This certainly reflects the idea of transformation, but if we start from the idea of transformation, that is, when we face a new problem, we will analyze our existing knowledge base and how to seek the way of transformation. It is the application of transforming ideas. When faced with the problem of finding trapezoidal area, the existing knowledge base is the calculation methods of rectangle, square, parallelogram and triangle area, and it is necessary to form a transitional thinking when introducing the midline. So we try to consider whether the calculation of trapezoidal area can be converted into related calculation methods.
Third, the way of teaching and learning.
First, in terms of teaching requirements, primary school mathematics teaching emphasizes intuition and image, while junior high school mathematics teaching focuses on abstraction on the basis of intuition and concreteness. Under this requirement, compared with primary school mathematics teachers, they attach great importance to students' life experience and often design vivid, interesting and intuitive mathematics teaching activities. Experimental operations, intuitive demonstrations and simulated performances can be seen everywhere in primary school mathematics classes. Junior high school mathematics teaching needs the help of existing knowledge base. More attention is paid to the establishment of abstract mathematical models. Teaching activities are often carried out in the mode of "problem situation-establishing models-explanation, application and expansion", and the teaching pace is relatively fast. These different requirements, suddenly facing the abstract and fast pace of junior high school mathematics classroom, are bound to make students uncomfortable. In view of this situation, we think it is advisable to let our math teachers take a half step back intentionally when implementing math teaching.
Secondly, from the organizational form of teaching, the content of primary school mathematics is relatively simple, and there are more opportunities for exploration, cooperation and communication. Storytelling, playing games, group cooperation and group competition are very common in primary school mathematics classes, but the teaching content of junior high school mathematics is more and more informative. The teaching form of junior high school mathematics is relatively simple, and the arrangement objectives of each teaching link are clear. Faced with the higher requirements of teaching methods, imagine that the sixth-grade primary school students become junior high school students after only a few tens of days of summer vacation, but are they really fundamentally different from primary school students? Therefore, for the "quasi-junior high school students" who are used to the teaching methods of primary school teachers, the new and higher requirements they suddenly face will inevitably make them unacceptable, incomprehensible and even tired of learning. Therefore, as a senior one math teacher, we can't ignore the importance of teaching organization and teaching method selection because of the many teaching contents, especially in the initial stage of senior one, the senior one math teacher should play the role of half a primary school teacher. Slowing down the pace and progress of teaching properly and adding some atmosphere of primary school teaching to math class will make students gradually realize that math class is not just relaxed and happy. With the introduction of new mathematics knowledge and the increase of content, mathematics class will be more challenging.
Thirdly, from the perspective of problem-solving ability, middle school math teachers pay more attention to generality and general methods, while most primary school math teachers pay too much attention to special skills to solve some specific problems. Broadly speaking, "commonness and specialty" belong to the category of problem-solving strategies, but the difference is that "commonness and general method" are "great skills" and "specialty" can only be counted. Pupils often blurt out: multiplication knows the unit quantity, division doesn't know the unit quantity. When solving the trip problem, students will skillfully say that the encounter problem is the sum of distance divided by speed, the pursuit problem is the difference of distance divided by speed, and so on. Students often remember these conclusions and ignore the analysis of problem-solving strategies, so that their mathematical thinking ability has not been developed accordingly.
To sum up, how to do a good job in the transitional teaching from primary school to junior high school is a comprehensive system. According to their own learning situation and teaching characteristics, we should design an appropriate transition mode to make students transition smoothly from the inside out, which can not only improve learning efficiency reasonably, but also make students more persistent in mathematics learning. This is the result that every math teacher wants to see.