"Using number pairs to determine position" is an important content in primary school mathematics teaching, which contains a lot of elements of mathematical thinking methods, such as symbolic thinking, simplified thinking, coordinate thinking and so on. In teaching, I made some attempts.
It is not unreasonable to tell students directly about the introduction of "number pairs", but the background and necessity of number pairs can't make students really feel it. In this session, I created an interesting game: let students use the existing method of "which column is which row" to quickly record the positions of six people: 1 column second row, 1 column fourth row, column fourth row, column fifth row, and column sixth row. Let them feel that "the teacher reported too fast" and "too late to remember", and experience the cumbersome and inconvenient existing methods, and naturally think of improving and optimizing the original description. Then, let the students focus on how to describe a person's position scientifically and simply, and give them more time to create. Facing the works of many students on the blackboard, let them say, "Which method do you like best? Which method do you like the least? " Guide the debate and seek common ground while reserving differences. After preliminary screening, extraction and concentration were carried out: "What are the similarities between these methods?" (there are two numbers, which is much simpler than "which column and which row"), thus giving birth to the prototype of the number pair. Such teaching activities enable students to acquire not only a mathematical knowledge formed by predecessors' abstract generalization, but also a mathematical abstract method for forming this knowledge, with the characteristics of simple and concise mathematical knowledge and simple ideas.
After mastering the method of using number pairs to indicate the position, I asked the students to play the game of "Watch the number pairs stand up": show the number pairs (3, 4), (5, 1), (2, y), (x, 3) and (x, y) in turn, so that the students can stand up. This game strengthens the difficulty of this lesson (column first, then row, which column is represented by the first number in the number pair and which row is represented by the second number); Adding the "special number pairs" of letters brings a strange "landscape": (2, y) a group of people stand up, (x, 3) a group of people stand up, and (x, y) the whole class stands up. After experiencing the process of confusion, epiphany and transparency, students can further understand the essence of number pairs (any two ordered numbers can represent any point on the plane) and feel the magical charm of mathematical symbols.
After determining the location of the scenic spots in the park on the grid, I designed the location where Xiaoming played in the park.
Sketch: One day, Xiaoming came to the park to play. (Show: Xiaoming's position is at the intersection of (4, 3). Can you find this point on the grid?
Xiao Ming walks four squares to the east. Can you still find his present position? Teachers guide thinking: first look at two points before and after translation. What's the connection between these two pairs of figures?
Imagine: What would happen if you walked 50 squares east? 100 square? If his position is (3,26), do you know how he walked?
In this process, firstly, students are guided to observe the changes of the number pairs after the object is translated, and think about the number from the shape; Then observe the changes of the number pairs and ask the students to imagine Xiaoming's movement. In this way, the relationship between number pairs is further strengthened, which is helpful for students to understand the changes of numerical values in number pairs caused by horizontal and vertical position changes, consolidate new knowledge, embody the idea of combining numbers with shapes, and cultivate students' spatial concept.
Coordinate geometry is an added content in the new curriculum, and "determining position by number pairs" is the beginning of the third phase of learning plane rectangular coordinate system. How to make the content of this course reflect the life value it deserves, and how to properly generate and infiltrate the corresponding mathematical value (that is, coordinate thought) in the symbol system is a problem that I think more about. For example, in the park map, we study the position of special points (0,0); Ask the students to describe how to find Xiaoming's points in the grid, and then think about "what kind of line determines the position of each point in the grid"; At the end of the class, I designed three progressive scenarios of "How to express the position of the red square", connecting how to determine the position of a point on a straight line, a point on a plane and a point on a three-dimensional graph, so that students can constantly enrich the connotation of "determining the position" in comparison: one-dimensional coordinate is actually a line, two-dimensional coordinate is actually a surface, and three-dimensional coordinate is actually a three-dimensional.
Generally speaking, the thinking method of primary school mathematics is mainly infiltration, which means: first, the thinking method of mathematics should be realized by taking mathematical knowledge as the carrier, through the "manifestation" of mathematical knowledge, through the formation and establishment of mathematical concepts, the induction and summary of mathematical laws, and the analysis and solution of mathematical problems; The second is to emphasize the experience and understanding of mathematical thinking methods, that is, to make mathematical thinking methods "sneak into the night with the wind, moisten things silently" and gradually grow into a kind of consciousness, concept and quality of students, and become a "thing that can be taken away", which will play a role at any time in future study, work and life and benefit them for life; Third, we should pay attention to the phased and long-term characteristics of infiltration behavior, because different mathematical thinking methods may be implied in the same knowledge point, and the same mathematical thinking method can also play a role in different knowledge points. Therefore, students' understanding and formation of mathematical thinking methods need a long-term and hierarchical process, in which they gradually enrich their knowledge, accumulate experience and deepen their feelings. (Author: Primary School Affiliated to Nanjing Normal University, Jiangsu Province)