First, the combination of numbers and shapes is conducive to stimulating students' interest.
Number and algebra are the main research contents of primary school mathematics. As a part of the field of number and algebra in the mathematics curriculum standard, "discovering the law" is a new teaching content in the experimental textbook of the compulsory education curriculum standard. It is the first time that this content has been listed as an independent teaching content of primary school mathematics in China, and its goal is to discover the simple laws contained in a given thing. For primary school students, this knowledge is abstract. In view of this situation, teachers should guide students to establish the thinking method of combining numbers and shapes, and teach students to use graphics as intuitive auxiliary means and methods to find laws. For example, when teaching "looking for rules" in the next semester, let students observe the arrangement rules of graphics first (pictured):
Let the students find that this group of figures is added with 2 circles, 3 circles, 4 circles and 5 circles in turn, and draw the conclusion that 6 circles, 7 circles and 8 circles should be added in turn in the future ... After the students find the pattern, the teacher changes the figures into corresponding numbers 1, 3,6, 10, 15. This demonstration process of "number-shape" transformation in mathematics makes the abstract "law" intuitive and vivid, and students grasp the essence and law of the problem at once.
Second, the combination of numbers and shapes is conducive to developing students' thinking.
If we can effectively guide students to experience the process of knowledge formation in the process of acquiring knowledge and solving problems, and let students see the knowledge-loaded methods and hidden ideas in the process of observation, experiment, analysis, abstraction and generalization, then the knowledge they have mastered is vivid and transferable, and students' mathematical quality can be qualitatively improved. For example, the biggest difficulty in the "tree planting problem" in the next semester of grade four is to understand the relationship between the number of trees planted and the number of intervals. In teaching, I ask students to choose a distance of 20 meters to study, use \ to represent trees, indicating that the distance between two trees is 5 meters, and draw three situations of planting trees:
Two-headed: \ \ \
Do not plant one head: \ \ \ \ \ \
Don't plant it at both ends: \ \
Through observation, students can draw the following conclusions: when planting at both ends, the number of plants is 5 and the number of intervals is 4, and the number of plants is more than the number of intervals1; If there is no seed at one end, it is all 4; No planting at both ends, the number of plants is 3, the number of intervals is 4, and the number of plants is less than the number of intervals 1. Through drawing, students can understand the relationship between the number and interval of planting trees, initially establish the appearance of planting trees, and realize the mathematical thought and method of "combination of numbers and shapes" through drawing strategy, which helps students to couple written information with thinking, develop their thinking and promote the transition from image thinking to abstract thinking.
Third, the teaching situation is tangible and more interesting.
All kinds of vivid situational pictures and beautiful patterns of translation, rotation and symmetry in the new curriculum reform textbooks can make students truly appreciate the beauty of mathematics and be influenced by beauty.
For example, understanding symmetric figures
(A), create a situation
There is a lovely little dragonfly in the forest. One day she met a butterfly and said to the butterfly, "We are a family." This little butterfly is very strange. I am a butterfly and you are a dragonfly. How can we be a family? The little dragonfly said with a smile: There are many things that belong to us in the forest.
(Design intention: Use multimedia to create situations and find the breakthrough point of new knowledge, so as to stimulate interest and arouse emotions. And let students ask some simple questions from the topic, which can not only cultivate students' courage and ability to ask questions, but also form a good habit of asking questions, which becomes the internal motivation to activate students' learning. )
(2) Appreciate the pictures and establish the appearance.
1, this is not, look. What did the dragonfly find?
Courseware display: leaves, ladybugs, cicadas, faces, etc. Are these figures beautiful? Students appreciate all kinds of symmetrical figures.
2, guide the observation of graphics, communication report.
These graphics that children have just seen are still many in daily life, so what characteristics do you find in these graphics? Talk about your findings in a group.
Who wants to tell you what your team found?
When students report, teachers try to encourage students to express themselves in their own language. There is no need to make excessive demands on students' inaccurate expressions and deliberately correct them. )
3. Teaching "Symmetry"
The children have just observed it very carefully and found that all these various figures have one thing in common, that is, their left and right sides are the same, which is verified by folding them in half. This kind of graph is called axisymmetric graph. The teacher revealed the topic.
(Design intention: Students look for similarities in a large number of symmetrical figures to master the essential characteristics of symmetry. )
Fourth, the combination of numbers and shapes is conducive to breaking through difficulties.
This is what I did when I was teaching 0 understanding.
(1) plotting observation,
How many peaches are there on the plate?
There are no peaches on the plate. What is the number? (naturally leads to 0, indicating no)
(3) the ruler is familiar with the order of numbers. Use a ruler to help students communicate the relationship between 0 and the number 1-5, and explain another meaning of 0, indicating the starting point and the beginning. This is the application of the combination of numbers and shapes, which can make some abstract mathematical problems intuitive and vivid, change abstract thinking into image thinking, and help to grasp the essence of mathematical problems; In addition, because of the combination of numbers and shapes, the understanding of 0 is easy to solve and the solution is simple.
5. Using the combination of numbers and shapes can make some abstract mathematical problems intuitive, vivid and difficult.
For example, the first volume of the new mathematics textbook for senior two introduces multiplication through the theme map of the playground. I use the media to show that there are three people on a boat in the actual classroom teaching, and then the second boat, the third boat and the sixth boat appear in turn. How can I express this scene? Students will naturally use the method of adding the same number to express it. Then, while showing the boats all over the lake, the teacher asked, "What would you do if there were 20 boats, 30 boats or even 65,438+000 boats?" The students were in an uproar: "Oh ~ ~! ! The formula is too long to write in the book. " At this time it is natural to establish the concept of multiplication! The combination of numbers and shapes makes students not only understand the meaning of multiplication, but also understand that multiplication is a simple operation of adding the same numbers. At the same time, the teacher led the students to observe the number of edges, one 3, two 3 … all the way to X 3, which strengthened the concept of adding the same number. Judging from the process of students' thinking activities, in this link, students have experienced a thinking process from concrete to abstract, that is, from intuitive boats to abstract addition formulas and multiplication formulas, from general to special. Let students know each other, it is best to let them experience and feel, rather than simply the teacher talking and the students listening. So, how can students feel for themselves? The effective method is to let students experience the process from addition to multiplication, supplemented by the visual impact of images. This is the most important starting point of this textbook and this lesson. It embodies the necessity and feasibility of the new curriculum concept infiltrating the idea of combining numbers and shapes, that is, the curriculum should provide students with rich learning experience, which is conducive to students' sustainable development.
In short, in primary school mathematics teaching, the combination of numbers and shapes can provide students with appropriate intuitive materials, concretize abstract quantitative relations and visualize intangible problem-solving ideas, which is not only conducive to students' smooth and efficient learning of mathematics knowledge, but also conducive to students' interest in learning, intellectual development and ability enhancement, making teaching more effective. The most crucial point is that it can concretize abstract and boring mathematics knowledge and make mathematics teaching full of fun. I believe that the clever use of the combination of numbers and shapes will definitely lead students to change from being afraid of mathematics to loving mathematics.