1. Pay attention to the conceptual quantitative relationship.
At present, some primary school mathematics teachers do not fully understand the concept of the new curriculum standards, and blindly focus on integrating the situation of teaching materials into life, ignoring the role of quantitative relations. As a result, some students cannot use formulas to solve some application problems. Students' understanding of mathematical knowledge is only superficial, and there are serious misunderstandings about some mathematical expressions. They memorize some key words mechanically and can't use them flexibly. This is mainly because students do not accurately grasp the essence of quantitative relations. For example, some students think that we must use the addition formula when we see "more", the subtraction formula when we see "less" and the multiplication formula when we see "times". When primary school students encounter the price calculation problem of "how much did they spend in total?", they mechanically add up all the figures, resulting in the phenomenon that some time quantifiers and price quantifiers are added indiscriminately. Xiaoming has 20 apples and Xiaohua has 2 apples. How many times are Xiaoming's apples more than Xiaohua's? Many primary school students have no idea about this kind of problem, and they don't know whether to add or multiply. In fact, we often encounter many "quantitative relations" in our lives, and our understanding, analysis and solution of things are inseparable from quantitative relations. At present, under the background of new curriculum standards and all-round development of quality education, the traditional teaching mode has been reformed. However, no matter how the teaching mode changes and the contents of the textbooks are updated, "quantitative relationship" is still the most important thing in primary school mathematics knowledge and an important way to solve life problems. Therefore, primary school mathematics teachers should attach great importance to the explanation of "quantitative relationship" in their daily teaching. They should not only learn quantitative relations by rote, but also entertain and educate. In a relaxed and harmonious learning atmosphere, guide students to understand the essence of "quantitative relationship" and skillfully integrate the mirror of life into the teaching of "quantitative relationship". Being integrated into the life situation does not mean that the relationship between "quantity" is not so important or you don't need to study hard. Integrating life situation teaching is an innovative traditional primary school mathematics teaching mode, which requires primary school mathematics teachers to use innovative teaching methods to reduce the pressure on students to master the "relationship of quantity", so that students can grasp its essence faster and better, and can easily solve mathematical problems by using the relationship of quantity. Therefore, primary school mathematics teachers should not classify mathematics topics in the general teaching process, but should integrate the "quantitative relationship" into the main line of general teaching, and stimulate students' interest by solving practical problems, so that they can learn the "quantitative relationship" more actively. For example, when teaching the calculation of "triangle perimeter", you can first propose that the three sides of the triangle are 8cm, 5cm and 4cm respectively, so that students can set related questions according to their own conditions [1].
Student: (1) How many centimeters is the maximum side length more than the minimum side length?
(2) How many centimeters is the maximum side length longer than the second side?
Teacher: "Can we add the three sides together?"
Student: How many centimeters are the three sides together?
By guiding students to ask and solve problems step by step, they can master the definition and solution of triangle perimeter while skillfully using quantitative relations, which improves students' enthusiasm and problem-solving ability.
2. Strengthen the mastery of quantitative relations through operation.
Strengthening operation is the concrete practice of mastering and applying "quantitative relationship". Only by strengthening the operation can we grasp the significance and essence of the quantitative relationship. The four basic quantitative relations of "addition, subtraction, multiplication and division" are closely related to our lives. For example, when learning addition and subtraction knowledge, we can integrate real-life situations into addition and subtraction operations, and we can ask corresponding questions, such as: "There are parents at home and ourselves. At this time, grandparents came, and grandma went out to buy food by herself. How many people are there at home at this time? This kind of situational setting is convenient for primary school students to think positively and let students initially realize the significance of addition and subtraction. After students come home from school, they can re-simulate the problem through their parents, thus consolidating their knowledge [2].
3. Explore the quantitative relationship in real life experience
Rich real life contains a large number of quantitative relations, and primary school mathematics teachers should guide students to explore the quantitative relations in life and actively play the role of quantitative relations. For example, "the unit price of a water cup is 12 yuan, the unit price of a toothbrush is 5 yuan and the unit price of a box of mosquito-repellent incense is 8 yuan. Let the students explore the mathematical model by themselves through the familiar things in concrete life. Students are calculating the total price of 7 cups: 12 x 7=84 (yuan); Total price of 3 toothbrushes: 3 x5= 15 (RMB); Total price of 5 boxes of mosquito-repellent incense: 5 x 8=40 yuan. Through this multiplication operation, the confidence and ability of primary school students can be increased. Through these operational exercises of mathematical relations in life, students' understanding of the essence of quantitative relations is gradually strengthened.
4. Explain typical application problems, draw inferences from others, and strengthen the understanding of quantitative relations.
Typical application problems contain a large number of quantitative relations and logics, which not only require pupils to have close quantitative relations and logics, but also require certain Chinese knowledge. For example, the common typical problem of "more times, less times" has troubled many senior two monks. Then primary school math teachers should refine and summarize in a targeted way. For example, A has 65,438+00, B has 5, and A is many times more than B. First, how much A is more than B is refined. Because this extra part is a multiple comparison with B, it is easy to get (65,438+00-5) ÷ 5 = 65,438+0. And how many times is B smaller than A, you can first calculate how many times B is smaller than A, because there is a word "Bi" in front of this A, which means that this small part is compared with A in multiples, so it is easy to get the calculation formula: "(10-5)÷ 10=0.5". Through the analysis of typical problems, primary school students can master the internal meaning of these keywords involving quantitative relations. And extrapolate. For example, the unit price of apples is 20 yuan, and the unit price of oranges is 10 yuan, so how many times is the unit price of apples more than that of oranges, and how many times is the unit price of oranges less than that of apples? Let the students do their own calculations to deepen their impression.
5. How to solve problems and strengthen the understanding of quantitative relations?
Mathematical logic is an important magic weapon for learning mathematics. At the primary school stage, the comprehensive quality of primary school students is in the enlightenment stage, and decimal mathematics teachers should pay attention to the cultivation of primary school students' mathematical logical thinking. Train their mathematical and logical thinking in a targeted and periodic way. For example, a typical mathematical problem of quantitative relationship can be solved in multiple ways, so that students can think from different angles and improve their understanding of quantitative relationship.
For example, Li Can eats 10 buns in 10 minutes on average, so how long does it take to eat five buns?
Generally, students will count how many buns they eat in one minute and get the formula: 10÷ 10= 1 (several buns per minute), and then divide this speed by the total number of buns: 5÷ 1=5 (minutes). Most students usually carry out quantitative relations operations based on such logical thinking. On this basis, we can continue to strengthen students' mathematical and logical thinking ability. From another perspective, eating five steamed buns is half of eating 10 steamed buns, that is, 5÷ 10= 1/2, so the time is naturally half of it, so we get 10 × 1/2 =. Through the similar method of multiple solutions to one question, students' logical thinking ability can be improved, and they can learn to see and do problems from multiple angles.