What is mathematical literacy? Generally speaking, a person's good mathematical literacy is similar to saying that a person has a mathematical mind. In the final analysis, he thinks from a mathematical point of view. Mathematical literacy refers to students' mathematical thinking consciousness and mathematical ability to observe the world, deal with problems and solve problems by mathematical methods. It is based on innate genetic factors and internalized in the development of disciplines through continuous understanding and practice. It is a comprehensive quality, which is mainly manifested in concept, ability, language, thinking and psychology, including five parts: mathematical consciousness, problem solving, mathematical reasoning, information exchange and mathematical psychological quality. We can take cultivating students' common sense of life as the starting point of teaching, advocate inquiry teaching mode in teaching, infiltrate mathematical ideas and methods in inquiry teaching, cultivate students' thinking ability and train students' mathematical language, so that students can gradually improve their mathematical literacy in the process of learning.
Mathematics is a highly ideological, logical and abstract subject. To learn mathematics well, ability is more important than knowledge, and method is more important than conclusion. As math teachers, we should not be satisfied with teaching students knowledge, but should devote ourselves to improving students' math literacy in an all-round way. The cultivation and improvement of mathematics literacy can not be achieved in one or two classes, and we must make unremitting efforts and explorations in many aspects in the long-term teaching process. In the process of teaching, I have made many attempts to cultivate and improve students' mathematical literacy.
(A), the infiltration of mathematical thinking methods in teaching.
Mathematical thought is an understanding of mathematics and its objects, mathematical concepts, propositions and the essence of mathematical methods. Mathematical method is the method and strategy to solve mathematical problems. While attaching importance to imparting knowledge, mathematics teaching should guide students to understand mathematical methods and ideas. Only in this way can students learn to analyze and solve concrete problems and other practical problems in mathematics with mathematical thinking, mathematical means and mathematical methods, which is the realm to be pursued in mathematics teaching and the essential requirement of mathematics teaching. Mathematical thoughts and methods are abstractions and generalizations of mathematical knowledge at a higher level, which are contained in the process of occurrence, development and application of mathematical knowledge. The teaching of mathematical thinking methods should be gradual from the outside to the inside. It is necessary to infiltrate mathematical ideas in the process of knowledge generation, reveal mathematical ideas in the process of problem exploration and solution, and let students master the knowledge about mathematical thinking methods from them, and apply these knowledge to subsequent learning to acquire mathematical knowledge scientifically. For example, in the teaching of "Looking for Laws" in senior one, students can easily find a series of numbers 1 1, 13, 15, 17,19,21. Fill in 23 inches (). At this point, this topic has been completed, but I didn't stop the children from thinking, but further infiltrated the mathematical ideas and methods. I ask the students to name this column of numbers and guide them: like this, some numbers are arranged in a column. Let's give it a name and two words. The enthusiasm of students to participate is very high, some say several rows, some say series. I told the children that mathematicians call it series. The children are glad to think of going with mathematicians. Next, I asked the children to continue to observe the characteristics of this series: the last number is always 2 more than the previous one. In mathematical language, the difference between two adjacent numbers is equal. What is the name of a series with the same difference between two adjacent numbers like this? Ask the children to add two words before the sequence. Some say it is an adjacent series, some say it is an equal series, and some say it is a difference series. I will guide you in time: the poor series is true, but it is not. The children immediately said that they were equally poor. I congratulate them on being right. A series with equal difference between two adjacent numbers like this is called arithmetic progression. In this way, arithmetic progression, a middle school, needs to contact and learn the professional knowledge of mathematics, which permeates the children in the first grade of primary school. At the same time, the method of summarizing the typical laws of naming is infiltrated. Next, I used the process of students trying to calculate the sum of this column number to infiltrate the methods of "Gaussian algorithm" and "decimal with large numbers" to students, and students really felt the wonderful use of mathematical methods. Similarly, in my teaching, some mathematical ideas and methods are infiltrated, such as "reverse deduction", "reduction", "hypothesis", "observation and comparison", "judgment and reasoning", "equivalent substitution", "corresponding thinking" and "moving with symbols". In this way, students' mathematical knowledge level has been improved, and with their own mathematical ideas and methods, they will be much easier in their future study.
"Giving people a fish" is not as good as "giving people a fish". The memory of knowledge is temporary, and the mastery of thinking methods is long-term. Knowledge benefits students for a while, and thinking methods benefit students for life.
(2) Cultivating students' thinking ability in teaching.
Thinking, as a kind of ability and quality, as the core of human intelligence, is the concentrated embodiment of human wisdom. A very important factor in cultivating a successful person lies in thinking and scientific thinking.
So, how can we cultivate students' thinking ability and make them truly masters of learning? Therefore, in the teaching process, I established a new teaching mode of "discovery learning", which created a platform for students to think.
The development of thinking needs soil and platform. A good teaching strategy is to guide students to "discover" and solve problems themselves. Only in this way can we further release students' thinking potential and further protect students' thinking sparks. All the knowledge that students can learn through their own efforts will never be given to students. All the problems that students can solve after thinking, let students think freely and return the freedom in the "teaching-learning" activity to students. Taking students as the main body, let students learn and explore independently. It not only gives students the freedom to think, but also gives them the pressure to find and solve problems themselves, thus forcing them to think. For example, there is such a problem in the basic training of Book 6:
☆+☆+☆+△+△=54 ☆=( )
☆+☆+△+△+△=56 △=( )
This problem is equivalent to a binary linear equation. Although it is difficult for the students in Grade Three, I didn't tell them how to do it, but guided them to observe and compare: Please observe and compare these two formulas carefully. What similarities and differences have you found? Through observation and comparison, the students themselves found that after the ☆ in the first formula was replaced by △, the result was 2 more, indicating that a △ was 2 more than A △, resulting in △=☆+2, and then replaced the △ in the first formula with the same amount of ☆+2. In this way, a ☆ means that 10 comes first, and then a △ can be obtained. In this way, students themselves have infiltrated the mathematical ideas and methods of "observation and comparison" and "equivalent replacement" by observing and comparing "discovery" and "solution" problems. For another example, before teaching every new knowledge, encourage students to "think about it", "try it", "try painting" and "try it …". At this stage, students actively think, fully try to explore and verify, and stick to it for a long time. Students will gradually form the habit of conscious learning, and have good reasoning ability, the will and spirit to explore and keep making progress.
Inquiry teaching conforms to the principles of Marxist philosophy, pedagogy and psychology, especially the psychological principles of students' curiosity, initiative, willingness to try, analogy and competitiveness. We can give full play to students' initiative and creativity, and more importantly, we can build up the courage and confidence to explore bravely from an early age.
(3) Cultivating students' mathematical language in teaching.
It is the basic task of primary school mathematics teaching to let students master the correct mathematics language. A·A· Stolia, a famous Russian educator, said: "Mathematics teaching is the teaching of mathematics language". The new curriculum standard also points out that mathematics is a kind of human culture, including content, thought, method and language, and it is an important part of modern civilization. The formation of mathematical literacy is closely related to language, which is the tool and shell of thinking. Correct mathematical language can reflect a person's thinking process more accurately and clearly and show the development level of thinking ability. Therefore, I strengthen the training of students' mathematical language in teaching and learn to express mathematical thoughts and opinions in mathematical language. For example, when learning 23-7 abdication subtraction, let the students put 23 sticks on the table, and then let the students swing the sticks to try to get the calculation results. Because students' learning enthusiasm was fully mobilized, they used different methods and got 16. They each told their own thinking process. Some people say: first borrow 1 bundle, 10-7 = 3, and then combine 3 with 13 to become16; Some people say that the number 3 is not enough to subtract 7. Take a bundle and add three, that is 13, 13-7 = 6, take a bundle and add six, that is 16. Some people say: ...
Under the personal experience, students can tell the calculation method and process in an orderly way and develop their language expression ability.
In teaching, it is a very effective way to train students to express their thoughts and opinions by letting them describe the operation in mathematical language while doing it. In operation, students are bound to think; How to move, why to move, how to move is the best ... and when describing, it transforms external material operation into students' internal thinking activities, which exercises students' thinking and helps students to concretize and visualize abstract language. At this time, as long as students speak their ideas according to the operation process, they can easily express their ideas in language and obtain the connotation of knowledge. With this natural combination, students can learn interesting, speak enthusiastically, learn from each other's strong points and improve together.
(D) Guide students to look at things from a mathematical perspective.
There are many math problems around us. In teaching, guiding students to abstract the problems in life into mathematical problems and further revealing the relationship between concrete things and abstract concepts will not only deepen their understanding of what they have learned, but also help improve their ability to solve problems. For example, help the residents in the building calculate the water and electricity bills every month; Calculate how many floor tiles are needed for indoor decoration households to lay the ground and how much paint needs to be purchased for spraying walls and roofs; On Arbor Day, according to the planting area and seedlings, calculate the row spacing and plant spacing ... Students think these questions are really interesting and have math around them. The more they learn, the more energetic they are, forming a good habit of integrating theory with practice.
In addition, paying attention to protecting and cultivating students' intuitive consciousness in mathematics teaching, telling some history of mathematics development and participating in social practice of mathematics can improve students' mathematical literacy to some extent.
In the final analysis, mathematics literacy is a kind of cultural literacy, and mathematics education is also a kind of cultural literacy education. Its cultivation cannot happen overnight, so our teachers should attach importance to it and insist on it. Through learning, students should feel that mathematics is not only a series of abstract knowledge, but also a method, a culture, an idea, and even a spirit and attitude, so that students can learn with fun and expectation.