1 How to use students' error resources in mathematics teaching
Using mistakes skillfully to stimulate students' interest in learning
The new "Mathematics Curriculum Standard" points out: "We should pay attention to students' emotions and attitudes in mathematics activities, help students know themselves and build up confidence. "Good mathematics emotion and attitude is an important driving force for students to participate in mathematics activities and a source of strength to overcome difficulties and explore and innovate.
The mistakes in students' learning come from students, close to students, and return to students' learning activities when teaching. As a teaching resource, "mistakes" can better promote students' emotional development as long as they are used reasonably. It plays a special role in stimulating students' interest in learning and arousing their thirst for knowledge. Studying in a relaxed environment, a happy, relaxed and positive mood and a good relationship between teachers and students have an excellent incentive for students' cognition and creation. Therefore, teachers should allow students to make mistakes.
Using mistakes to guide students to explore independently
Bruner once said: "Inquiry is the lifeline of mathematics. Without inquiry, there will be no development of mathematics. " "Mathematics Curriculum Standard" also points out: "Everyone learns valuable mathematics; Everyone can get the necessary mathematics; Different people have different developments in mathematics. " Mathematics teaching should meet the needs of every student to the greatest extent and open up the wisdom potential of every student to the greatest extent. Students' acquisition of mathematical knowledge should be carried out in constant exploration. In this process, students' thinking methods are different. Therefore, it is normal to have deviations and mistakes. The key lies in how teachers use the wrong resources. Fully tap the potential intellectual factors in mistakes, put forward targeted and enlightening questions, create self-inquiry problem situations, guide students to look at problems from different angles, and let students find and solve problems independently in the process of error correction, deepen their understanding and mastery of knowledge, and cultivate their inquiry ability.
Guide students to make mistakes and strengthen their true feelings.
The survey shows that frequent exams and intensive problem-solving training make many students feel depressed when they make mistakes. Therefore, teachers should pay more attention to students' emotional experience, correctly guide the analysis and evaluation of mistakes from classroom teaching, let students experience the joy of success from error correction, and establish students' confidence in learning mathematics. Constructivism holds that students' mistakes cannot be corrected by correct demonstration and repeated practice, but must be a process of "self-denial". Mathematics curriculum standards emphasize the constructiveness of mathematical facts, that is, mathematical knowledge should not be directly taught to students by teachers and textbooks, but generated dynamically in the process of students fully experiencing mathematical activities.
2 mathematics classroom teaching methods
Make good use of mistakes and inspire students to explore independently
The value of mathematics lies not in imitation but in innovation, and the essence of mathematics is not skill but thought. Mathematics learning is not only a process of following instructions, but also a process of self-construction by constantly using one's own knowledge and experience. What students need is not to copy others' mathematics, but to construct their own mathematics. In other words, students should discover or create what they want to learn in mathematics learning, and the task of teachers is to guide and help students to do this re-creation, rather than instilling ready-made knowledge into students. Therefore, teachers should take measures to correct mistakes in class, give students a chance to reflect, guide students to seriously review and analyze their own problem-solving ideas, and let students understand why they made mistakes in the process of reflection and avoid repeating the same mistakes.
For example, in the problem-solving exercise: saw a piece of wood into five sections, each section takes 3 minutes, how many minutes can it be sawed? At first, the students said in unison without thinking: "15 minutes". I thought for a moment, if I insist on teaching my methods to students, they may not learn well, and I am still tired of teaching, so I might as well leave the problems to them to solve. I'm really excited. Is it 15 minutes? Who can find a way to prove that his answer is correct? So, some people take paper to fold, some people use sticks to fold, some people draw and analyze, and some people make lists. Through various forms of inquiry activities, they find out the causes of mistakes and come up with solutions to such problems, so that students' potential can be brought into play and their wisdom can converge and collide. In real classroom teaching, it is impossible for students not to make mistakes. It is precisely because of such mistakes that classroom teaching is more exciting and more real. Because teachers can not only adjust classroom teaching in time by excavating students' error resources, but also guide students to explore actively by using students' error resources.
Using mistakes skillfully and flying the invisible wings of students' thinking
Mistakes are precious because their value is sometimes not limited to the mistakes themselves, but lies in the new enlightenment gained by teachers and students through thinking about mistakes and correcting them. Teachers should deal with learning mistakes from students according to local conditions, make them play their due role, and let students "exercise" and "grow" in this kind of "mistakes" with learning value and improve their ability. If a student answers an application question: "How many people can live in a hotel with 25 double rooms and 45 triple rooms?" It should be said that this is an extremely simple three-step application problem. In the course of my tour, I found that most students quickly listed the correct formula 2×25+3×45, but one student listed (25+45)×2×3, which is obviously wrong. At that time, I was noncommittal, just writing these two formulas on the blackboard for the whole class to judge. For the first formula, the students unanimously agreed, but for the second formula, they unanimously opposed it. Students who make mistakes are embarrassed. I smiled and asked the student who made a mistake to talk about his problem-solving ideas at that time.
Well, there is a bright spot in this wrong formula and this student's answer, because he regards 70 rooms as double rooms. I immediately caught the spark of this idea and inspired students to continue their own ideas. As a result, he not only found his own mistakes, but also listed the correct formula: (25+45)×2+45. At this time, everyone could not help applauding him. A stone stirs up a thousand waves. Inspired by his innovative thinking, the students' thinking suddenly became active, and everyone scrambled to express their views. Soon, two other different solutions were found. Moreover, students have been well trained in many aspects such as thinking ability, oral expression ability, emotional attitude and so on. While gaining mathematical understanding, I really realized the fun of "doing" mathematics. Imagine that if I had arranged it easily in class and put forward the correct conclusion instead of following the trend, then such a good teaching opportunity would have been missed. Students can't get a good thinking space, let alone insert the invisible wings of wisdom.
3 Mathematics classroom teaching methods
Take advantage of the "wrong" resources
Stimulate inquiry interest with "mistakes". Learning mistakes come from students' learning activities themselves, and using students' mistakes can stimulate students' interest in inquiry. For example, if a section of railway is 30 kilometers long, it will take 10 days for the first construction team to complete it alone, and 15 days for the second construction team to complete it alone. How long will it take the two construction teams to cooperate in the construction? In explaining this problem, the author encourages students to think independently and explains the reasons. Then, the question is extended: "If the railway is 60 kilometers long, how long will it take for each construction team to complete it alone?" 12 days. "The students answered without thinking." Is it? Can you answer after you have calculated it? "The result is beyond their expectation: In 6 Days, the distance is expanded by 1 times, but the time is unchanged!" If the distances are 15km, 45km, 120km respectively, what is the time? "The students got the answer with questions, and it took them all six days.
"Why is the time always the same no matter how long the railway is?" Teachers will be guided by persuasion, and the classroom efficiency is completely different. It can be seen that proper mistakes in class can help students find contradictions, but can cultivate students' ability to find and solve problems, stimulate students' active thinking ability and help cultivate students' inquiry spirit. Teachers use "mistakes" to activate students' innovative thinking, help students break through the immediate obstacles and make learning a process of re-creation. In teaching, the process of students making mistakes is a process of trial and innovation, and it is an opportunity for teachers to cultivate students' innovative thinking. We should see the success behind mistakes and add vitality to classroom teaching.
Consolidate and strengthen, so that "mistakes" no longer appear.
The ultimate goal of using "wrong resources" is to make mistakes rather than repeat them. What is important in teaching is to consolidate and strengthen students' cognition, and help them to establish a knowledge system in their minds, so that mistakes will not happen again. In teaching, students can list and correct mistakes, and consolidate and form a system in time. Teachers can list students' mistakes on the blackboard, let students be "mathematics doctors", guide them to discuss "truth" on topics, and draw more common mistakes from individual mistakes. In this way, students can find mistakes, recognize them, correct them, and better prevent them.
Set a record to remind yourself. Teachers can ask students to prepare a "correction book", sort out the typical mistakes in learning and their causes, record the mistakes that usually appear, and let students read the "correction book" regularly. Once students read it, it is a memory of the process of making mistakes and correcting them. "correcting mistakes" not only accumulates students' mistakes, but more importantly, it is the courage to admit mistakes and the perseverance to correct them. Accumulate progress in error correction, and gradually, students' repeated mistakes are reduced, their grades are improved, and their learning enthusiasm is improved.
4 Mathematics classroom teaching methods
Induce "mistakes" and cause deep thought.
"The conclusion in the book is wrong?" When teaching the volume of a cone, the teacher asked the students to do experiments in groups: put sand in an empty cone, then pour it into an empty cylinder to see how many times it can be filled. Each group operates separately, and then exchanges the relationship between cylinder and cone. As a result, the answers are endless: some students said, "We fill an empty cone with sand and then pour it into an empty cylinder, which means that the volume of the cone is one-third of that of the cylinder." Some students say that "we" teachers will do the same. You should observe carefully. "The teacher fills the empty cone with sand, and then pours it into the empty cylinder once or twice." The volume of the cone is half that of the cylinder? What happened? Is the conclusion in the book wrong? "The students talked about it, and the teacher said," What do you think? A student said, "Teacher, your cylinder is too big." I recommend you to use this empty cylinder. "The results just drank three times. The student suddenly realized that the teacher had made a small mistake and deliberately used a big cylinder. Only when the bottom and height are equal, the volume of a cone is one-third of that of a cylinder.
The change of one or two keywords often determines whether the concept is correct or not. Carefully designed beautiful traps induce students to make mistakes, so that students can experience cognitive conflicts and ups and downs in their mistakes. Children who come out of the wrong confusion will certainly remember the establishment of this concept deeply and profoundly.
Use the "wrong" resources to experience the joy of success.
Effective mathematics learning comes from students' participation in mathematics activities, and the degree of participation is closely related to students' emotional factors, such as motivation, successful learning experience, sense of accomplishment and self-confidence. Therefore, teachers should pay more attention to students' emotional experience, start with classroom teaching, correctly guide the analysis and evaluation of mistakes, and appreciate success from mistakes. Realize the transformation of students from "losers" to "winners". For example, there is such a thinking question in the math homework of grade three: 1 cat eats 1 fish needs 1 minute. How many minutes does it take for five cats to eat five fish at the same time? Most students think that 1 cat eats 1 fish needs 1 minute, so it takes five minutes for five cats to eat five fish at the same time.
Obviously, the student's answer is incorrect. At this time, I ask the students to analyze whether this answer is correct. Some students think that 1×5=5 (minutes), so it takes five minutes for five cats to eat five fish at the same time. Some students think that 5÷ 1=5 (minutes), so it takes five minutes for five cats to eat five fish. At this time, I am not in a hurry to draw conclusions, but leave them enough time to think. At this time, some students think that 5÷5= 1 (minutes), which means that five cats eat five fish to 1 on average, so it takes 1 minute for each cat to eat one fish. Some people say that no matter how many cats are eaten at the same time, students need 1 minute to feel refreshed and refreshed when they are relaxed and stress-free. They feel the success and happiness of learning in the process of correcting mistakes, judging mistakes and rewarding mistakes.