Around this problem, we also carried out teaching and research activities in Binyang County. There are many puzzles and misunderstandings when teachers put algorithm diversification into teaching practice. In our school, teachers have also established school-level projects for research. When it is really developed, they really feel that the understanding of the concept of "algorithm diversification" put forward in the mathematics curriculum standard is rather vague, and there are also many doubts in operation, so it is difficult to grasp the scale of algorithm diversification teaching. Through the training organized by the teaching and research section, continuous study, practice and reflection, we have some experiences in the process of groping:
First, the diversity of the algorithm does not represent the comprehensiveness of the algorithm.
Algorithm diversification is a collection of various calculation methods formed by hands-on practice, independent exploration and cooperative communication in order to solve a certain problem. It is aimed at a person who is learning, not an individual who is learning. Diversification does not mean pursuing comprehensiveness.
First of all, advocating algorithm diversification is not about all algorithms. For example, when teaching 13 minus 9, students only think of the following four methods:
(1) put 13 first, then take away 9, leaving 4;
(2) When calculating subtraction, we have to add, because 9 plus 4 gets 13, and 13 subtracts 9 to get 4; (3) 10 minus 9 is 1, plus 3 is 4;
(4) subtract 3 from 13 to get 10, and then subtract 6 from/kloc-0 to get 4.
In addition to the four methods that students think of, there are other methods, such as: 9 MINUS 3 gets 6, 10 MINUS 6 equals 4. However, the students didn't say that it will take a long time to get it if the teacher deliberately pursues and inspires repeatedly, which shows that this method is far from the nearest development zone of children's cognition. Forcing students to accept this method will increase the burden on students and is not conducive to their development. Algorithm diversification teaching is to teach students, not textbooks. Students should not spend a lot of time on some difficult problem-solving methods in pursuit of comprehensiveness. As long as it does not affect the follow-up study, it is best to dilute the form and pay attention to the essence.
Secondly, the diversification of algorithms can't require every student to come up with one or several different calculation methods, and can't reduce the unprincipled requirements for mathematical thinking. Every student has his own characteristics, and the differences in students' learning mathematics are objective. In the diversified teaching of algorithms, different requirements should be put forward for different students. Teachers should give full affirmation to students who come up with methods and encourage them to continue to explore; For students who have not come up with an algorithm, on the basis of affirming their active brains and hard exploration, they are required to learn to listen to other people's ideas and understand other people's methods. At the same time, they are required to study harder in the future and look forward to greater progress.
Thirdly, algorithm diversification teaching does not require every student to master multiple algorithms. The diversified teaching of algorithms encourages students to explore and solve problems in different ways, but it must not require every student to master multiple algorithms. In teaching, teachers can put forward different requirements on the basis of guiding students to understand different problem-solving methods, experiencing the diversity of problem-solving strategies and guiding students to analyze and compare various methods. Students who have spare capacity for study can be encouraged to master two or more methods they like and broaden their horizons; For students with learning difficulties, as long as they can master a method that suits them.
Recognizing that the diversity of algorithms is not comprehensive, it is not necessary to achieve the expected algorithms, and it is not necessary to present every algorithm that appears in textbooks. It is not that every student should master every algorithm, but proceed from the students' own cognitive level, and wait and deal with the diversified teaching of algorithms with an open and inclusive attitude, so that students can succeed as much as possible.
Experiencing work, feeling the value of self-exploration and the fun of mathematics learning, and promoting the sustainable development of students, this is the purpose of advocating algorithm diversification.
Second, choose the best from many and use it wisely.
What to do after "diversification" The answer is yes: "Optimization!" Because algorithm diversification is not a simple calculation method diversification, it is more important to have a corresponding optimization process. The thinking method of "choosing the best and using the best" is indispensable in students' study and life, and it is also an important method to develop students' mathematical thinking and cultivate their innovative consciousness. In the research, some of our teachers unilaterally think that the diversity of algorithms means that the more methods students speak, the better. They deliberately pursue the diversity of algorithms and ignore the optimization of algorithms, which leads to the inefficiency of computing teaching. Some teachers think that if the algorithm is optimized, there will be no diversity of algorithms. It seems that diversification and optimization are contradictory. Actually, it is not. Algorithm optimization is the process of students' learning, experience and perception. If the algorithm is not optimized, our students will not gain or improve.
1, build a bridge of diversification and optimization.
Algorithm diversification is not a simple calculation method diversification. There is no difference between good and bad calculation methods, but there is a difference between complex and simple. We should be clear about the potential connection between every seemingly complex or simple calculation method and the scheme we finally want to optimize. For example, in the calculation method of teaching 9 plus several, there are putting rods, counting, using counters, adding ten and so on. The method of adding ten is the simplest and most practical method, and the stick releasing, counting and counter are all related to the method of adding ten. For example, in the process of putting sticks, the students are counted one by one, so the teacher can guide the students to make ten bundles and then count the rest for everyone to see at a glance. Counter is an application of the ten-point method. Ten beads are filled in one place, and the beads in the other place become 9+3 * * *. At this time, if the teacher can demonstrate the inherent meaning of these methods to the students through operation, and sum up how to calculate the addition of 9 plus several in time, let the students have a deep understanding of the method of making up 10 from intuition to abstraction, so as to urge the students to choose their own methods.