Reduction method is one of the most basic thinking methods in mathematics. It is a means and method for indexer to reduce the problem to be solved to a kind of problem that has been solved or is relatively easy to solve through some transformation process, and finally get the answer to the original problem. There are all kinds of contents that can be solved by transformation in primary school mathematics. We can gradually infiltrate this way of thinking in teaching, so that students can gradually understand it until they can simply apply it in senior grades.
The two classes that the author is teaching now start from the second grade. In the teaching process of these years, I have carried out the infiltration teaching of transformation method. By the fifth grade, I found that students can naturally think of using it to solve math problems. In teaching, I deeply realized that the transformation method is an effective way of thinking and has a wide range of uses. Mastering it will benefit my students for life. The following are some of the author's explorations and experiences:
First, find the growing point and turn the unknown into the known.
When learning new knowledge, I always inspire students to try to find similarities with new knowledge from existing knowledge and transform unfamiliar forms or contents in new problems into familiar ones. For example, students have been learning the comparison of numbers since the lower grades. With the deepening of logarithmic learning, students should compare two digits with three digits, numbers within 10,000, multiple digits, decimals, percentages and fractions. When I first started to learn integer size comparison, I asked students to make it clear that the number on each digit has different meanings because the counting unit is different. Then I let them know the basic method of comparing integer sizes: the more digits, the larger the number (the larger the counting unit); Numbers with the same number of digits are compared from the high order (the number on the digit with the largest counting unit), and then compared in turn until the size is compared. With the foundation of these basic knowledge, students have been able to solve examples through teacher's inspiration, classmates' discussion and their own thinking when learning the lesson of "Comparison of Numbers within 10,000".
In the class of "Comparison of Decimal Size", students can use their old knowledge to solve the size comparison of integer parts, which is based on the meaning of decimal parts, to understand the similarity of the methods of comparing decimal and integer sizes and to pave the way for old knowledge. Students naturally classify "comparison of decimal size" as a problem similar to "comparison of integer size", which is quickly solved in students' thinking and discussion.
Similar content often appears in primary school mathematics textbooks. Finding out the similarities between new knowledge and old knowledge and finding out the growing point of knowledge can turn the unknown content into something we are familiar with, and students gradually learn the thinking method in the infiltration process of transformation method.
Second, master the law and simplify the complex.
With the increase of grade and the deepening of mathematics knowledge, the problems that students encounter in the learning process become more and more complicated. The transformation method can change the more complicated form and relational structure into simpler form and relational structure, and the effectiveness of this method is more prominent in middle and high grades.
In middle school, students began to come into contact with the area of some plane graphics. After learning the rectangular area formula, students have successively obtained the area formulas of parallelogram, triangle and trapezoid through cutting, spelling, cutting and supplementing, and at this time, students have a hazy understanding of the reduction method. With this learning experience, students will naturally think of the method of dividing or splicing the combined graphic area or more complex graphic area into the learned graphics, and then get the area.
Third, broaden your thinking and make it easier.
Senior students gradually enriched their knowledge of mathematics. With my constant encouragement, students always like to start work, think and discuss problems, and then boldly put forward their own opinions through their own independent thinking process. With the continuous infiltration of changing thinking methods, students realize that almost all difficult problems can always be solved by relatively simple problems after being inspired by teachers or discussed among students. This way of thinking is often thought of when they solve problems.
The new curriculum standard requires teachers to encourage students to think independently and guide students to explore independently and cooperate and communicate. That's exactly what I did in practical teaching. The deeper students study mathematics, the more diverse their understanding and thinking methods will be. In class, many students are scrambling to express their views, and they can also explain their views reasonably. For example, after learning the relevant content, 1/5 < () < 1/4 appears in the textbook, so it is required to fill in the appropriate score. I know this is a challenging job, and the answer is not unique. If students can use their existing knowledge flexibly, it is easy to get the answer. So, I handed this problem to the students and let them find a way to solve it themselves. When the students face it for the first time, they frown, and then they either bow their heads in thought, or bury their heads in calculation, or whisper. After a period of thinking and brewing, they all raised their hands confidently. According to their own understanding of the meaning of the question, students divide it into the following topics: ① Comparison with denominator scores. 8/40 < (9/40) < 10/40 ② Comparison of scores of different denominators. 2/ 10 < (2/9) < 2/8 ③ Comparison of two decimal places. 0.2 < 0.24 (6/25) < 0.25 ④ Large number (decimal) approximation method. 1/5