George Polya is an outstanding mathematician and mathematics educator. Starting from 1944, he published How to Solve Problems, Mathematics and Paradox Reasoning, and Discovery of Mathematics, all of which became world famous works.
In particular, the book How to Solve Problems gives a list of how to solve problems. Thinking according to the program in this list can make students "not only try to find the answer to this or that question, but also understand the starting point and method of this answer". (See the preface to the first edition), which is of great help to students who have difficulty in solving problems.
Using the thinking program provided by the "How to Solve Problems" table, an experiment was carried out on five math "students with learning difficulties" in the last semester of Senior Two/KLOC-0. After half a year, most students have made remarkable progress (by "students with learning difficulties" we mean students with backward math scores and normal intelligence).
The "How to Solve the Problem" table is divided into four parts: clarifying the problem; Draw up a plan; Realize the plan; Review. For the first part, what is the unknown? What is the known data? What are the conditions? Just wait for the students. For the fourth part, except "Can you test this argument?" Besides, the rest of the questions are difficult for most students to do, so our focus is on the second and third parts. Combined with the characteristics of students with learning difficulties, mainly from the following three aspects.
First, go back to the basics and strengthen analogy.
When making a plan, most students are interested in "Have you seen it before?" ? Have you ever seen the same problem appear in a slightly different form? Do you know the problems related to this? "I can't answer them, because the foundation of these students is too poor. In order to realize Paulia's program, we must first go back to the basics, and the teacher will help students sort out the basic problems. For example, when we talk about solving application problems with equations, we should not be so bored as to explain to students the relationship between multiples and trips that primary schools should master, and then inspire students to think according to Bilia's problem-solving procedures.
Returning to nature is only to make up for the lack of knowledge, and its real purpose is to strengthen analogy. In the preface of the first volume of Discovery of Mathematics, Paulia said: "Solving problems is a practical skill, just like swimming, skiing or playing the piano, which can only be learned through imitation and practice." Imitation is analogy.
However, many enlightening languages in Making a Plan actually let students learn analogy, so we emphasize the cultivation of students' analogy ability in the experiment.
Second, students discuss and teachers comment.
This discussion is not blind. The key to the effect depends on whether the discussion topics and procedures designed by the teacher conform to Paulia's basic views and should be carried out under the inspiration of the teacher. Before each discussion, five students make key preparations and be the core speakers.
It is very important for students to say it out loud. Teachers can discover the implementation of Paulia's problem-solving program through students' speeches. Do you really know every step? Is there any deviation in understanding? What are the main differences? Guide them to the right ideas in time.
In the discussion, teachers should discover and praise a student's slight progress in time to enhance students' learning confidence. The first two practices are indispensable to ensure "making a plan" and "realizing the plan". In "Can you test this argument?" This problem is easy for good students, but difficult for poor students, so we should do the following in teaching.
Third, the norms of study habits.
Non-intellectual factors often play a major role in students with poor academic performance, and most students are inattentive and careless. Teachers should make different adjustment plans according to different students, help them analyze the causes of carelessness and the correct ways to overcome it, and make some small goals so that they don't feel out of reach.
It is not enough to apply Paulia's problem-solving program to transform "students with learning difficulties", nor is it enough to implement it step by step according to the "How to solve problems" table. The teacher must read the books mentioned by the author at the beginning of the article, find out the reasons for each question drawn by Paulia, and then make choices, supplements and uses according to the actual situation.
It is only a preliminary attempt to transform "students with learning difficulties" with Paulia's problem-solving program. Today, Paulia's viewpoint is more and more accepted by people, and we hope that more teachers will devote themselves to this research to achieve better results.