Broadly speaking, case teaching can be defined as a teaching method that guides students to discuss this special situation through the description of an educational situation. This method was first used in law and medicine, then in management, and then in education after 1970s. It is considered as a promising method in teacher education, with outstanding practicality, profound inspiration and dynamic process. According to the needs of teaching content and teaching objectives, case teaching is mainly implemented in the basic problems of mathematics teaching (mathematics teaching and its process, principles and methods of mathematics teaching), mathematics teaching design and mathematics teaching research (teaching of mathematical concepts, propositions and problem solving) in the course of mathematics teaching theory. The practice in recent years shows that the implementation of case teaching in the course of mathematics teaching theory is conducive to improving the quality of classroom teaching, mainly in the following aspects.
1, using case teaching is helpful to improve students' learning awareness.
Paulia, an American educator, wrote in the book Discovery of Mathematics: "What teachers say in class is of course important, but what students think is more important. Ideas should be generated in students' minds, and teachers only play a guiding role. "The implementation of case teaching in the course of mathematics teaching theory requires students to make clear the time background of the case after the teacher selects the case, and understand and make reading notes through extensive reading and intensive reading of the case. Students come into the classroom with their own feelings and problems. In this way, students are brought into a real world, and theoretical teaching is transformed into case analysis, so that students can experience practical knowledge and theoretical knowledge, understand the "form" and "spirit" of teachers in teaching, and thus clarify the learning purpose and improve their learning consciousness.
2. Using case teaching is helpful to improve the interaction between teachers and students.
The traditional teaching of mathematics teaching theory is often based on the teacher's "word for word", teaching and learning are out of touch, and students' initiative and enthusiasm in learning have not been fully mobilized and brought into play. The implementation of case teaching requires students to collect and sort out information, understand, analyze, discuss, summarize and evaluate cases, and interact with teachers, students and students. In the whole process, teachers are no longer the lecturers of the course content in the traditional sense, but as part of the learning body, they become the organizers and guides of case teaching. Students are not traditional learners, but active participants and sharers. They cooperate with each other, constantly discover and put forward new problems, and sort them out and discuss them. For example, after discussing the case of teachers' selection in the process of teaching mathematical concepts, a student gave the following case: after listening to a "general" class that was quite successful in the traditional sense, a teaching researcher invited five students at random to try to answer: In order to meet the city sports meeting, the school received the task of preparing a batch of colorful flowers for the conference. Six students were sent to make 42 flowers on the first day, and eight students were sent to make 106 flowers on the second day. The day before the sports meeting, the general assembly suddenly asked the school to make 250 more flowers and finish them in one day. Do you think it appropriate to send several students to complete the task? Why? As a result, all five students can't understand the meaning of the topic, don't know what to ask, and of course there is no way to find a solution to the problem. The researcher inspires students: Think about it, what does this have to do with the average level just learned? Two students replied: it doesn't matter. The researcher further asked: Why? Two students replied: there is no average. After listening to the case, the students talked about it in succession, and the teacher promptly guided: Can you analyze it with what you have learned? Encourage students to discuss further. Students spoke enthusiastically one after another ―― some students commented with the concept of curriculum standard: let mathematics come from life and then return to life, which is the real cultivation of students' application consciousness. Therefore, teachers should encourage students to "do mathematics" and help them learn, understand, experience and master mathematics. Some students use Professor Zhang Dianzhou's article "On Academic Form and Educational Form of Mathematics ―― Hot Thinking and Cold Beauty" to explain that the teaching process has been in a dynamic state. Through the interaction between teachers and students, students experienced the whole process of solving problems, found the growing point of educational theory in practice, and gave full play to their initiative and enthusiasm.
3. Using case teaching can stimulate students' interest in learning.
"Mathematics Curriculum Standard" points out: "Good mathematics education should start from learners' life experience and existing knowledge background, and provide students with opportunities for practical activities and exchanges." The implementation of case teaching in mathematics teaching theory course is mainly divided into three steps: case selection and understanding, case analysis and discussion, case summary and evaluation. From these steps, it can be seen that case teaching is centered on practical problems and is a process of exploring problems, so that students can truly feel and appreciate how teaching theories and curriculum concepts should be applied to concrete and real math classes and combined with teaching practice. In other words, case teaching can stimulate students' desire to apply what they have learned and make teaching lively and interesting.
For example, when learning mathematics proposition teaching, teachers arrange students to read the following cases before class: In a division class in a primary school, teachers show examples: 9/20÷3/5 for students to discuss. The teacher's original intention was to let the students think of the law of divisible fractions for migration. I didn't expect the students to answer: 9/20 ÷ 3/5 = 9/3/20 ÷ 5 = 3/4. The teacher asked why this was calculated. The student replied: Isn't that how to multiply fractions? Obviously, students have migrated the law of fractional multiplication. However, the teacher's treatment is: it can't be counted like this. Although the reason is sufficient, it is only a coincidence example and cannot be regarded as a general solution. The teacher then wrote down a formula: 3/5÷2/3, and thought that this formula could not be solved like this. But in a short time, some students answered: 3/5 ÷ 2/3 =18/30 ÷ 2/3 =18 ÷ 2/30 ÷ 3 = 9/10. Is that really the case? Of course, the teacher finally uses his own teaching art to guide the students in the process of initial conception (also textbook design), so that students can understand that dividing by a number is equal to multiplying the reciprocal of this number. After the teacher presented the case to the students, many students took the initiative to discuss with the teacher: Is there any truth in the method proposed by the students in the case? What should the teacher do when the child's math study is not carried out according to the preset procedure? How do teachers affirm and analyze students' migration patterns? What are the strategies and methods of mathematics proposition teaching and what should be paid attention to? Wait a minute. The students are enthusiastic and interested in learning more and more.
4. Using case teaching helps students to further internalize what they have learned.
The traditional teaching of mathematics teaching theory is mainly based on educational theoretical knowledge, lacking practical background materials as support, so it is difficult for students to deeply understand and reflect on the mathematical knowledge they have learned, let alone apply it. Case teaching has profound enlightenment, which can inspire students to establish a set of thinking methods and thinking modes to analyze and solve problems, so that they can look at problems from a higher angle. UNESCO conducted a survey to compare the teaching effects of case teaching, classroom teaching, seminar, simulated role, self-study and film and television teaching, so as to determine the advantages and disadvantages of various teaching methods in imparting knowledge, improving analytical ability, changing concepts and retaining what students have learned. After a large number of investigations and statistical analysis of a large number of data, the conclusions are as follows: the effect of case teaching ranks first in improving the ability of analyzing and solving problems and cultivating concepts; The second effect of case teaching is to impart knowledge and retain what you have learned.
5. Using case teaching is helpful to improve teachers' professional level.
In case teaching, teachers play the role of organizer, guide and collaborator, and mainly undertake three tasks: first, select typical cases before class and sort out problems that may confuse students; The second is to guide students to analyze and discuss cases in class; The third is to organize students to summarize and evaluate cases. This requires teachers to constantly improve their own quality. First, in order to select typical cases, teachers should have a broad and profound knowledge base, as well as certain decision-making ability and overall planning ability; Second, in order to make students' discussion and analysis meaningful and valuable, teachers should constantly improve students' ability to listen, ask questions and obtain information; Thirdly, in order to guide students to sum up and evaluate cases scientifically, teachers should constantly improve their knowledge structure and strengthen their theoretical cultivation. Therefore, in order to implement case teaching in the course of mathematics teaching theory, teachers must practice deeply, study hard and explore constantly.
In fact, the implementation of case teaching is also helpful to improve students' research awareness and design awareness, and also helps to cultivate students' creative thinking and critical thinking. According to the characteristics of teachers' professional knowledge, the rational use of case teaching is one of the effective ways to improve the classroom teaching quality of mathematics teaching theory.
(Author: Hunan First Normal University)