This teaching mode emphasizes the combination of teaching theory and practice. It is not a simple compilation of teaching experience, nor a mixture of empty theory and teaching experience, but an intermediary between theory and practice. Because of this, teaching mode is regarded as a bridge between theory and practice.
The teaching model reflects the combination relationship among the three elements of the teaching structure, namely, teachers, students and textbooks, and reveals the vertical relationship among all stages, links and steps in the teaching structure, as well as the horizontal relationship among the factors that constitute classroom teaching, such as teaching content, teaching objectives and teaching methods, which is manifested in the combination of factors that affect the achievement of teaching objectives in a certain teaching link within a certain time-space structure.
Firstly, it introduces the main teaching modes of middle school mathematics teaching.
1, the classification of teaching mode
From the psychological point of view, the teaching mode can be divided into: information processing teaching mode based on cognitive school theory; Behavioral teaching mode based on behaviorism school theory: personalized teaching mode based on humanism school theory: cooperative teaching mode based on humanism and social-oriented education thought.
Modern teaching theory divides teaching modes into: cognitive development-centered teaching modes, such as Ausubel's meaningful acceptance learning teaching mode, Kailov's five-link classroom teaching mode and Genschein's demonstration teaching mode;
Pay attention to the whole teaching mode, such as optimizing the teaching mode; Focus on the teaching mode of inquiry discovery, such as Bruner's discovery teaching mode and inquiry teaching mode; Teaching models that focus on skill training and behavior formation, such as Skinner's program teaching model and Bruner's mastery teaching model; Pay attention to irrational and open teaching modes, such as Rogers' unguided teaching mode.
From the characteristics of teaching activities, it can be divided into: guiding-accepting teaching mode; Self-study-guidance teaching mode;
Explore-discover the teaching mode; Teaching mode of interest cultivation; Example-Imitating teaching mode, etc.
2. Several teaching modes commonly used in China.
1. "Guide-discover" mode
"Guide-discovery" mode is a widely used teaching mode in the new mathematics curriculum. In teaching activities, instead of instilling ready-made knowledge into students, teachers turn the materials stated in the form of "conclusions" into carefully set question chains, change passive absorption learning into active inquiry learning, stimulate students' curiosity, and let students discover and solve problems through independent exploration and cooperative exchange under the guidance of teachers, so as to master knowledge and skills, construct knowledge independently and develop their abilities.
The main theoretical basis of this teaching mode is Bruner's "discovery learning" theory, Dewey's "activity teaching" theory and Brenda's "inquiry-discussion" teaching theory. The research of modern mathematics teaching theory shows that the process of students' learning mathematics is the process of students' self-construction, self-discovery and re-creation. If a person wants to learn mathematics well, he must create mathematical knowledge according to his own experience and his own way of thinking.
The teaching goal of this model is to learn the methods of finding problems and cultivate and improve creative thinking ability.
The teaching structure of "guidance-discovery" mode is: creating situations-asking questions-exploring and guessing-reasoning and verification-drawing conclusions.
The essence of "guide-discover" mode is to give full play to students' subjectivity, stimulate students' interest in learning, generate intrinsic motivation for self-conscious learning, help develop students' intelligence and creative thinking ability, help cultivate students' ability to discover, ask and solve problems, and help cultivate good team spirit. However, this teaching mode has higher requirements for teachers, students and teaching materials. Teachers should not only be familiar with students' thinking process of forming concepts and mastering laws and students' ability level, but also have broader knowledge and the ability to design teaching situations, organize and guide students to explore and discover new knowledge from situations, and students should also have a good cognitive structure. At the same time, teaching takes a long time, needs teachers to teach, and is difficult to grasp, which increases the difficulty and requirements of teaching management.
2. "Activity-participation" mode
The "activity-participation" model emphasizes students' activities, organizes teaching centered on students' subjective inquiry activities, emphasizes students' direct experience acquisition and the cultivation of practical ability, guides students to practice, use their mouths and brains in teaching activities, and internalizes knowledge into the experience in students' minds through mathematics activities such as learning by doing and participating in practice. So as to master the occurrence and development process of mathematical knowledge and mathematical modeling methods, and form the consciousness of using mathematics.
The theoretical basis of this model is Piaget's genetic epistemology and Friedenthal's "Mathematicization" thought. The influence of activity participation on individuals is extensive, not limited to learning. Participation in activities is of great significance to students' psychological development, and is of positive significance to mastering knowledge, developing thinking ability, improving academic performance, learning interest, attitude and will quality.
This teaching mode has many forms, such as mathematical experiment, mathematical investigation, problem solving, mathematical games, model making, measurement activities and so on.
The teaching objectives of this model are: to cultivate students' awareness of active participation, to promote emotional communication between teachers and students, to improve students' hands-on, brain-thinking and practical operation abilities, and to form the awareness of using mathematics.
The general teaching structure of this model is: creating problem situations-practical activities-cooperation and exchange-induction and conjecture-verification and mathematicization.
In the process of implementing the "activity-participation" model, teachers should not appear as experts and authorities, but should create an environment and atmosphere that enables students to study freely, help students correctly understand themselves and objective things, establish a democratic and equal relationship with students, and avoid imposing personal will on students, which will affect the full development of students' subjectivity and personality.
Exchange and discuss the case [case 2] the probability of touching the red ball (Beijing Normal University Edition, grade 7.3)
Design concept: By organizing students to carry out observation, experiment, guess and other mathematical activities, we can help students understand the meaning of probability. Understanding probability is a mathematical model that describes the uncertain phenomena in rich practical problems, and help students make reasonable decisions through probability.
Teaching material analysis: This lesson is the last section of Chapter 7 "Possibility". It is based on students mastering the concepts of definite events and uncertain events and actually operating the "roulette game". Because students have some experience and feelings about the relationship between frequency and probability in the first two classes, they may get a score to describe the probability of an event. On this basis, the teacher guides the students to list all possible results through games and learn the formula to calculate the probability of an event.
Teaching objectives:
Knowledge and skill goal: to understand the calculation method of the possibility of a class of events and the meaning of probability; You can simply calculate the probability of a class of events.
Process and Method Objectives: Go through the activity process of "guessing-testing and collecting test data-analyzing test results", understand the meaning of probability, realize that probability is a mathematical model to describe uncertain phenomena, and develop random concepts.
Emotion, attitude and values: Through game activities, we can develop active participation in mathematics activities and gain a successful experience in learning activities.
Teaching emphasis: the significance of uncertain events; You can simply calculate the probability of a class of events.
Teaching difficulty: understanding the meaning of probability.
Preparation of teaching AIDS: multimedia courseware, a number of balls with different colors and identical shapes and sizes.
teaching process
The first step is to create a problem situation.
Teacher: Organize and study the simulated shopping mall lottery.
1) Show a poster with the following contents: A shopping mall holds a lucky draw, and whoever touches the red ball will win the first prize, the green ball will win the second prize and the yellow ball will win the third prize.
2) Prepare a box with white, red, yellow and green balls in the same shape and size.
Student activities: 1) A student went to the podium to simulate the lottery; 2) Students touch a ball from the box on the stage; 3) After touching the ball, students guess the probability of finding all kinds of balls.
Teacher: ask a question: the possibility of touching the red ball.
(Comments: Through the life cases around students, suppose the problem situation, stimulate students' interest in exploring knowledge, and cultivate students' random concepts. )
Graphic Movement and Function ① (Cyndi Luo)
First, teaching design
In the late review stage of the senior high school entrance examination, it is not advisable for teachers to train students only by "sea tactics". Although the students trained in this way can solve some difficult problems with some fixed models and skills, they are helpless when they encounter flexible, open and capable problems. Therefore, the review class should not only repeat and reproduce knowledge mechanically, but also highlight the relationship, reveal the law and improve the ability.
The content of this lesson is based on a review question in the textbook quadratic equation of one variable. This topic is chosen because it is typical, and its typical feature is to present the topic from the perspective of sports, which is enlightening, applied and innovative, and is conducive to stimulating students' curiosity and thirst for knowledge. This topic mainly examines students' ability to solve problems by using quadratic equations with one variable. Before that, students have learned the knowledge of similarity and function. When guiding students' learning, teachers should link the changes of this topic with the above knowledge, and communicate vertically and horizontally, step by step, solve multiple problems in one topic, and bring forth the new, so as to achieve the teaching goal of efficient review.
Second, the constructivist theory of teaching mode
Constructivism is a learning theory with great influence in the current education field. Therefore, the teaching practice based on constructivism theory has been widely carried out in the world, and the following mature teaching models have been formed:
1. Scaffolding teaching
This kind of teaching thought comes from the theory of "zone of proximal development" of the famous psychologist Vygotsky in the former Soviet Union. Vygotsky believes that there may be differences between the problems to be solved and the original abilities in children's intellectual activities. Through teaching, children can eliminate this difference with the help of teachers, which is the "zone of proximal development". In other words, the zone of proximal development refers to the distance between the actual development level (the first development level) when children solve problems independently and the potential development level (the second development level) when teachers guide or cooperate with peers to solve problems. With the help of the word "scaffolding" in the construction industry as the image metaphor of the above conceptual framework, its essence is to use the above conceptual framework as scaffolding in the learning process. Therefore, in teaching design, we should aim at students' recent development fields, design reasonable teaching tasks, decompose complex learning tasks, and promote students' intelligence from one level to another new and higher level through the support of scaffolding, so as to truly make teaching move towards the foreground of development.
Scaffolding teaching consists of the following links:
Hand-held tripod-Starting from students' existing cognitive structure, closely following the current learning theme, and establishing a learning framework according to the requirements of the nearest development zone.
Enter the situation-according to the law of students' thinking development, create problem situations and introduce students into certain learning situations.
Independent exploration-let students explore independently.
Collaborative learning-organizing students' communication and cooperation on the basis of independent exploration, so as to deepen the comprehensive and correct understanding of relevant knowledge and promote the improvement of learning quality.
Effect evaluation-the evaluation of learning effect should pay attention to the evaluation of students' participation in activities, students' individual self-evaluation and mutual evaluation among group members. The evaluation contents mainly include: ① autonomous learning ability; ② Contribution to group cooperative learning; ③ Whether the meaning construction of the learned knowledge is completed.
2. Anchored teaching
This teaching mode requires students to be interested in problem situations closely related to reality, and the process of presenting infectious real events or real problems can be vividly compared to "decomposition". The determined learning theme is the so-called "anchor". Once this "anchor" is determined, the whole teaching content and process will be determined (just like a ship breaking down). Constructivism believes that the best way for learners to complete the meaning construction of what they have learned, that is, to achieve a deep understanding of the nature and laws of things reflected by this knowledge and the relationship between this thing and other things, is to let learners feel and experience in the real environment of the real world, rather than just listening to others' introduction and explanation of this experience. Because anchored teaching is based on real cases or problems, it is sometimes called "example teaching" or "problem-based teaching".
Anchored teaching generally has the following links:
Create a situation-through the presentation of the problem situation that students are interested in and linked to reality, learning can be carried out in a situation that is basically consistent with or similar to the actual situation.
Anchor Location-In the above situation, the real events or problems closely related to the current learning topic are selected as the central content of learning, and the selected events or problems are "anchors", and the role of this link is "description".
Autonomous Exploration-Teachers provide students with relevant clues to solve this problem, thus developing students' autonomous learning ability.
Collaborative learning-through supplementing, modifying and questioning different viewpoints in discussion and communication, students can deepen their understanding of current problems.
Effect evaluation-because anchored teaching requires students to solve practical problems, the learning process is the process of solving problems, that is, the learning effect of students can be directly reflected through this process, and accordingly, the evaluation should also pay attention to process evaluation.
3. Random Access Teaching
Random access teaching mode pays attention to the randomness of teaching, which embodies a post-modern teaching mode, and its theoretical basis is a new branch of constructivism learning theory-elastic cognitive theory. It believes that teaching is preset and even more generated. Because of the complexity of things and the multifaceted problems, there will be different understandings of the same teaching task from different angles. Therefore, in teaching design, we should pay more attention to the randomness and generativeness of teaching, and pay attention to presenting the same teaching content in different ways at different times, in different situations and for different teaching objectives. In other words, learners can enter the same teaching content through different channels and ways at will, so as to gain multi-faceted knowledge and understanding of the same thing or the same problem, which is called "random access to teaching".
Random access teaching mainly includes the following links:
Exhibition center problem-problem is the heart of mathematics. Teachers directly introduce students into the situation of teaching content by setting typical questions closely related to the learning theme.
Randomly enter the teaching-according to the students' reaction to the problem situation and the content selected by the students, present new problem situations (situations related to different aspects of the current learning theme).
Thinking development training-Because the content of random learning is usually not preset, it presents disorder and complexity, and the problems studied often involve many aspects. Therefore, teachers should pay special attention to developing students' thinking ability in this kind of learning.
Group cooperative learning-group discussion around the knowledge obtained by presenting different situations, thinking, communicating, deepening and understanding different opinions in teaching, and achieving * * * knowledge.
Evaluation of learning effect-evaluation is not only given by teachers, but also includes group evaluation and self-evaluation. The evaluation content is the same as before.
After understanding and mastering the basic teaching mode, we should also pay attention to more specific operating methods, means and teaching approaches, that is, the design and selection of classroom teaching methods.
Section 2 Middle School Mathematics Teaching Methods
First, an overview of teaching methods
Teaching method is a means to achieve teaching objectives and tasks, and it is one of the most important components in the process of mathematics learning. It is a group of purposeful activities that enable students to master mathematics knowledge, form innovative consciousness, develop general ability and develop good emotional attitudes and values, including teachers' teaching activities and students' learning activities.
Teaching methods include not only teachers' teaching methods but also students' learning methods. It is a way for teachers to guide students to master knowledge and skills, gain physical and mental development and develop together with teachers and students. It is a cooperative and interactive activity between teaching and learning, and it is the unity of teaching and learning.
Choosing appropriate teaching methods is of great significance for improving classroom teaching efficiency, giving full play to the role of teachers as organizers and guides, mobilizing students' enthusiasm and initiative in learning, and fully realizing teaching objectives. High-quality teaching is closely related to the teaching methods chosen by teachers. Reasonable and appropriate selection of teaching methods can inspire students to learn and master mathematics knowledge and skills consciously, actively and creatively, develop students' ability and make them achieve all-round and full development. Therefore, it is the basic skill of every teacher to study and master some common teaching methods.
Second, the relationship between teaching mode, teaching strategy and teaching method
Teaching mode refers to a typical, stable and simplified teaching theory formed through long-term teaching practice under the guidance of certain teaching concepts. The teaching mode provides a certain structure, procedures and steps for organizing the teaching environment. Statically speaking, teaching mode is a multi-factor structure, while dynamically speaking, teaching mode is a series of interrelated activities.
Teaching strategy is the embodiment of teaching mode and an organic part of teaching design. It is an implementation process of arranging, adjusting and controlling teaching forms and methods in order to achieve teaching objectives and complete teaching tasks in a specific teaching situation on the basis of a clear analysis of teaching activities. It includes three basic meanings: first, teaching strategies are subordinate to teaching design; Second, the formulation of teaching strategies should be based on specific teaching objectives and teaching objects; Third; Teaching strategy has conceptual function and operational function.
Teaching method is a more detailed and concrete way, means and approach, a concrete way to complete teaching tasks, a series of activities, operational means and implementation paths. It includes the coordination of teaching and learning activities. Teaching mode belongs to a higher level, which stipulates teaching strategies and teaching methods. Teaching methods are subject to teaching modes and teaching strategies, and are between teaching strategies and teaching practice. The design of teaching mode and teaching strategy should finally be implemented in teaching methods. From the above analysis, we can find that the teaching mode is not the same as the teaching method, nor is it the same as the teaching strategy, but the teaching mode and teaching method can not be completely separated, and many methods are often used comprehensively in the teaching process according to certain procedures.
Third, the introduction of middle school mathematics teaching methods
(A) teaching methods
Teaching method is a kind of teaching method in which teachers give a focused and systematic explanation and analysis of the teaching content and students concentrate on listening.
This teaching method is conducive to controlling the classroom teaching process, making the teaching process coherent and smooth, and saving time and manpower.
Generally speaking, factual knowledge; Synthesis, generalization and summary of a certain knowledge and method; Guiding analysis of definition, theorem connotation and extension; Clear mathematical knowledge such as revealing and guiding the problem-solving process can be used as the teaching content.
For example, some basic mathematical concepts (such as parallelogram, logarithm, exponent, etc. ), some basic mathematical representations (such as parallel and vertical representations, etc. ), basic mathematical operations, basic mathematical propositions (such as the judgment conditions of parallel lines) and mathematical historical facts (such as the introduction of numbers, the discovery history of irrational numbers and complex numbers).
In the teaching design, we should also give full consideration to the educational value of the learned mathematics knowledge.
For example, if we only pay attention to the acquisition of students' operation skills when solving a quadratic equation by collocation method, we can directly teach students some examples of solving a quadratic equation by collocation method, sum up the operation steps and formats, and then consolidate this problem-solving skill through examples. If we pay more attention to the cultivation of students' mathematical transformation ability in the learning process of solving quadratic equations in one variable, we can also design this content as students' inquiry activities. By asking typical questions with a certain level, students can explore, communicate and summarize under the guidance of teachers, which can better develop their transformation ability.
Under certain conditions, some knowledge is beyond the daily experience and self-perception ability of most students, and needs to be externalized and properly taught to students. For example, some important mathematical thinking methods in mathematics should be more about students' feelings, but it does not rule out that teachers can find them in time when students' knowledge level cannot be refined. For example, in the teaching of solving binary linear equations, students can be asked to think about the essence of various solutions, thus summing up the idea of elimination.
Although some contents are more valuable for students to experience the corresponding inquiry process, it is difficult for students to explore because of their limited cognitive level, and they can also be taught directly.
For example, the concept of irrational number is beyond people's daily life experience, and it is the result of pure rational thinking. It is impossible for students to explore according to their own life experience. Therefore, by introducing the story of ancient Greeks discovering irrational numbers, it can be expounded from the height of human rationality to help students accept the existence of irrational numbers and understand irrational numbers. The concept of complex numbers can be the same.
Teaching methods also directly affect students' acceptance. The same content, taught vividly, will stimulate students' interest in learning and leave a deep impression on students; The lecture is enlightening and easy for students to accept and understand. If we can set up appropriate situations and question strings, we can leave some space and time for students to think in teaching, which can also stimulate students' thinking activities and make them think actively. Therefore, when using the teaching method, we must concentrate on speaking and practicing more, arrange enough time, and consolidate training at different levels.
The main disadvantages of this teaching method are that students have few opportunities to take the initiative, are generally in a passive state, have no predetermined direction and requirements for learning action, can not give full play to students' subjective initiative, and can not develop their observation, thinking and imagination rapidly, which is not conducive to cultivating students' ability to explore actively. Therefore, this teaching method should be combined with other teaching methods in order to better cultivate students' mathematical ability.