Constructivism "learning environment" theory holds that learners' knowledge is obtained through the construction of meaning with the help of others under certain situations, such as cooperation, exchange and use of necessary information between people. The ideal learning environment should include four parts: situation, cooperation, communication and meaning construction.
(1) Situation: The situation in the learning environment must be conducive to the learners' construction of the meaning of what they have learned. In teaching design, it is the most important link or aspect to create a situation conducive to learners' construction of meaning.
(2) Collaboration: It should run through the whole learning process. The cooperation between teachers and students and between students plays a very important role in the collection and analysis of learning materials, the proposition and verification of hypotheses, the self-feedback of learning process, the evaluation of learning results and the final construction of meaning.
(3) Communication: it is the most basic way or link in the process of cooperation. For example, members of the study group must discuss how to complete the prescribed learning tasks through communication to achieve the purpose of meaning construction, and how to get more guidance and help from teachers or others. The process of collaborative learning is actually the process of communication, and each learner's ideas are shared by the whole learning group. Communication is an important means to promote each learner's learning process.
(4) Meaning construction: the ultimate goal of the teaching process. The meaning of its construction refers to the essence, laws and internal relations of things. Helping students to construct meaning in the process of learning is to help students reach a deeper understanding of the nature and laws of things reflected in the current learning content and the internal relationship between this thing and other things.
Constructivism "cognitive tool" theory holds that learning is mediated by thinking. In order to influence the learning process more directly, we should pay less attention to transmission technology and pay more attention to how to ask learners to think in different tasks. On this basis, cognitive tool theory came into being. Cognitive tools are psychological or computing devices that support, guide and expand learners' thinking process. The former lies in learners' cognitive and metacognitive strategies; The latter is external, including computer-based equipment and environment; Are auxiliary tools for knowledge construction. Modern information technology with multimedia teaching technology and network technology as the core has become the most ideal and practical cognitive tool. [2]
Fourthly, the operational characteristics of the independent inquiry teaching mode in senior high school mathematics.
The operating characteristics of the autonomous inquiry teaching mode of senior high school mathematics with autonomous learning as the core are as follows:
1. Creating a situation: Teachers create as real a situation related to the subject as possible in the mathematical virtual laboratory by carefully designing teaching procedures and using modern educational technology, so that learning can be carried out in a situation that is basically consistent with or similar to the actual situation. Students studying in actual situations can stimulate students' associative thinking, stimulate students' interest and curiosity in learning mathematics, and enable learners to assimilate and index the new knowledge they have learned by using the relevant experience in the original cognitive structure, thus establishing a connection between the old and new knowledge and giving new knowledge some meaning.
2. Questioning: Teachers guide students to ask questions with themselves, between students and between teachers and students through well-designed teaching procedures, topic questioning, causal questioning, associative questioning, method questioning, comparative questioning and critical questioning, so as to cultivate students' questioning ability and promote students' development from mechanical acceptance to active exploration.
3. Independent inquiry: Let students explore independently under the guidance of teachers. First of all, teachers should inspire and guide students (such as demonstrating or introducing the process of understanding similar concepts), and then let students analyze themselves; In the process of exploration, teachers should prompt in time to help students gradually climb along the conceptual framework. It includes self-discovery method, inductive analogy method, formula breaking method and invention operation method.
Students are always in the cognitive subject position of active exploration, active thinking and active construction of meaning, but this can not be separated from the careful teaching design made by teachers in advance and the guidance in the process of collaborative learning. Teachers say little in the whole teaching process, but it is of great help to students in constructing meaning, which fully embodies the combination of teachers' guiding role and students' main role.
4. Online collaboration: Teachers guide students to conduct group consultation, exchange and discussion on the basis of individual independent exploration, which is cooperative learning, further improving and deepening the meaning construction of the theme, and supplementing, revising and deepening each student's understanding of current issues through the confrontation of different viewpoints. Through this kind of cooperation and exchange, students can see different aspects of problems and solutions, thus generating new insights into knowledge. Teachers should pay attention to the relationship between cooperative learning and autonomous learning and put students' autonomous learning in the first place. Cooperative learning should be guided by teachers on the basis of autonomous learning.
5. Online testing: Under the guidance of teachers, students use a new generation of online testing and evaluation software system for senior high school mathematics, focusing on students' self-evaluation, and evaluate the learning effects of various forms of senior high school mathematics.
We have integrated the basic functions such as design, revision, quota formulation, etc. required by online testing and evaluation, and made full use of multimedia and network technology, database management technology, object-oriented programming method and other technical means to assist the realization of the system, making the system truly a powerful tool to assist online testing and evaluation. In order to make students with low scores have a sense of accomplishment and students with high scores have an incentive effect, we design the test questions into four levels: the first level is the standard level, which is designed according to the requirements of the syllabus; The second level is to improve the level, on the basis of reaching the standard level, to increase the analysis level of learning and variant exercises; The third level is excellent level, which adds comprehensive level exercises to link old and new knowledge; The fourth level is the appreciation level, which provides the analysis and solutions of the college entrance examination questions and mathematics competition questions related to the learning content.
6. Class summary: either completed by students or teachers or teachers and students, or written by students in the form of small papers. If necessary, you can hold a thesis defense: each group recommends one person and the teacher to form an "expert review group", and the group leader draws lots to decide the defense order. Before the defense, each group uploads the small papers to the designated location in the server. When defending, the respondent will introduce the work of the group within the specified time (including how to choose the topic, the basic idea of solving the problem, how to overcome the difficulties, how to cooperate, etc.). ), and then the respondents will answer the questions of "experts" (teachers or students, etc.). ) or the audience is interested in their works. Reviewed by the expert review group, it is divided into four grades: first prize, second prize, third prize and successful participation prize.
Fifth, the implementation environment of high school mathematics independent inquiry teaching mode-virtual laboratory.
At present, we have initially constructed the implementation environment of the independent inquiry teaching mode of senior high school mathematics-the virtual laboratory of senior high school mathematics, which is composed of hardware, software and software.
1, hardware:
Our campus network is equipped with hardware facilities such as Cisco switch, Inspur server, Great Wall client, Gigabit backbone 100M to desktop, and there will be many multimedia classrooms [① Broadcast multimedia classrooms (equipped with high-profile computers, projectors, video recorders, high-performance DVD players, wireless microphones, electronic pointers, etc.); ② Interactive multimedia computer room (LAN equipped with server, teachers' computers and students' computers, with winschool interactive teaching system installed)] and electronic reading room.
2. Software:
We have configured the following application software systems in the campus network: network CD resource sharing system, network video on demand (VOD) system, internet resource sharing system, video broadcasting system, screen broadcasting system, online learning and creative editing system for teachers and students, new generation high school mathematics teaching software system and new generation high school mathematics online testing and evaluation software system.
The "New Generation High School Mathematics Teaching Software System-Various Integrable Ware Libraries and Integrable Ware Combination Platforms" developed by us consists of the following parts:
(1) According to the close relationship with the current high school mathematics classroom teaching, the high school mathematics textbook resource database is divided into three categories: the most commonly used database, the second commonly used database and the extended database, and is equipped with convenient, fast, automatic and intelligent CD-ROM and network retrieval means.
⑵ Establish a short and pithy interface "High School Mathematics Microteaching Unit Library" which meets the requirements of integrable ware combination platform.
⑶ Establish a high school mathematics virtual integrable ware resource database for teachers to directly call the online materials of this teaching resource for classroom teaching.
⑷ Summarize and classify the presentation modes of various materials, design icons for teachers to easily call and assign values, and form a "presentation mode library of high school mathematics textbooks".
5. Establish a "high school mathematics teaching and learning strategy database". Different strategies are designed into a fillable and reconfigurable framework, which is represented by simple icons, so that teachers can combine micro-teaching units with different materials, different information presentation methods and different teaching strategies according to their needs in teaching, resulting in a "combination explosion" effect and adapting to various teaching situations; Let students, according to their own needs, combine different materials and microteaching units, adopt different material presentation methods and learning strategies, give full play to students' autonomy and subjective initiative, and carry out active exploration and cognitive learning.
[6] Establish a "tool software library" (including tools such as Founder Aosi, Authorware and Microsoft PowerPoint, as well as mathematical experimental tools such as geometry sketchpad, mathematics laboratory and Mathcad). )
(7) Build an integrable ware platform similar to a "fool camera", which is especially suitable for classroom teaching-a high school mathematics integrable ware combination platform. The basic features of the platform software are:
(a) no programming is required.
(b) It is convenient to combine the integrable ware library with various multimedia and online resources.
For all high school math teachers and students, it is easy to learn and use.
The "New Generation High School Mathematics Online Testing and Evaluation Software System" we developed consists of the following parts:
(1) Test Paper Generation Tool
The test paper generation tool has the function of randomly generating questions, which can generate different test papers for each student to prevent cheating.
(2) Test process control system
The system mainly controls the online examination process, such as locking the system when necessary, not allowing students to browse the content unrelated to the examination, controlling the examination time, and automatically handing in papers when necessary.
(3) Automatic correction and immediate feedback function
The system provides "automatic grading and instant feedback function" for the test, and can also provide personalized feedback content according to the students' answers. The system allows teachers to further control the test environment by weighting some questions.
(4) Automatic scoring system and intelligent system
The system also provides an automatic grading system. After students complete the automatic grading of the test system, they automatically log in the scores. In addition, the system can automatically provide feedback information and automatically suggest the next learning content for students. Another example is to provide an e-mail classification system to classify the letters sent to the teacher's course mailbox, automatically distinguish which homework is submitted by students, and record whether the time submitted by students is timely, and then further provide an intelligent system to automatically analyze the e-mail content, classify it, or automatically answer it or provide it to the teacher for a unified answer.
(5) Test result analysis tools
According to the knowledge points in each question and students' answers, the system diagnoses specific students and puts forward suggestions for further study. The system can also use the theory of educational evaluation to analyze the quality of questions, such as discrimination and difficulty, according to the statistical data of exams and tests.
3. Diving parts:
We attach importance to the cultivation of researchers and students in experimental classes. Researchers focus on self-study, and adopt special training, lectures, discussions and going out to participate in training to learn modern educational theories, especially constructivism "learning and teaching" theory, constructivism "learning environment" theory and constructivism cognitive tool theory, update teaching concepts and ideas, and master educational experimental research methods; Learn modern information technology, master multimedia and network teaching methods and multimedia and network teaching software development methods. Students in the experimental class are trained by project team members and computer teachers. Computer teachers are responsible for training students in basic computer operations and input methods, and we are responsible for training students to use mathematical experimental tools and software such as geometric sketchpad and math laboratory.
Sixth, the strategy of "creating situation" in senior high school mathematics based on network environment.
Mathematics itself is a subject closely related to life. The difference is that the knowledge students want to learn is indirect experience accumulated by human beings for thousands of years, which is highly abstract. It is impossible for teachers to fully accept and digest them only by their words and deeds in the classroom now. This forces teachers to change their teaching concepts and explore teaching skills. I use modern information technology to create high school mathematics teaching situation from the following aspects.
1. Create real situations to stimulate students' interest and curiosity in learning mathematics.
Constructivist learning theory emphasizes the creation of real situations, which is considered as a necessary premise of "meaning construction" and one of the important contents of teaching design. Multimedia technology is the most effective tool to create real scenes. If it is combined with simulation technology, it will produce a more immersive and realistic effect.
Teachers use modern educational technology with multimedia technology and network technology as the core to create realistic situations related to the theme, so that learning can be carried out in situations that are basically consistent with or similar to the actual situation.
For example, in the introductory course of Solid Geometry, the author showed the courseware "Let all solid geometric figures move" with a multimedia computer.
Students studying in actual situations can stimulate their associative thinking, stimulate their interest and curiosity in learning solid geometry, and effectively reduce their fear of solid geometry. Learners can use the relevant experience in the original cognitive structure to assimilate and index the new knowledge they have learned at present, so as to establish a connection between old and new knowledge and give new knowledge some meaning.
2. Create questioning situations and change "mechanical acceptance" into "active inquiry"
"Learning begins with thinking, and thinking begins with doubt". Only when students have doubts can they further think, develop and create. Suhomlinski once said, "In people's hearts, there is always an inherent need to regard themselves as discoverers, researchers and explorers ..." In traditional teaching, students are less actively involved and more passively accepted; Less self-awareness and more dependence. Students are bound in the circle of teachers, textbooks and classrooms, and dare not cross the line. Their creative personality is suppressed and curbed. Therefore, in teaching, we propose that students are the masters of teaching, and teaching serves students' learning. Students should be encouraged to question independently, find problems and ask questions boldly. Creating questioning situations to make students develop from mechanical acceptance to active exploration is conducive to developing students' creative personality.