Based on Piaget's and Bruner's pioneering research on children's genetic epistemology and discovery learning, a branch of cognitive theory-constructivism learning theory is developed. It emphasizes learners' subjective understanding, and pays more attention to establishing a situation conducive to learners' active exploration of knowledge. Constructivists believe that although the world exists objectively, people construct or explain the reality based on their own experience, and their understanding of the external world is different because of different experiences and beliefs about experience, but through the cooperation of learners, understanding can be more correct, rich and comprehensive. These ideas of constructivism provide a solid theoretical basis for us to explore the elements of classroom teaching evaluation of primary mathematics.
(A) effective teaching should guide students to actively participate in learning.
1. Learners participate in proposing or establishing goals or sub-goals.
Constructivism holds that learning can only be successful if learners are clearly aware of their work goals and form expectations corresponding to the expected results. In order to make learners clear their learning goals, constructivism emphasizes that learners should participate in the proposal or establishment of goals or sub-goals in the teaching process.
2. Learners learn by doing.
Once the goal is established, learners will inevitably rely on some operating objects in the process of active construction, which means that there is always something for children to do. Teachers should fully mobilize students' various sensory organs, and encourage students to use their mouths, hands and brains to learn in activities and in the process of solving problems. In traditional teaching, teachers usually teach the concepts and principles to be learned first, and then ask students to do some exercises and try to answer related exercises. The underlying assumption is that learning and doing are two independent processes, and only by learning first can we do it and solve related problems. The modern teaching idea advocated by constructivism is to design teaching with the opposite idea. Encourage students to do it first and learn while doing it. Because in the process of students' doing, students should comprehensively use the original knowledge and experience, and may even consult relevant materials, so as to make reasonable synthesis and inference, analyze and explain the current problems, and form their own assumptions and solutions. In this process, learners can construct corresponding knowledge and experience. On this basis, the teacher refines and generalizes to make the knowledge constructed by learners clearer and more systematic.
(2) Effective teaching should maintain an effective interactive process between teachers and students.
According to the viewpoint of constructivism, the individual's understanding of the external world based on his own experience is different and has limitations. Only through the sharing and coordination of meaning can we make our understanding more accurate, rich and comprehensive. Therefore, the communication in students' learning should be multi-directional, and the teaching process should include not only the interaction between teachers and students, but also the interaction between students and other students. In teaching, teachers should always act as promoters, instructors and collaborators of students' learning. The specific performance is as follows:
1. Counselor: Teachers participate in consultation, encouraging and supervising students' discussion and practice. However, it is not a substitute, let alone the result of controlling students' discussion.
2. Instructor: Teachers should grasp the contradictions in students' learning, design corresponding problem situations and inspire students to think; Provide students with necessary clues and feedback, develop students' ability of judgment, communication, reflection and evaluation, and promote the construction of students' knowledge; Through demonstration, explanation, especially refinement and generalization, help students to carry out meaningful learning.
3. Collaborators: Teachers regard themselves as learners, study with students, and dare to admit that they are not as good as students; At the same time, I am willing to cooperate with teachers and professionals in other disciplines and dare to venture into fields outside my major.
(3) Effective teaching should provide students with learning materials, time and space for active construction.
The learning materials provided by teachers should be more based on real life and linked with problem solving to a great extent, so that students can feel the existence of problems, learn to use all kinds of original data provided in the materials to analyze, think and explore, put forward assumptions, and then test the assumptions and draw conclusions. Second, teachers should provide enough time for students' knowledge construction in teaching. . Because when learners face a new problem, they should first be asked to think independently with their own minds. With certain ideas and efforts, they began to try to explore the problem in some ways. According to the results of the experiment, learners need to be prepared to exchange the required information in the group, and even need to write a written outline if necessary. In group discussion, on the one hand, learners need to make others understand their own problem-solving strategies, on the other hand, they need to try their best to understand others' problem-solving strategies, and constantly review and reflect on their own and others' right and wrong, similarities and differences in problem-solving strategies. They need to give evidence or explain the right reasons, find out the wrong reasons, compare the characteristics of different methods and optimize the strategy to solve the problem. Thirdly, teachers should provide space convenience for students' knowledge construction in teaching. The space here mainly refers to the arrangement of student seats. The traditional form of teaching organization is often to arrange seats by transplanting rice seedlings, which makes learning often regarded as an isolated, personalized and competitive activity. If we arrange children into working groups and make some adjustments in space, children will be very willing to communicate with each other, listen, explain, think about other people's views and reflect on themselves, thus completing the construction of knowledge more effectively.
(D) Effective teaching aims to enable learners to form a real understanding of knowledge.
From the viewpoint of constructivism, students' real understanding should be emphasized in teaching, not superficial understanding. In this way, in class, the teacher wants to ask, "Do you understand?" Or "Do you have any questions?" It will become meaningless to judge whether students really understand. Whether students have formed a profound understanding can be judged from the following aspects:
(1) Can you explain and express what you have learned in your own words?
(2) Whether inference and prediction can be made according to this knowledge, so as to explain related phenomena and solve related problems.
(3) Whether this knowledge can be used to solve variant problems.
(4) Whether more complicated problems can be solved by integrating several related knowledge.
(5) Whether the learned knowledge can be transferred to practical problems.
In these aspects, teachers can judge students' real understanding and mastery of knowledge through effective classroom questioning and practice. To achieve these aspects, teachers should not only pay attention to the results of students' learning, but also pay attention to the process of students' learning, because only by understanding and paying attention to how students learn can learners form a real understanding of knowledge.
Effective teaching must attach importance to learners' reflection on their own and others' learning.
Constructivism emphasizes that learning is not simply to let learners possess other people's knowledge, but to let learners actively construct their own knowledge and experience and form their own opinions. Therefore, in the process of learning, learners are required to constantly monitor their understanding of knowledge, judge the gap between their progress and goals, adopt various strategies to promote and help thinking, and constantly reflect on whether their inferences contain logical errors and so on. Therefore, teachers should pay attention to cultivate students' reflective habits in the teaching process, that is, reflect on their cognitive consciousness and guide students to think: "What do I think?" "Why do you think so?" "Is my way of solving problems the best?" "Is there a better way to solve the problem?" "What is the connection between the knowledge (or research questions) learned today?" ..... Through these questions, guide students to gradually develop the consciousness and habit of reflection. Some people even regard whether a person has the habit of reflection as an index to measure his intelligence. It can be seen that it is undoubtedly an important evaluation index for teachers to cultivate students' self-monitoring and reflection ability when evaluating classes.
(6) Effective teaching should enable students to gain positive experience and emotion when learning this subject.
When students study a certain subject, they always have certain emotions. This kind of emotional involvement is closely related to the experience gained by students in the process of learning this subject. Positive experience will make students constantly have strong interests and needs, show great enthusiasm for learning, and get excitement and happiness from learning. Positive experience is based on a democratic and harmonious learning atmosphere, on students feeling the power of knowledge, and on continuous success and progress. Therefore, in the teaching process, students' mistakes should be allowed and understood, not excluded and attacked; Students' creativity should be respected and protected, not ignored and obliterated. Constructivism teaching view especially emphasizes the importance and guiding role of teachers' evaluation of students' success and progress in the learning process in promoting students' positive experience of the subject.