First, the function of high school mathematics education evaluation
In the high school stage, the role of mathematics education evaluation in improving teaching effect can be summarized as the following functions:
1. Diagnostic function
Evaluation is an analysis process of teaching results and causes. Through evaluation, we can understand all aspects of teaching and judge the effectiveness, defects, contradictions and problems of teaching. Comprehensive evaluation can not only estimate the degree to which students' grades reach the teaching objectives, but also explain the reasons for poor grades, such as school, family, society and individuals. As far as students are concerned, it is mainly due to non-intellectual factors such as intelligence factors and learning motivation, or both. Teaching evaluation, like physical examination, is a rigorous and scientific diagnosis of teaching conditions, thus pointing out the direction for teaching decision-making or improvement.
2. Incentive function
Evaluation can supervise and control the teaching process, and at the same time promote and strengthen teachers and students. Evaluation reflects teachers' teaching effect and students' academic achievements. Experience and research have shown that, within a certain limit, regular examination records have a great stimulating effect on students' learning motivation, because higher evaluation can give teachers and students psychological satisfaction and spiritual encouragement, and can stimulate their enthusiasm for higher goals; Even if the evaluation is low, it can make people think deeply, arouse the enthusiasm of teachers and students, and play a role in promoting and supervising.
3. Adjustment function
The result of evaluation must be a kind of feedback information, which can make teachers know their teaching situation in time, and also make students experience success and failure in learning, thus providing objective basis for teachers and students to adjust their teaching behavior. Teachers should revise teaching plans accordingly, improve teaching methods and improve teaching guidance; Based on this, students can change their learning strategies, improve their learning methods and enhance their learning awareness. Teaching evaluation is conducive to making the teaching process a controllable system that can be adjusted at any time, and making the teaching effect closer to the expected goal.
4. Teaching function
Evaluation itself is also a mathematical activity. In this activity, students' knowledge and skills will be improved, and even a leap will be made. For example, an exam is an important learning experience, which requires students to review textbooks in advance, consolidate and integrate the knowledge and skills they have learned, analyze test questions afterwards, and confirm, clarify and correct some concepts. In addition, on the premise of estimating students' level, teachers can present relevant learning contents in the form of test questions, so that the topics contain some meaningful enlightenment, so that students can explore and understand themselves, gain more learning experience or achieve higher teaching goals.
As pointed out in the Outline of Basic Education Curriculum Reform (Trial) (hereinafter referred to as the Outline), the goal of curriculum evaluation reform is to "reform the function of selection and give play to the function of evaluation in promoting students' development and improving teachers' teaching practice".
In fact, the function of new curriculum evaluation is to promote the development of students. The function of new curriculum evaluation focuses on "development", that is, from "selecting children suitable for education" to "creating education suitable for children". The new curriculum evaluation should create equal and fair opportunities and conditions for the good development of all students. It can be seen that the transition from "selection" to "development" means that educational evaluation should be based on differences and accept students with different intelligence, hobbies and individual psychological qualities from the aspects of thought, emotion and action; It means that evaluation is no longer regarded as a screened tool, but an effective means to diagnose problems in time, summarize achievements, improve teaching objectives, optimize teaching programs and promote students' development. The transformation of educational evaluation from "selection" to "development" means the transformation from "proof" to "improvement", that is, from understanding the current situation and finding out the value to evaluating not only afterwards but also whether the educational results have reached the goal, paying more attention to the guiding role of educational evaluation before and during educational activities, promoting the improvement of educational activities, gradually realizing educational goals and enabling the educated to develop.
In a word, the function of high school mathematics education evaluation includes not only comprehensively evaluating students' achievements and progress in mathematics learning, improving students' attitudes, feelings and values towards mathematics, providing feedback information and promoting students' learning, but also collecting relevant information and improving teachers' teaching. At the same time, it also includes providing effective information for modifying project plans such as curriculum plan and teaching plan, so as to promote the continuous updating of teaching and curriculum. This is just as M. NISS, Secretary-General of the International Mathematics Education Committee, said: ① The evaluation of mathematics education can not only provide effective information to teachers, students, parents, schools and so on. , but also become the basis for establishing decisions or actions, regulating the education system, schools, teachers and their teaching, especially the revision or reform of various courses. For students, evaluation can control their own learning activities and play a role in restraining or strengthening students' mathematics learning; At the same time, it can promote the formation of social reality, that is, the evaluation of mathematics education will have a strong impact on the social reality of students, teachers and schools. That is to say, for students, the evaluation and its results will directly affect the priority of students' energy and time investment in mathematics learning, their habits and attitudes towards mathematics learning, and their attitudes towards competition and society (especially school life).
Second, the content of high school mathematics education evaluation
The contents of primary and secondary education evaluation generally include teacher evaluation, student evaluation, school evaluation, curriculum evaluation and teaching evaluation. In the high school stage, the core content of establishing the developmental evaluation of middle school mathematics education is to do a good job in mathematics classroom teaching evaluation, students' academic evaluation and mathematics teacher evaluation. Developmental evaluation is a kind of teaching evaluation with the fundamental purpose of promoting the development of evaluation objects. Developmental evaluation emphasizes people-oriented and takes promoting the development of the evaluation object as its fundamental purpose. Therefore, it is particularly important to pay attention to the implementation of developmental goals in the evaluation of senior high school mathematics education.
1. Mathematics classroom teaching evaluation
Mathematics classroom teaching evaluation is the analysis and evaluation of mathematics classroom teaching effect and the interaction among various elements (including teachers, students, teaching content, teaching methods and teaching environment, etc.). ) constitutes the classroom teaching process. With the shift of the focus of mathematics education to pay attention to students' all-round, sustained and harmonious development, students' feelings, attitudes and values in the process of mathematics learning have increasingly become important educational goals, and it is an inevitable trend to build a developmental mathematics classroom teaching evaluation system. In this regard, it can be implemented in the following aspects:
(1) The evaluation of mathematics classroom teaching should be diagnostic, formative and constructive.
Classroom teaching is a process of interaction and common development between teachers and students. Classroom teaching evaluation only shows the rich and varied possibilities and clues of this development. So there is no need to make a comprehensive evaluation of a course. It is important to grasp the core of classroom teaching, examine its successes and shortcomings, investigate its reasons, and put forward practical methods or suggestions to improve the teaching process and improve teaching efficiency, so as to make suggestions for the value-added of classroom teaching.
(2) Paying attention to students' performance in mathematics classroom teaching should be the main content of classroom teaching evaluation.
The effect of any classroom teaching can only be achieved by adjusting students' learning state. No matter whether classroom teaching is based on students' development or not, students have the deepest feelings and experiences. Therefore, we advocate evaluating the success or failure of classroom teaching by understanding how students discuss, communicate, cooperate, think, draw conclusions and their processes in class. Even if we pay attention to teachers' behavior, we should also pay attention to how teachers organize and promote students' discussion, how to evaluate and motivate students' learning enthusiasm and interest, and how to evaluate the value of teachers' classroom behavior to students' "learning", that is, "promoting teaching with learning".
(3) Establish teachers' dominant position in mathematics classroom teaching evaluation activities.
In classroom teaching activities, teachers are the creators and organizers of learning situations and the participants and promoters of students' learning activities. Participating in the evaluation and analysis of classroom teaching quality should be an important part of teachers' teaching activities. Just like preparing lessons carefully before class, reflection after class should also become a way of life and behavior habit of teachers. This kind of practical reflection is the internal power source of teachers' self-development, and also the essential expression of teachers' sense of responsibility and enterprising spirit.
In fact, classroom teaching is a practical channel to transform text courses into practice and students' development. The quality and effect of classroom teaching are the key factors to determine the learning effect of students. Therefore, it is particularly important to adjust and improve teaching through classroom teaching evaluation. The evaluation of mathematics classroom teaching under the new concept advocates promoting the development of teachers and students, and obtains real evaluation information through various evaluation methods. The evaluation objectives mainly include the following aspects:
(1) Whether the classroom teaching objectives are clear and appropriate, whether they follow the requirements of curriculum standards and syllabus, and can be appropriately adjusted according to actual needs.
(2) Whether the teaching goal pays attention to the all-round development of students.
(3) Whether the teaching content is selected around the teaching objectives, and whether it meets the students' tolerance and development needs.
④ Whether the choice of teaching methods follows the teaching content and the actual requirements of students, and whether it can improve the teaching efficiency and students' interest in learning.
⑤ Whether the participation and scope of students are deep enough.
⑥ Whether the teaching effect is effective and the teaching efficiency is ideal. Wait a minute.
Of course, at present, the evaluation of mathematics classroom teaching in senior high school is in a period of development and change, and some topics deserve further study. For example, what is the standard of a good math class? What are the effective evaluation methods for mathematics classroom teaching? How to effectively carry out cooperative learning under the current teaching class conditions? What are the main aspects of communication in math class? How do these exchanges promote teaching and learning? Wait a minute.
Evaluation of students' academic achievements in mathematics.
At present, the evaluation of senior high school students' mathematics learning is in a critical period. The newly introduced high school mathematics curriculum reform requires a new evaluation method, which not only examines students' practical level in mathematics learning, but also examines their development potential in mathematics. In particular, the evaluation of students' academic achievements in mathematics should not only reflect students' mastery of mathematical knowledge and skills, but also pay attention to students' learning process and mathematical thinking process and examine students' ability to solve problems. They should also know their emotions and attitudes when learning mathematics, because effective mathematics learning comes from students' participation in mathematics activities, and the degree of participation is closely related to the emotional factors generated by students when learning.
Under the new educational concept, the new concept of evaluating students' academic achievements in mathematics is embodied in the following aspects:
(1) Realize the transformation from the view of examination to the view of developmental evaluation. Mathematics education should be oriented to all students, reflecting the foundation, popularization and development of middle school mathematics curriculum. Therefore, it is required that the evaluation should be changed from paying too much attention to exams to adopting diversified evaluation methods, so as to collect and reflect the information and materials of students' learning results and behavior changes more comprehensively and promote students' all-round development.
(2) The evaluation content should reflect the integrity of the goal of mathematics education. We should not only pay attention to the evaluation of the mastery of knowledge and skills, but also pay attention to the evaluation of high-level mathematical creative skills, mathematical application, hypothesis and demonstration, organizational planning, prediction and prospect, as well as the evaluation of emotions and attitudes in mathematics learning. To fully implement the goal of mathematics education, we must adopt various methods and forms to further improve mathematics teaching and enrich the evaluation content.
(3) The evaluation method should be operable, hierarchical and diverse. Although written test is still an important way to evaluate students' academic performance in mathematics, it is not the only way. We should adopt more open and diversified methods, such as oral examination, classroom observation, after-class interview, investigation, writing small papers and project activity reports, establishing personal growth records, etc., to comprehensively investigate the present situation, potential and development trend of students' learning mathematics, and strive to make the evaluation index concise, the method simple and easy to use.
Generally speaking, high school students' mathematics learning evaluation (including academic performance evaluation and daily formative evaluation, etc. ) includes the following aspects:
(1) Basic knowledge and skills of mathematics
Mathematical knowledge not only includes "objective knowledge", that is, mathematical facts that are not transferred by regions and learners. For example, the multiplication algorithm, the summation formula of equal ratio series, the positional relationship between straight line and plane, etc. , is recognized by the whole mathematics, reflecting the human understanding of mathematics; Mathematical knowledge also includes students' own "subjective knowledge", that is, mathematical activity experience with distinct individual cognitive characteristics. For example, the understanding of the function of "complex number", the basic idea of decomposing three-dimensional graphics and the habitual method of solving a certain mathematical problem are all subordinate to the specific learner himself, reflecting his understanding of the corresponding mathematical object at a certain learning stage, which is wrong. It mainly includes some basic mathematical facts, such as definitions, theorems, formulas, concrete proofs, historical materials and so on.
The evaluation of knowledge and skills also includes the evaluation of procedural content, such as the process of abstracting some practical problems into algorithms; Explore the shape, size, position relationship and transformation process between objects and graphics; The process of asking questions, collecting and processing data, making decisions and making predictions.
(2) Mathematical ability
Mathematical ability, first of all, is based on the above basic knowledge of understanding, expression and application. At the same time, we should also pay attention to the evaluation of students' mathematical expression ability, communication ability, cooperation ability, problem finding and problem solving ability.
Mathematical ability has rich meanings. For example, Mr. Zhang Dianzhou scientifically defined the mathematical ability and innovative ability of conventional thinking from the perspective of reviewing history and looking forward to the future. ② Data collection and analysis; ③ Geometric intuition and spatial imagination; ④ Mathematical representation and mathematical modeling; ⑤ Mathematical operation and transformation; ⑥ Inductive conjecture and rational reasoning; ⑦ Logical thinking and deductive proof; ⑧ Mathematical connection and mathematical insight; Pet-name ruby mathematical calculation and algorithm design; ⑩ Think rationally and build a system.
10 mathematical innovation ability: ① the ability to ask mathematical questions and questions; The ability to establish new mathematical models and apply them to practice; ③ Ability to discover mathematical laws; ④ The ability to generalize the existing mathematical conclusions; ⑤ Ability to construct new mathematical objects (concepts, theories and relationships); ⑥ Ability to connect knowledge in different fields in a mathematical way; ⑦ Summarize the ability of existing mathematical achievements to reach a new level of understanding; ⑧ Proficient in logical connection and rigorous argumentation; Pet-name ruby is good at using computer technology to show the mathematical characteristics of the information age; Attending to know what is "good" math and what is "not so good" math.
(3) Mathematics learning attitude, emotion and mathematics values.
The purpose of evaluation is to promote the development of students. Development includes not only cognitive development, but also emotional development and mathematical values. When evaluating students, we should not only evaluate the cognitive development of students' memory, understanding and thinking ability, but also pay attention to the evaluation of students' emotions and attitudes. It is necessary to examine whether students actively participate in teaching, whether they have confidence and interest in learning mathematics, whether they are curious about mathematics-related problems, and whether they can actively try to overcome and solve problems when they encounter them.
At present, in the field of senior high school students' mathematics academic achievement, there are still the following problems worthy of in-depth study: how to effectively avoid the phenomenon that students only learn without knowledge and skills? How to evaluate students' participation in mathematics activities, their behavior, awareness and ability of cooperation and communication? How to evaluate students' mathematical thinking strategies, thinking level and thinking quality in the learning process? From what aspects should we evaluate students' ability to ask questions, analyze problems and solve problems? When is the best time to evaluate emotions and attitudes? What are the methods to evaluate emotions and attitudes? Comparatively speaking, what method (such as grades, grades, comments, or growth record bags) best reflects the characteristics of students and is convenient for teachers to operate? Wait a minute.
In particular, the new concept focuses on the evaluation of students' mathematics learning process and can be implemented in the following aspects:
(1) Student participation evaluation ③
The success or failure of teaching depends on the students' own efforts in the final analysis; All teaching effects are determined by whether, how and how much students participate. In this regard, we can evaluate the degree of students' participation by evaluating the comprehensiveness, depth and initiative of students' participation in thinking activities.
(2) Evaluation of students' awareness of cooperation and communication.
To evaluate a student's awareness of cooperation and communication, we should consider the following six factors.
① Students should be responsible not only for their own study, but also for other students in their group;
② Students discuss and communicate together under the guidance of teachers, and the wisdom and thinking of learners can be shared through groups. So whether we can learn from each other's strengths and play a guiding role for others has become the standard of evaluation and measurement.
③ Students are personally responsible for mastering learning tasks;
④ Improving cooperative communication ability is a sign that students learn to cooperate, so whether they have a good sense of division of labor becomes one of the keys to measure.
⑤ Students can explain what they have learned to each other, help each other understand and finish their homework;
⑥ Students can establish and maintain mutual trust among team members and communicate effectively.
(3) Evaluation of students' emotion and attitude
Emotion and attitude are unconsciously revealed by students in their usual mathematics learning process. We should be good at catching students' little progress, combining with specific teaching process and problem situations, affirming students' advantages or staged success, and actively encouraging and evaluating students.
(4) Evaluation of students' mathematical thinking process.
The evaluation of students' thinking process should not only pay attention to whether students can think independently, but also pay attention to students' mathematical thinking strategies, level and thinking quality in the learning process.
In addition, mathematical expression ability is the ability of students to express their thinking and understanding of mathematics accurately and reasonably by using mathematical language (whether oral description, pen and paper or demonstration). This is an important index to evaluate students' mathematical ability.
3. Evaluation of the professional level of mathematics teachers.
As the implementer of mathematics teaching activities, mathematics teachers are the leading force of teaching reform, and the degree of teachers' understanding, recognition and participation in education and teaching reform directly determines the effectiveness of education and teaching reform to a great extent. How to establish an evaluation system based on teachers' self-evaluation and involving principals, teachers, students, professionals and parents? It has become an important content of educational evaluation research to enable teachers to obtain information through multiple channels, continuously improve their teaching level and really mobilize their enthusiasm and enthusiasm for work. The basic ideas of evaluating the professional level of mathematics teachers are mainly reflected in the following aspects.
(1) The evaluation should aim at promoting teachers' professional development. A teacher's job is a specialized profession. Every teacher needs to constantly reflect, summarize and improve his education and teaching work, which has the inherent need and possibility of continuous development in the process of education and teaching. Evaluation should be an important means to promote teachers' professional development.
(2) Evaluation should pay attention to the individual differences of teachers. It is the great differences in teachers' personality, professionalism, teaching style, types of communication between teachers and students, and working background that make education and teaching colorful. Evaluation should respect the individual differences of teachers, establish individual evaluation standards, evaluation priorities and corresponding evaluation methods according to these individual differences, and clearly put forward the improvement suggestions, professional development goals and learning needs of each teacher.
(3) Evaluation should emphasize teachers' democratic participation and self-reflection. Compared with other comments, teachers know themselves best, their working background and working objects best, and their strengths and difficulties best. Therefore, the evaluation of teachers must give full play to their own role, highlight the main position of teachers in the whole evaluation process, and encourage teachers to conduct self-evaluation.
Of course, there are still some topics worthy of in-depth study on the evaluation of mathematics teachers' professional ability, such as the level of professional knowledge, such as what professional knowledge mathematics teachers need to update urgently? About teaching ability and teaching style, for example, how to formulate corresponding evaluation standards according to the evaluation content? What are the evaluation tools commonly used by math teachers? What are the principles of teachers' self-evaluation? How to determine the content and standard of self-assessment? What are the procedures and methods of self-assessment?
In short, in the evaluation of senior high school mathematics education, the main purpose of evaluation is to fully understand students' mathematics learning process, motivate students' learning and improve teachers' teaching. Therefore, the evaluation of mathematics learning should pay attention not only to students' learning results, but also to their learning process, their mathematics learning level, their emotions, attitudes, will and mathematics values in mathematics activities.