Cultivating mathematical thinking ability is the core of mathematics teaching, and the evaluation and reflection after solving mathematical problems is very important to cultivate students' mathematical thinking ability. In the current mathematics teaching practice, we often pay attention to the analysis, judgment and comparison of solving problems to cultivate students' flexibility, agility and creativity, while ignoring the cultivation of evaluation consciousness after solving problems, which is not conducive to the all-round development of students' thinking. "Mathematics Curriculum Standard" points out: "Through mathematics learning in compulsory education, students can initially learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, enhance their awareness of applied mathematics, and initially form a sense of evaluation and reflection." Therefore, this paper starts with the analysis of the current phenomena in mathematics teaching, and through the summary of teaching practice, discusses how to reform the evaluation method of solving problems and establish students' evaluation and reflection consciousness for reference.

First, the current evaluation of mathematical problem-solving problems

There are generally two forms of evaluation for students after solving problems. Proofreading the topic in class, I only heard the teacher say, "Raise your hand on this question!" " How clever you are! "or" If this question is wrong, please raise your hand. What's the matter? Do you understand now? "This is especially true in practical classes. Practice marking with "√" or "×" after class. The form is single, lacking emotional communication between teachers and students, neither paying attention to the cultivation of students' non-intellectual factors, nor realizing that this is an opportunity to cultivate students' thinking ability.

At the lower stage of learning, many teachers require students to check and sign their homework by their parents, which encourages students' dependence on learning and hinders the cultivation of their self-evaluation ability and sense of responsibility. Modern teaching theory holds that students should not only actively participate in classroom learning activities, but also participate in the evaluation of learning results. If there is a lack of evaluation, it is incomplete learning. Therefore, teachers should respect students' ideas, provide students with more opportunities for self-evaluation and advocate students' self-evaluation and mutual evaluation. In the process of learning, we should make a value judgment on our learning behavior and effect according to our own goals, and standardize and optimize the learning process based on this.

Second, the main way to reform the evaluation method to solve the problem

1, formulate standards and conduct preliminary evaluation.

When assigning classroom assignments, specific evaluation criteria are put forward at the same time, and then students evaluate themselves.

Example 1. Use two triangles to spell out angles with different degrees, at least four.

Evaluation criteria: just answer one ☆ correctly, and get one ☆ point for each additional corner.

Example 2. Write the simplest integer ratio.

(1) The radius of the small circle is 3cm, and the radius of the big circle is 8cm.

(2) School art performance, including 60 boys and 75 girls.

Evaluation criteria: those who can ask 1 questions and answer them correctly are qualified; Can ask two questions and answer them correctly, well done; If you can ask more than two questions and answer them correctly, you will get one more point for each question.

Students give feedback collectively after self-evaluation and award homework prizes. At the same time, we should also strive to cultivate the habit of students' self-evaluation homework. Whether it's classroom exercises or homework, students can't let their parents do the evaluation task after they finish it, which is what we often call inspection. Students should correct their homework one by one like teachers, find out the mistakes and correct them, and then give corresponding scores. At first, students may not be used to it, but when teachers often set an example by praising and encouraging, and patiently guide the method of self-evaluation, students will carefully check their homework, or revise it, or confidently tick "√". Such a habit may benefit students for life. Self-evaluation and mutual evaluation under the guidance of teachers is a process in which students learn from each other and know themselves.

2. Batch operation and mid-term evaluation.

Typing "√" or "×" is a simple and direct way to judge whether homework is right or wrong, but it can't fully reflect the problems that students encounter in the process of solving problems. For the wrong question, use "check the question, ok?" "Is it reasonable to do this" and "Check it again" instead of "X", so that students can correct their mistakes in a targeted manner instead of recalculating when they see the wrong questions without analysis. When you see a subtle solution, you can supplement it with √ "Great", "I want to add a ☆ to your solution and" Really good ". These short comments affirm students' excellent thinking ability and are conducive to cultivating students' study habits of independent thinking and Excellence. Using this correction method, we can affirm the advantages and point out the disadvantages, and at the same time, we can communicate with students and get feedback from their previous evaluations.

3. Apply portfolio and improve post-evaluation.

Through a period of study, evaluation and accumulation, students exchange and display the learning achievements of the previous stage, stimulate their interest in learning and establish the consciousness of active evaluation. At this time, students can exchange their learning results in the form of "portfolio". Putting the works that students think are "the best" into the portfolio can be the best answer to the teacher's questions; The best description of problem solving (describing the best process of problem solving); The best photos, charts or concept maps about mathematical ideas explored by students; It can also include the best homework (week, month, unit, etc.). ), it is best to wait. In a relatively stable period of time, students have the right to freely choose and adjust their works. If the study period is one month, he can sort out the study situation every week, choose the best homework, and then pick out the best works and put them into the portfolio; You can also choose some better works to put into the portfolio first, and then replace them with better ones. The purpose of portfolio evaluation is to let students learn to judge their own progress. Students' grades are based on continuous inspection of their progress, rather than regular review of what students have mastered. At every step of the portfolio evaluation process, students are participants in creation, development and evaluation. In this process, establishing the consciousness of active reflection and self-evaluation is the greatest wealth that the later evaluation brings to students.

Three. Main viewpoints of establishing evaluation consciousness and cultivating reflection consciousness

1, establish a correct sense of evaluation.

The evaluation of students after solving problems is nothing more than these: clear process thinking and strong sense of final control; The process is correct, but in the end, the sense of control is not strong (that is, there is no inspection); The process is chaotic and the ability to control the thinking process is weak. It's impossible to check, and it won't. It is understood that students' awareness of problem-solving evaluation is generally not strong. On the one hand, the lack of sense of responsibility and mathematical ability is more due to the lack of evaluation experience. Teachers should infiltrate evaluation methods in learning activities to increase students' opportunities to experience the evaluation process.

(1) Establish the consciousness of "there is no definite method for uncertainty"

In the analysis of application problems, many teachers like to put a problem into a certain type for explanation and evaluation, such as "this is an application problem that summarizes more than one" and "when we see' calculate by this', we know that this is an application problem that is normalized to one". In fact, from the perspective of teaching practice, most students will not find a breakthrough in solving problems from the type. Instead of defining the application questions in the evaluation, it is better to ask a few more questions: "What will you think of when you see these two conditions?" "What two conditions do you want to know about this question?" Cultivate students' thinking ability.

This is an example that happened in my teaching. Xu, a third-grade student, solved a fourth-grade "travel problem" in his own way:

Two cars leave from a and b at the same time. One car travels 40 kilometers per hour, and the other car travels 48 kilometers per hour. They met at a distance of 24 kilometers from the midpoint. How many kilometers is it between A and B?

The first solution: 24÷(48-40)×(40+48)=264 (km).

Test: midpoint 264÷2= 132 (km)

(132+24)÷48=3 (hours) ... 12 (kilometers)

Conclusion: It is inconsistent with the conditions and the answer is wrong.

Adjustment: 24(48-40)×2×(40+48)= 528 (km)

Inspection: midpoint 528÷2=264 (km)

(264+24)÷48=6 hours (264-24)÷40=6 hours.

Conclusion: It meets the requirements and the answer is correct.

Xu didn't learn the "trip problem" and didn't know the formula of "distance-speed = time", but he completed the learning task with his own problem-solving evaluation method. It can be seen that students' contact with new problems does not necessarily depend on the help of teachers, but can be completed through their own learning strategies. Cultivating students' analytical ability and evaluation consciousness can enrich students' learning strategies, promote the development of thinking and help cultivate students' subjective consciousness.

(2) establish a sense of self-evaluation

The evaluation after solving problems is usually completed through self-evaluation, mutual evaluation and other evaluations. These evaluation methods can help students adjust their thinking and solve problems. However, if the conclusion needs to be prompted by others and explained by teachers, it will limit students' thinking space. Some students rely too much on mutual evaluation and others' evaluation, which leads to the phenomenon that teachers will do it after explaining it and others will do it after pointing it out, but they can't do it themselves. Such students often lack the experience of "self-evaluation". Therefore, teachers should encourage and advocate self-evaluation on the basis of mutual evaluation and other evaluation, so that students can improve their thinking ability in the process of thinking, feeling and internalization.

There is even "I have another solution!" ""My method is better! " , "I want to come out! "In this case, the assessment is the most effective.

2. Strengthen the cultivation of reflective consciousness.

Reflection is an important part of students' self-monitoring learning process, and it is also an important indicator to reflect students' learning ability. I once practiced this question with my students: Uncle Wang kept the year-end bonus of 2,500 yuan in the bank for half a year. Based on the current interest rate of 0. 1.422%, how much interest can he get after deducting 20% interest tax at maturity?

Most students answered: 2500× 0.1422× 6× (1-20) =17.064 (yuan).

Only one student raised an objection. The third place after the decimal point cannot be paid in RMB, and the approximate value should be 17.06. Students are exposed to such topics from time to time, but similar mistakes are still common. The reason is that students lack reflective consciousness and their ability to solve practical problems is not strong. In the usual teaching, when solving problems, we only pay attention to thinking methods, watching steps and calculating results, which unconsciously binds students' thinking.

Cultivating reflective consciousness can not only guide students to "rethink" and ask "why" more, but also start with changing the way of correcting mistakes. Let the students find the mistakes and mark them first, then revise them, prepare an error correction book, copy down the questions they made wrong, and write down the correct answers and the reasons for the mistakes. From the error correction book, they can find the mistakes that they used to make easily or often, and draw inferences from others to improve their learning efficiency. Improve students' thinking ability through reflection after solving problems.

In a word, primary school mathematics education should pay attention to students' learning strategies, methods and ways, and cultivate students' awareness of evaluation and reflection in solving problems, which can not only improve students' mathematics quality and cultivate students' mathematics awareness, but also promote the development of students' thinking ability and lay the foundation for students to gain basic ability and creative ability for life.