"High-level" questioning can prevent students from making superficial answers to questions, guide students to reflect on the basis of answers and ideas, optimize students' thinking, enhance students' logical thinking ability and discrimination ability, and improve the depth of answers. "High-level" questioning can expand students' thinking, disperse students' thinking in an orderly manner, and promote students to consider problems from multiple angles and aspects, thus improving the creativity of thinking; "High-level" questioning can dig out the hidden knowledge points behind the questions, help students to establish the connection between new knowledge and old knowledge, and cultivate students' ability to draw inferences from others. "High-level" questioning can sometimes provide teachers with some learning information of students, such as students' knowledge sources, thinking trends and patterns, which helps teachers to accurately grasp students' learning trends and make questions more targeted and effective. So, what are the types of "high-level" problems in math class? What should we pay attention to when designing "advanced" classroom problems? Let's talk about some understandings based on our own teaching practice.
I. Types of "high-level" questions
According to Bloom's cognitive goal classification theory, "high-level" problems can be divided into three categories: analytical problems, comprehensive problems and evaluation problems.
1. Analytical question. Analysis questions require students to understand the relationship between knowledge by thinking and analyzing the information provided. The key words commonly used in asking questions are "why" and "analysis".
For example, when teaching the simple calculation of continuous subtraction, the example is: I read 66 pages yesterday and 34 pages today. This book has 234 pages. How many pages are left to read? After guiding students to analyze the meaning of the question, let them try to calculate independently, and then let student representatives from different algorithms perform on stage:
The first type: 234-66-34 =168-34 =134 (page)
The second type: 234-66-34 = 234-(66+34) = 234-100 =134 (page)
The third type: 234-66-34 = 234-34-66 = 200-66 =134 (page)
After the students' performance, I asked the students, "Which of the above three algorithms do you like?" Why? "If students want to answer this question, they will naturally compare, analyze and think about the above three algorithms. Students will also learn the simple calculation method of continuous subtraction when answering questions.
This kind of analysis questions can help students analyze and sort out what they have learned and cultivate their analytical and thinking abilities.
2. Comprehensive problems. Comprehensive questions require students to combine what they have learned in new or creative ways, form new relationships and solve problems that should be solved. The key words commonly used in asking questions are "synthesis", "induction" and "summary".
For example, when teaching multiplication and division, for example, there are 25 groups involved in planting trees. Four people in each group are responsible for digging holes and planting trees, and two people are responsible for carrying water and watering trees. How many people are planting trees? After analyzing the meaning of the problem collectively, students try to calculate independently, and then ask students with different algorithms to perform the following:
Method 1: (4+2)×25 =6×25= 150 (person)
Method 2: 4× 25+2× 25 =100+50 =150 (person)
After the students performed, I asked such a question: "What do you find by observing the above two formulas? Can you sum up the rules you found in your own language? " Through observation, students find that the calculation results of (4+2)×25 and 4×25+2×25 are equal, that is, (4+2)×25 and 4×25+2×25 are equal, which can be written as (4+2)×25=4×25+2×25. In this way, students synthesize two different calculation methods into multiplication and division method, which achieves the teaching goal of this course.
Such comprehensive questions can help students broaden their thinking and cultivate their comprehensive ability and imagination.
3. Assess the problem. Evaluation questions require students to judge and choose some ideas and schemes, put forward opinions and make evaluations, which can help students judge the value of things and materials according to certain standards. The key words used in asking questions are "judgment", "evaluation" and "what do you think …".
For example, when teaching "true score and false score", after students understand and know the meaning and characteristics of true score and false score, I put forward such a question: "Can you judge the statement that' true score must be less than false score'?" In order to answer this question, students should judge this question through the meaning of true score and false score, taking their own characteristics and knowledge as the standard.
Second, "high-level" questions should be paid attention to
1. Ask questions in different ways. A person's learning ability is different, so teachers' classroom questions should vary from person to person. For students who are good at learning, it is more difficult to ask questions, that is, to ask some high-level questions; It is easier for students with learning difficulties to ask questions, otherwise they will lose confidence in answering questions.
Therefore, the topic of high mathematics questions should be biased towards students with strong learning ability. Asking profound or flexible questions to the top students, and the top students will answer after thinking, which will help to inspire all students' thinking.
2. The combination of sufficient presupposition and random strain. Fully presupposing classroom questions is the key to preparing lessons. The content, methods and timing of questions should be preset in advance, and different plans should be prepared. However, in the process of classroom teaching, teachers still need to improvise according to the phenomena and problems that appear at any time in the classroom.
For example, in the teaching with points, there is a small link to turn 1 into false points. Before class, I only designed two examples for students. In class, students are 1, such as "1=". Student 2, for example: "1=". Just when I wanted the students to summarize according to the design of the lesson plan, one student raised his hand and said loudly, "Teacher, I can give different examples." I saw the student's sincere and eager look, so I said to him, "Well, please tell me your unique example." The students said loudly: "1=". After that, the students looked proud. The student's answer really surprised me. Suddenly, the classroom exploded and the students raised their hands. "I have different examples" is getting louder and louder, "1=" and "1 =" ... taking advantage of the climax of students' thinking, I asked, "Who can express the problems you found in one sentence?" In this way, the rule that 1 becomes a false score is not summed up by the teacher, but by the students themselves.
It can be seen that teachers should fully affirm students' answers in class to generate inspiration, and at the same time adjust the angle and way of asking questions in time, so that teaching will achieve better results than expected.
3. Control quantity and improve quality. In the actual classroom teaching, teachers are sometimes easily disturbed by various factors, and sometimes they deviate from the main teaching objectives and entangle or expand too much on a certain issue.
It can be seen that teachers should carefully select questions in the classroom, firmly grasp several major issues, abandon some unnecessary questions, and design "high-level" classroom questions closely around the key points, difficulties and keys of teaching, so as not to be worthless.
Confucius said, "Learning begins with thinking, and thinking originates from doubt." Students' thinking process often begins with questions, and "high-level" questions help students understand the teaching content comprehensively and deeply, and promote the profundity and creativity of students' thinking.
Cultivating students' innovative spirit and ability to find and solve problems is inseparable from the above three kinds of "high-level" problems, and keep in mind the problems that should be paid attention to when raising "high-level" problems.
(Author: Ningwu Primary School, Ningwu Town, Wuming County, Nanning, Guangxi)
(Editor: Yangzi)