How to consider the relationship between teaching resources and teaching design?

Instructional design and case reference answers

Fill in the blanks

The so-called new curriculum primary school mathematics teaching design is an operable process of planning and arranging teaching content, teaching means, teaching methods and teaching activities under the guidance of mathematics curriculum standards, based on modern educational theory and teachers' experience, based on the understanding of students' needs and the analysis of the nature of the curriculum.

The essence of cooperative learning is to establish a positive interdependence between students. Each team member should not only take the initiative to learn, but also have the responsibility to help other students learn. With the goal of learning well for every student in the whole group, the teacher will reward the group according to its overall performance.

3. Mathematics curriculum objectives are divided into four dimensions: mathematical thinking, problem solving, emotion and attitude, knowledge and skills.

4. Teaching objectives have the function of guiding, encouraging and evaluating the whole teaching activities.

5. The organization forms of mathematics classroom teaching activities are seats and wings: semicircle, paddy field, group cooperation, etc.

6. The general structure of teaching cases is theme and background, case background, case description and case reflection.

7. Teaching mode refers to the standardized practice mode gradually recognized and summarized by the majority of teaching workers through long-term teaching practice.

8. The "zone of proximal development" refers to the second development level of children's intelligence, that is, the potential development level of students under the guidance of teachers.

9. Emotional attitude goals involve curiosity, thirst for knowledge, self-confidence, self-responsibility spirit, willpower, mathematical value consciousness, seeking truth from facts and many other aspects.

10, the so-called "autonomous learning" is about the quality of learning, which is relatively "passive learning", "mechanical learning" and "other learning". The concept of autonomous learning advocated by the new curriculum. It advocates that education should focus on cultivating students' spirit of exploration and innovation, guide students to actively participate in the learning process and carry out autonomous learning activities, and promote students' independent development under the guidance of teachers.

1 1. There are many writing formats of instructional design, which can be summarized into three categories: text format, table format and program format.

Teaching methods refer to teaching methods, the combination of teachers' teaching methods and students' learning methods in the teaching process, the general name of methods to complete teaching tasks and the general name of methods to complete teaching tasks.

13. Exercise is a teaching method for students to consolidate knowledge and form skills and skills under the guidance of teachers.

14, "Mathematics classroom teaching mode characterized by problem inquiry" means: instead of presenting learning conclusions, students are allowed to discover and explore the relationships and laws between certain things through experiments, attempts, speculations and reflections on certain materials.

15, learners' knowledge and skills, as well as their understanding level and attitude towards learning, is called priming behavior or priming ability.

18. Heart-to-heart method refers to a method in which teachers organize the contents of teaching materials into several questions according to students' existing knowledge and experience, and guide students to actively think, discuss and draw conclusions, so as to acquire knowledge and develop intelligence.

2 1. What are the characteristics of writing teaching design? P 15

(1) science;

(2) pertinence;

(3) practicality;

(4) Subjectivity;

(5) Reflect the concept of curriculum resource integration.

22. Give an example to illustrate the steps of "trying teaching method". P24

Step 1: Show the test questions and then ask questions. The test questions presented are generally similar to the examples in the textbook, which is convenient for students to solve the test questions through self-taught textbooks.

For example, a textbook example: a store brought four boxes of thermos bottles, each box 12. 6 yuan for a water heater, how much can a * * * sell?

Try: The stationery store has 20 boxes of ping-pong balls, each with 6. Each ping-pong ball is 20 cents. How much can a * * * sell?

At the beginning of the new class, when the teacher announces the topic, he must clearly point out: what to learn in this class and what the requirements are, and then show the trial questions. After trying to ask questions, some enlightening language must be put forward to stimulate students' interest. For example, "Who will do this problem before the teacher teaches?" "See who can solve this problem by himself?" When most students shake their heads, go to the second step.

Step 2: Teach the textbook by yourself. Before reading the textbook, the teacher can ask some guiding thinking questions.

For example, learning the addition and subtraction of fractions with different denominators can be mentioned as follows: ① What if the denominators are different? (2) Why do you want to divide it?

When most students have finished teaching materials by themselves and found the solution to the test questions, they will enter the third step.

Step 3: Try to practice.

Step 4: Students discuss. That is, discussing problem-solving strategies.

Step 5: The teacher explains the induction.

23. Briefly describe several steps in the formation of teaching cases. P49

(1) Determine the thinking level and requirements of teaching tasks;

(2) Observe and record the teaching process in class;

(3) After-class investigation between teachers and students;

(4) Analyze the basic characteristics of teaching and compare them with the requirements of thinking ability;

(5) Writing teaching cases.

24, the formation of difficulties generally have several situations? What strategies should teachers adopt in teaching? P29

25. Give examples to illustrate the steps of trying teaching methods. (Same as Question 22)

26. What is the reason for emphasizing the return of mathematics teaching to life? P49 (New Curriculum Instructional Design) Red Cover

27. What are the characteristics of the mathematics teaching model that meets the requirements of the new curriculum? P27 (ibid.)

First, the active participation and effective interaction of learning subjects.

The second is the emotional experience and activity construction of the learning subject.

The third is the cooperative exploration and personality development of learning subjects.

Fourth, strengthen the connection between learners and the life world and encourage them to innovate boldly.

28. Briefly describe the structural elements of autonomous activity teaching mode. Page 28-29

Develop independently and build a dynamic field.

Role confirmation, independent exploration

Activity construction, independent evaluation

Self-reflection and Activity Extension

29. Briefly describe the basic steps of practical teaching design. P29

① Basic training. It focuses on training students' oral expression ability, formula memory and understanding of quantitative relations.

(2) announce the contents and requirements of the exercise. Clearly announce the content and requirements of this class exercise, so that students can clearly understand their learning objectives and requirements.

(3) check and review the new professor's knowledge. Generally speaking, blackboard writing exercises can find problems in time and get feedback, which is conducive to the development and standardization of teaching.

④ Classroom exercises. This is the main part of the practice class, which generally designs special exercises, targeted exercises, comprehensive exercises and expanding exercises.

⑤ Job evaluation. Including practice evaluation, runs through every level of practice.

30. What aspects does inquiry learning emphasize more than receptive learning?

The basic idea of inquiry learning is to let students learn in the process of "rediscovering" and "reassembling" knowledge, which is a learning method that emphasizes students' autonomy and active participation. Compared with receptive learning, it emphasizes: ① participation and process; ② Equal cooperation; ③ Encourage innovation.

3 1. What are the main problems in group cooperative learning at present? P4 1

1, the organizational form is not in place.

2, the degree of cooperation is not in place

3. The evaluation mechanism is not in place.

32. What are the precautions in the design of the review class? P3 1

The same material is presented in different forms and explained with different examples, which makes students feel novel and helps students to study a phenomenon carefully from different aspects, so as to fully understand it.

(2) Review everything and use average strength. Practice should focus on the important and difficult points, and practice the weak points and doubts that students have mastered.

(3) Review is not to stand still and do the same level of circulation, but to systematically sort out and sort out knowledge, so that scattered and isolated knowledge can form a network and students can have new knowledge and understanding.

④ Exercises should embody "breadth", "gradient" and "depth" so that every student can participate in thinking training; It is necessary to go from shallow to deep, from easy to difficult, step by step, so that students can gradually deepen their understanding and mastery of knowledge; Practice should be extended, comprehensive integration should be deepened, and students' comprehensive application ability and migration ability should be improved.

33. Briefly describe the elements of the problem-inquiry teaching model. P35 (red)

Problem generation

Active inquiry

Achievement exchange and feedback promotion

34. Briefly describe the problems that should be paid attention to in the application of activity construction teaching strategy.

(1) Relocation of Teachers and Students' Roles

(2) Pay attention to openness, democracy and effectiveness.

(3) Questions should be thoughtful, interesting and life-oriented.

35. What are the characteristics of situational experience? P92 (red)

One is to emphasize "situation" as a teaching method. The most prominent function of the situation is to guide students' emotions and mobilize their life experience.

The second is to emphasize "emotion" as the starting point. Emotional factors are the primary factors of situational experience.

The third is to emphasize the concern for the life of teachers and students. "In the world of experience, all objects are alive and full of the meaning and feeling of life", so our classroom teaching should emphasize the concern for the lives of teachers and students.

The fourth is to emphasize the experience and construction of the learning process.

The fifth is to emphasize the interactive influence and activities between teaching and learning.

Fourth, the essay questions

1. Do students need teachers for autonomous learning? If so, please explain the reasons and point out what teachers should do.

Students' autonomous learning certainly needs the guidance and participation of teachers.

The so-called "autonomous learning" is about the quality of learning, which is relative to "passive learning", "mechanical learning" and "learning by others". The new curriculum puts forward the concept of autonomous learning, and advocates that education should "focus on cultivating students' independence and autonomy, guide students to question, explore and practice learning, and promote students to learn actively and individually under the guidance of teachers".

The biggest feature of autonomous learning is initiative. This initiative is reflected in the following aspects: first, in terms of participation intention, learners can determine their own learning goals and plan their own learning progress; Secondly, in terms of learning strategies, learners have a positive attitude and personalized thinking strategies in line with their own characteristics, and are willing to learn by solving problems; Thirdly, in the aspect of emotional input, learners' learning motivation comes from themselves, and they can get positive emotional experience from learning; Fourthly, in terms of self-regulation, learners have strong self-regulation ability, and can adjust their behavior in time in cognitive activities to adapt to new changes.

At present, some teachers have a wrong understanding that as long as students are given study time and allowed to study by themselves, it is classroom teaching with autonomous learning as the core. We should realize that the original intention of autonomous learning is to let students explore and learn to explore.

First of all, we should stimulate students' learning motivation. The core factor of autonomous activities is to stimulate students' learning motivation, which should be implemented from four aspects, namely: first, the guidance of interest; The second is the orientation of the goal; The third is the incentive of evaluation; The fourth is the promotion of competition.

Secondly, we should pay attention to students' autonomy in learning.

2. Why do teachers write teaching reflections? P50

What is teaching reflection?

What is the significance of teaching reflection?

3. How to achieve teamwork and pursue practical results, and prevent it from becoming a mere formality? P42

What is teamwork?

The present situation of mass group cooperation

tactics

4. Discuss "inquiry" and "teaching".

The definition of inquiry in American national science education standards is: "Inquiry is a multifaceted activity, including observation; Ask questions; By browsing books and other information resources, we can understand what conclusions we know and make investigation and research plans; Evaluate existing conclusions according to experimental evidence; Collect, analyze and interpret data with tools; Propose solutions, explanations and forecasts; And communicate the results. Inquiry needs to determine assumptions, think critically and logically, and consider other alternative explanations. "

What is teaching? When students are confused in learning, want to understand but can't understand, but want to say but can't understand clearly, teachers use their own views, experience and accumulation to inspire, inspire and guide, which is teaching.

Our classroom needs both students' inquiry activities and teachers' lectures. We should decide whether to design inquiry activities or lecture activities according to the teaching objects (students' level and learning materials). Of course, in many cases, inquiry and teaching are mutually infiltrated, and teachers' teaching is needed in inquiry activities and effective inquiry activities; Similarly, teachers' teaching is also to cultivate students' ability to explore independently.

5. How should teachers treat textbooks? P9

Textbooks are the text resources of curriculum implementation, the "topic" of teacher-student dialogue, the introduction, or the case, not the whole curriculum.

Teachers should take textbooks as models.

Teachers should take mathematical thought as the main line.

Teachers choose content from students' real life to reorganize teaching materials.

Teachers should reorganize teaching materials according to students' existing experience.

6. Does the new curriculum reform need a teaching model? Why? P25-28 (red)

In essence, teaching mode should be regarded as a set of methodology system for implementing teaching. As a set of "methodology system", the elements of teaching mode should include the concept basis, teaching objectives and principles, teaching procedures, teaching strategies, teaching methods and skills, teaching means and teaching evaluation. These elements are interrelated and mutually restricted, thus forming a certain teaching mode. Relatively stable, but at the same time showing the characteristics of dynamic opening.

The mathematics teaching model adapted to the requirements of the new curriculum needs to embody the following basic characteristics:

First, the active participation and effective interaction of learning subjects.

The second is the emotional experience and activity construction of the learning subject.

The third is the cooperative exploration and personality development of learning subjects.

Fourth, strengthen the connection between learners and the life world and encourage them to innovate boldly.

Several new teaching models in the process of reform

(A) a new classroom teaching model characterized by autonomous activities

(B) the basic characteristics of inquiry teaching mode

7. Why should the new curriculum advocate cooperative learning? P38—39

(1) Cooperative learning refers to the teaching theory and strategy system that promotes students to help each other in heterogeneous groups and accomplish learning tasks together, and rewards them according to the overall performance of the group.

(2) Advantages of cooperative learning:

It is conducive to enhancing the spirit of cooperation among students;

It is beneficial to stimulate students' learning motivation;

Conducive to the establishment of a harmonious and equal relationship between teachers and students;

It is beneficial to form a correct evaluation of fish and cultivate good quality;

Conducive to the realization of curriculum objectives.

8. What kind of "question" is a good question? P8 1 (red)

First, be clear and specific;

Second, we should have thinking value;

Third, we should pay attention to the achievement of multi-dimensional teaching objectives;

Fourth, the question should have situational function.

9. What do you think can be done to write reflection on teaching?

(1)P50 The so-called teaching reflection is to re-recognize, re-think, re-explore and re-create the teaching process. Teaching reflection is a process in which teachers take their own (others') teaching activities as the object of thinking, and examine and analyze their own (others') behaviors, decisions and the resulting results. Improving participants' self-awareness level is an effective way to promote ability development.

(2) Reflection on P5 1

(3) How to reflect on P53

10, what do you think should be paid attention to in problem design? P88-89 (red)

It is necessary to create a good environment for the development of students' problem consciousness and questioning ability.

Provide students with a successful experience and treat students' every problem correctly.

A Case Study of verb (abbreviation of verb)

1, case description

Two teachers had a lesson on "Understanding the Circle".

When teaching the relationship between radius and diameter, Teacher A organizes students to measure and make tables, and then leads students to find that "in the same circle, the radius of a circle is half the diameter".

Teacher B designed this when teaching this knowledge point:

Teacher: Do you know the relationship between radius and diameter by self-study?

1: In the same circle, all radii are half the diameter.

Health 2: In the same circle, all the diameters are twice the radius.

Health 3: If expressed in letters, it is d=2r. r=d/2 .

Teacher: This is obtained by students through self-study. How do you prove that this conclusion is correct?

1: I will measure the length of diameter and radius with a ruler, and then examine the relationship between them.

Teacher: Then let's use this method to test it.

……

Teacher: Is there any other way?

Health 2: You can see their relationship by origami.

……

Thinking about the problem:

(1) What are the main similarities between the two cases?

(2) Do you really understand the students' starting point?

(3) Analyze the two teaching methods from linear and nonlinear perspectives. Predict the teaching effect of the two teaching methods.

Case Study: P25

Both cases pay attention to students' practical operation, and understand the characteristics and relationship between diameter and radius through hands-on operation.

B Teachers' design is a process in which students constantly activate "memory". Constructivism attaches great importance to individual experience, and all individual learning activities are based on experience. It is the premise of efficient dialogue between teachers and students to let students fully mobilize and show their experiences. We should not only fully admit that students are not a blank sheet of paper, but also try our best to understand what colors students already have.

Obviously, the second teacher created a successful math activity for students. We can foresee that such an activity will definitely make students feel the infinite charm of mathematics. This charm, on the one hand, is because it inherits students' original cognitive experience, and students feel that mathematics is simple, everyday, fun, confident and interested in learning. On the other hand, through multi-sensory activities, students explore the principles behind these intimate and interesting phenomena, establish certain mathematical models, cultivate certain mathematical abilities, and thus gain greater development space and sustained motivation.

2, case description:

When teaching "Multiplier is the multiplication of three digits", the original content was that a grain store sold 674 bags of flour in March, each bag was 25 kilograms. How many kilograms of flour did a grain store sell? Such examples make students feel too far away from their own lives and not very close to themselves, so they can't stimulate students' interest in learning. If we follow the original example, students will definitely find it boring. So, we contact the students' life to extend it. At the beginning of the class, let the students guess how many kilograms of water a dripping faucet will drain away in vain every day. As soon as the students listened, they were very interested. Some guessed 5 kg, some guessed 12 kg, some guessed 20 kg, and some students saw the content after class and said it was 12 kg. The teacher then asked, according to this calculation, how many kilograms of water will be lost a year? The students immediately figured out that the average year is 4380 kilograms and the leap year is 4392 kilograms. With the appearance of the calculation results, the students were surprised: "Wow! So much! " Looking at the students' surprise, the teacher put forward new requirements: "How many households are there in the building where your family lives?" According to a faucet, how much water will run away a year? "

Thinking question: What are the similarities and differences between the original topic and the revised topic (including the connection with students' life, the dimension of goals, and the teaching effect)?

Case study P5 1

"Multiplier is the multiplication of three digits" is a relatively abstract mathematical knowledge exercise, but it also contains rich process learning objectives. Teachers should provide concrete and interesting materials in teaching, guide students to gain the learning experience of "multiplier is the multiplication of three digits" through observation, comparison and thinking, and master the theory that "multiplier is the multiplication of three digits".

As can be seen from the above two scenes, in the first scene, because students lack real experience and materials to attract students, it is difficult for students to have the enthusiasm to learn this textbook, and it is impossible for them to participate in the learning process well.

Many experts point out that "textbooks are only tools for teaching and learning, and they are by no means the only resources". It is a teacher's professional right to deal with teaching materials boldly and creatively, or even reorganize or adapt them. Therefore, in the second teaching scene, the teacher made bold replacement and transformation, and replaced it with life materials that students are familiar with, interested in and close to students' reality. In the above fragments, we can deeply understand that students have initially learned to observe and analyze the world around them with mathematical thinking mode, and in this realistic, meaningful and challenging inquiry activity, students have deepened their understanding and mastery of mathematical knowledge, truly realized that life is full of mathematics, and felt the true meaning and value of mathematics.

3, case description

Teaching fragment of "Send a Car" in the second volume of Grade 2 of Beijing Normal University Edition;

(1) Question: During the holiday, our class organized 25 outstanding students to conduct social practice summer camp, and the school arranged two kinds of cars to pick them up. Among them, each van is limited to 8 people and each car is limited to 3 people. If you were a teacher, how would you deliver the car?

(2) Students think independently and communicate in groups.

(3) Student report:

Students 1: 2 vans and 3 cars, formula: 2×8= 16 (person) 3×3=9 (person).

Teacher: Applause!

Student 2: Send four vans and leave seven seats for luggage. Formula: 8×4-7=25 (person)

Health 3: Send five vans.

Teacher: Tell me your reasons.

Health 3: There are five people in each van, leaving three seats for luggage. The formula is 5×5=25 (person).

Teacher: Never mind!

Student 4: Send six vans, five of which are for four people each and one for five people. There is room for luggage.

……

There are various ways for students to answer, and the teacher affirms them one by one no matter how the students answer, so as to show the democracy of teaching and reflect "encouraging the diversification of problem-solving strategies". After 20 minutes, when the students come up with 1 1 car dispatching schemes (eight of which are more than one car seat), the teacher summarizes the exercises: The students are really capable and have come up with so many schemes, each of which. If you add four teachers and there are 29 people, how would you send a car?

……

Case analysis (from the perspective of problems that should be paid attention to in the diversification of problem-solving strategies);

The diversification of problem-solving strategies means that dozens of people solve the same problem, which does not require each student to solve the same math problem in different ways. Therefore, for individual students, students with different learning abilities should have different requirements. Students with low learning ability only need to solve problems in one way, while students with high learning ability need to solve the same problem in different ways.

Too much pursuit of algorithm diversification will often lead to students' lack of understanding of each algorithm, and their thinking only stays at the level of horizontal comparison. At present, the general emphasis on algorithm optimization is to make students' thinking develop vertically and deeply, and at the same time, algorithm optimization is also conducive to better completing the teaching objectives of a class, such as the goal of "various schemes for renting a car" in this class. Because the optimization method is often recognized, suitable for most students to master and has the value of popularization and use, students can only complete skilled skills on the premise of mastering the optimization method.

4, case description:

Teacher: (presents a rectangle and a square) What are these two figures?

Health: The one on the left is a rectangle, and the one on the right is a square.

Teacher: Today we will continue to learn rectangles and squares.

Teacher: (while gesticulating) You can find out the characteristics of the sides of rectangles and squares by measuring. What can you find by measuring the four corners of a rectangle and a square with the right angle of a right triangle?

(Students explore in groups of four according to the materials provided by the teacher and the prescribed methods.)

1: Our group found that the opposite sides of a rectangle are equal and all four corners are right angles.

Teacher: How did you find it?

Health 1 (edge strokes): measured with a ruler and origami, it is found that the opposite sides of a rectangle are equal and the four sides of a square are equal; measured with the right angles of a right triangle, it is found that all four corners are right angles.

Teacher: What's the difference?

Health 2: Our group found that the opposite sides of a rectangle are equal and the four sides of a square are equal by rope measurement.

Case analysis (from the perspective of question quality): Reference: What kind of questions are good in composition?

First, be clear and specific;

Second, we should have thinking value;

Third, we should pay attention to the achievement of multi-dimensional teaching objectives;

Fourth, the question should have situational function.

5. [Case Description] Teaching fragment of parallelogram area formula derivation:

1. The teacher arranges students to think independently: How do we transform the parallelogram into a plane figure with known area formula to study its area formula?

[Case analysis] (mainly from the perspective of the purpose and openness of the problem):

When designing problems, our teachers first consider the openness of problems. In the process of mathematical inquiry, they design a large number of open problems with certain thinking space. But these questions also have the shortcomings of weak purpose and irrelevant answers. When students answer these questions, they have such and such answers, and teachers can only make some reasonable comments on their answers. However, students' answers and teachers' comments make our math class farther and farther away from our ideal math class. Therefore, when designing a problem, our teachers should not only fully examine the openness of the problem, but also consider the purpose of the design problem. The questions you design should be clear, specific and measurable, and most students can find correct answers. (Refer to Scenario 2.

There are 56 students in Class 6, Grade 4 in a school. In the teaching practice class "Autumn Tour Plan", the teacher asked the students to figure out the items and money needed for the autumn tour, and then designed another activity-buying tickets by car. "A bus can take 50 people, each 300 yuan; A medium-sized bus can seat 30 people, each 200 yuan. Individual ticket 10 yuan/person, group ticket 8 yuan/person (10 person is a group). " According to the data provided by the teacher, it is more reasonable for students to discuss how to rent a car and how to buy a ticket (in the second cooperative study, some students continue to calculate what kind of food to buy, while others are playing with each other's calculators).

Scene three.

When a teacher was teaching the second-grade math class "grams and kilograms", he asked the group to work together to say what they were interested in. When the group reported, a student said, "My name is clarinet, and its weight is 8 grams." The teacher asked, "Is it 8 grams?" The student sitting next to me reminded me, "It weighs 85 grams." The student finally gave a reasonable answer.

Question: What is missing from the cooperation of scene 1? Scene 2 In the second cooperative learning, some students continue to calculate what kind of food to buy, while others are playing with each other's calculators. What is the main reason? Why is the third game 8 grams for the first time and 85 grams for the second time? Case study: P63 (red)

Case study:

Teaching activities must be based on students' cognitive development level and existing knowledge and experience, which shows that the learning process of students is a process of self-construction and self-generation under the guidance of teachers. Students do not simply passively accept information, but actively select, process and process external information, thus gaining the meaning of knowledge. The process of learning is a self-generating process, which is irreplaceable by others. It grows from the inside out, not from the outside in, and is based on students' original knowledge and experience. Students' original knowledge and experience are the starting point of teaching activities.

Ausubel famously said, "If I can reduce all educational psychology to only one principle, then I can put it in a nutshell: the only most important factor that affects students' learning new knowledge is what learners already know. We should find this and teach accordingly. "The teacher's teaching does not take into account the students' existing knowledge and experience level, which makes the inquiry activities in the classroom seem boring. We must seriously understand the idea that "mathematics teaching activities must be based on students' cognitive level and existing knowledge and experience" advocated by the new curriculum.