The seventh grade mathematics lecture courseware 1. Teaching objectives
1. 1 status and function
In junior high school, it is necessary to cultivate students' computing ability, logical thinking ability and spatial imagination ability, so that students can transform practical problems into mathematical consciousness of mathematical problems according to some realistic models, thus enhancing students' understanding of mathematics and their ability to solve practical problems. The cultivation of computing ability is mainly completed in the first stage. The operation of rational number is the basic operation of elementary mathematics, and I have mastered the operation of rational number. As a kind of rational number operation, rational number addition is one of the important foundations of rational number operation and also a foundation of the whole junior high school algebra. It is directly related to the study of rational number operation, real number operation, algebraic operation, solving equations, studying functions and so on.
1.2 Analysis of learning situation
In junior high school mathematics teaching, non-intelligence factors play a very important role in the cognitive process, and interest occupies a special position among non-intelligence factors. It is the core factor of students' learning consciousness and enthusiasm, and it is the enhancer of learning. Therefore, cultivating students' interest in mathematics from the first day of junior high school is an important guarantee for them to learn mathematics well. Around this point, students at different levels should have the opportunity to experience success in teaching. Only by taking teachers as the leading factor and students as the main body can we fully understand the beginning. Competitive; Weak abstract thinking ability, relying too much on intuition; Weak will, lack of perseverance.
On the other hand, the teaching of textbook knowledge conforms to the characteristics of students' cognitive development. In the early stage, students have stored the addition of two positive numbers, the subtraction of the larger number and the subtraction of the smaller number, and introduced the negative number. It is necessary to learn the addition of rational numbers again, and then transition to other operations of rational numbers, and then transition to operations of formulas, equations and functions. At the same time, the study of negative number, number axis and absolute value laid the foundation for the learning method of this lesson.
1.3 teaching objectives
According to the status and role of this section, combined with the specific learning situation of students, the teaching objectives of this section are determined as follows:
Knowledge goal: By transforming the problems in life into the whole process of rational number addition, students can intuitively understand the meaning of rational number addition, master the rules of rational number addition and use them correctly.
Ability goal: to cultivate students' exploration and innovation spirit through situational design. In the process of students' learning, the ability of classification, combination of numbers and shapes, synthesis, induction and generalization is infiltrated.
Emotional goal: through the exploration under the guidance of teachers, let students feel the value and fun of mathematics learning.
1.4 teaching material processing
According to the content of this textbook, I divide the addition of rational numbers into two categories. In the first class, I learned the addition rules of rational numbers, and I can add two numbers accurately. In the second class, learn the addition law of rational numbers, and you can add up multiple numbers accurately.
2. Key points and difficulties
2. 1 teaching focus: understanding and application of rational number addition rules (rather than simple back rules).
2.2 Teaching difficulties: the practical significance and laws of the addition of different numbers of two symbols are summarized.
3. Teaching methods and means
This course adopts multimedia-assisted teaching, starting from people familiar to students, to stimulate students' desire to explore; Guide students to explore new knowledge by using the mathematical tools they have learned through layers of bedding; On the basis of students' exploration, consciously guide students to sort out the diversified results; Cultivate students' learning ability of analogy, induction and generalization in the process of refining laws.
In the design process of this section, open-ended exercises are used to lead out topics, so that students can learn and cultivate their abilities in the research and fully span the students' recent development areas.
4.？ Teaching process:
4. 1 Create situations to "move" students' thinking.
[Life] Liu Xiang is the champion of the world men's youth championship 1 10 meter hurdles and the pride of China people. From his sports spirit, we should learn from his perseverance and efforts, encourage students to be patriotic and determined, abstract the runway into several axes, and take the starting point as the origin to mathematize life problems.
Description: This modeling from life to mathematics, starting from the subjects that students are interested in, provides an exciting stimulus for creating the following exploration situations, so that every student has confidence and can actively try and explore.
4.2 Experience the process to make students' thinking "live".
Mathematics is the core of the problem and the starting point of teaching.
[Open Exploration] Liu Xiang runs back and forth on an east-west runway for training. He ran two paragraphs in a row and * * * ran 80 meters. Ask Liu Xiang twice where he might be.
Design intention: This is an open question with unique conditions and results, which is challenging for students. Its advantages are: as long as you understand the meaning of the question, any student can answer at least one correct answer correctly; At the same time, its answer is also divided into many situations. Because of the incompleteness of thinking, students can easily lose their answers, and this kind of mistake can be suddenly realized under the reminder of others. This is a good question, which can exercise the flexibility and rigor of students' thinking, apply the answers to classified discussions and cultivate students' generalization ability. This topic includes students' understanding of the meaning of rational number addition and exploring several types of rational number addition addend (from positive to negative). In the process of summation,
Teaching methods: using courseware to help students transition their thinking from "physical operation" to "representation operation" and optimize their thinking; Give students full opportunities to think; Be good at grasping the weakness of students' thinking and guide them according to the situation.
Predictability: ① Students intuitively understand that "* * * ran 80 meters" is 80 meters away from the starting point. This is the confusion between the concepts of distance and displacement, and it is not appropriate to add new concepts to teaching. ② What quantities do the "two segments" and "80 meters" in the conditions correspond to respectively? Some students don't understand the meaning of the question and may give up.
Solution: ① The weak point of students' thinking in teaching may also become the bright spot of his thinking in this class, so that students can try to practice the thinking mode of "physical operation" on paper and break through the bottleneck of thinking by themselves. ② After students correctly understand the conditional usage of 80 meters, they can compare the relationship between 80 and the absolute value of addend and sum, and they can distinguish students with different levels of understanding by going up a flight of stairs.
Teaching notes: We should make clear the teaching focus and objectives of this class, explore open questions, do not delve into all the possibilities of the questions, and edit the students' answers as soon as possible to lead to the topic.
4.3 Explore the law, so that students' thinking "jumps".
It is the key and difficult point of this course to discuss and summarize the addition law of rational numbers by classification. Teachers should discover organizational language according to students' existing learning, reduce mandatory or imperative language, and try to reduce the time when the class is still or students don't understand.
In the process of summing up the answers, we should affirm students' exploration, cherish students' interest in learning and desire to explore, let students become the masters of the classroom, state their own results, and appropriately postpone the evaluation of students' incomplete or inaccurate answers. In order to encourage students' creative thinking, teachers should seize the flash of students' wisdom in time. This moment of psychological encouragement is an effective way to cultivate students' creativity and fully tap their potential.
Imagine students' thinking in advance, and may classify and summarize from the following aspects to explore the law:
① From the different sign situations of addend (encounter situation: positive number+positive number; Negative number+negative number; Positive number+negative number; Number +0)
(2) From the different numerical situations of addend (addend is an integer; Appendix is decimal)
(3) from the classification of rational number addition rule (adding two numbers with the same symbol; Add two numbers with different signs; Add 0)
(4) From the aspect of vector superposition (summation of addend absolute values; Subtract the absolute value of addend)
(5) from the aspect of determining the sign of sum (determining the sign of adding two numbers with the same sign; Determination of the addition sign of two numbers with different signs)
In teaching, we should avoid the excitement in the classroom and fall into the shallowness and poverty of mathematics teaching.
4.4 Pay attention to reflection and make students' thinking "profound".
[Reflection application 1] Example 1: Calculation? (-3)+(-9) ; ? (-4.7)+3.9;
[Reflective Application 2] Example 2: In the football round robin, the red team beat the yellow team 4: 1, the yellow team 1 beat the blue team, and the blue team 1 beat the red team. Calculate the goal difference of each team?
Design intention: When mathematical knowledge is transformed into representational knowledge, students must be transformed from formalization to symbolization and digitization. These two examples are examples from textbooks. In the teaching process, we should reduce students' concrete thinking, let them get used to doing problems with rules as much as possible, and cultivate students' mathematical consciousness.
4.5 The combination of expansion and application can sublimate students' thinking.
[Exercise 1] Calculate15+(-22); ? (- 13)+(-8);
[Exercise 2] Use formulas to express the following results:
(1) The temperature rises from -4C to 7C (2) Income from 7 yuan and Expenditure from 5 yuan.
[Exercise 3] Look for mistakes with keen eyes:
Purpose of practice: I can use rules to calculate and strengthen my skills.
[Teaching Understanding] When you learn rational number addition in this class, the most impressive knowledge is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _; Which learning process of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ are you most satisfied with? What do you think you or the teacher need to improve in class is _ _ _ _ _ _ _ _ _ _ _ _.
Design intention: Making full use of evaluation is a powerful means for learners to reflect and improve. In the evaluation, helping students to attribute correctly will be beneficial to their follow-up study.
[Homework] Homework mode: Choose 3 questions from three groups of homework: A, B and C.
Group A (basic questions): textbook P29 exercise 1.3 exercise: questions 1.
Group B: ① Please design a calculation problem and fill in the blanks:
(2) Stationery stores, bookstores and toy stores are located in an east-west street in turn. The stationery store is 20 meters west of the bookstore, and the toy store is 20 meters east of the bookstore 100 meters. Xiaoming walked 40 meters east from the bookstore, and then walked 60 meters west. At this time, Xiao Ming's position is ().
A. Stationery store B. Toy store C. Stationery store 40 meters west? D. 60 meters west of the toy store
Group c:? ① Find the law: find the law from table 1 and fill in the appropriate numbers in the blank of table 2 according to the law.
② ? In order to show the society's respect for teachers, on the morning of Teachers' Day, taxi driver Xiao Wang picked up teachers on the east and west roads for free. If the east is positive and the west is negative, the taxi trip is as follows (in kilometers):+15, -4,-13,-10, -65438+.
(1) If the last teacher arrives at the destination, what is the distance between Xiao Wang and the starting point?
(2) If the fuel consumption of the car is 0.4 liters/km, how many liters will this car consume this afternoon?
Design intention: design exercises in different levels to meet the needs of students with different basic levels and different thinking levels. Class a questions train students' directional thinking and cultivate their basic skills; Class b questions mainly train students' divergent thinking and cultivate their flexibility; Class C questions are challenging, which can cultivate students' profound thinking and willpower in the process of challenging.
[Blackboard Design]
Instructional design description
Bruner's cognitive theory holds that people's cognitive process should go through a process from "physical operation" to "representation operation" and then to "symbol operation", and then knowledge can be truly internalized into people's cognitive structure. I think this cognitive law should be followed and realized in the teaching design of this course.
Rational number addition is a pure operation skill course. How to make students feel that they are the masters of knowledge in this course that we take for granted and students are at a loss, and how to have the right to explore and discover on their own initiative is the theme that I pondered repeatedly when preparing lessons. How to effectively play the guiding role of teachers in a traditional "teaching, memorizing and practicing" class, make the class full of vitality and really cultivate students' abilities in all aspects is what I pursue. I think math should be.
When classifying the language interaction between teachers and students, Flanders believes that there are three ways of communication between teachers and students in the classroom: response, neutrality and spontaneity. In this class, I hope students can express their needs and explore spontaneously. I fully imagine the difficulties that students may encounter and fully trust them, fully mobilize their enthusiasm and sense of participation, make their thinking move, jump and sink again, and make the students' thinking transition from formalization to symbolization and digitalization.