Teach less and learn more, combine learning with guidance, and learn to learn. Teach students to study independently, learn to think, learn to listen, learn to share, learn to ask questions, use questions or learning tasks to drive students' learning, experience "process learning" and expose students' thinking process.
How to teach math well?
Correct, clear, vivid and profound. Five levels from incompetence to expert level: SOLO classification
Pay attention to students' understanding and thinking structure level, and promote students' advanced learning. If you want to understand mathematics, you must first figure out what to study.
What is the core of the content, what to learn and what to do now?
What to learn: the mathematical essence of learning content; knowledge
Key points and difficulties; The starting point and purpose of students' learning
Standards (knowledge and skills, ability and accomplishment, emotional attitude)
How to organize:
(1) Determine appropriate learning methods and design reasonable learning paths.
(2) Choose appropriate learning and teaching methods, choose appropriate learning materials, design good learning tasks and adopt reasonable teaching strategies.
In this class, teachers should pay more attention to how students think, listen to children's ideas, lead children to learn and discuss mathematics, and experience the process of knowledge development.
In such a class, the following words should become the norm-
What kind of questions can be asked;
How do you want to study this problem?
Tell me what you think;
Discuss in groups and form your group's plan;
What else can we do in the face of such a problem?
Does anyone understand his idea? Who else has different opinions? mathematics
Graphics and geometry
First unit
Cylinders and Cones —— Understanding cylinders and cones from static to dynamic
Understanding of cylinder and cone-the volume of cone Understand the meaning of cylinder surface area, volume and cone volume.
The surface area and volume of a cylinder-if you explore the calculation method, you will calculate and solve simple practical problems.
The connection between plane graphics and three-dimensional graphics has experienced the movement from plane rotation to cylinder and cone, which has communicated the internal connection between two-dimensional graphics and three-dimensional graphics, and realized the connection of "point, line, surface and body" through operation and imagination. Introduction to the specific content of the unit
The first period: intuitive recognition
The second period:
One is from "static" to "dynamic", that is, the plane figure rotates to form geometry.
Secondly, from "overall identification" to "local representation", the characteristics of cylinders and cones are studied. Understanding the surface is another development of cognition.
Third, from observing "physical objects" to understanding "direct vision". mathematics
In the information age, the effective integration of information technology and subject teaching can greatly promote the effectiveness of students' learning. The integration of AR technology and mathematics teaching will change the teaching methods and means, and achieve better results than traditional teaching mode. It plays the role of a learning and research tool and a learning environment.
Explanation of key issues and case II:
Textbooks attach great importance to the achievement of learning objectives of mathematical thinking methods.
Such as "analogy" and "transformation".
Cylinder volume
The volume of cylinder adopts the presentation mode of "asking questions-analogical conjecture-verification induction-practical application", which guides students to experience the exploration process of "conjecture and verification", understand and master the calculation method of cylinder volume during exploration, experience the thinking methods of "analogical thinking" and "transforming unknown problems into known problems", and accumulate experience in learning graphics.
Explanation of specific courses
Question 1: analogy conjecture. Guide students to experience the guessing process of calculating cylinder volume and experience mathematical thinking methods such as analogy and transformation.
Question 2: Try to verify your conjecture from many angles, and finally deduce the calculation method of cylinder volume.
Question 3: Calculate the volume of the cylinder and the volume of the water cup by using the cylinder volume formula. Introduction to Mathematics Unit as a Whole
Graphics and geometry
Third unit
Graphic motion
Interpretation of key issues and cases
Knowing the rotation of a simple figure, you can rotate the simple figure 90 degrees on a square paper. Students' spatial imagination ability is required, which is a difficult point in learning.
The textbook is divided into two classes to guide students to understand rotation;
The first lesson is to know the rotation of line segments.
The second lesson is to know the rotation of the plane. Explanation of specific courses
Rotation of graph (1)
Question 1: Understand the center and direction of rotation by combining the clock face. Make sure that the hour hand, minute hand and second hand are all rotating around the center point, and know the clockwise and counterclockwise rotation directions.
Question 2: Understand the angle of rotation, and try to understand the three elements of "around which point", "in what direction" and "how many degrees of rotation"
Observe and describe the rotation phenomenon of graphics.
Question 3: Draw a line segment that rotates 90 around one end of the line segment on the grid paper to consolidate the understanding of line segment rotation. Explanation of specific courses
Rotation of Graphics (2)
Question 1: Design a learning activity of "Draw a figure after the flag rotates 90". The flag in the picture has a flagpole, and the rotation of the line segment is helpful to understand the rotation of the whole figure.
Question 2: The key to drawing the rotation of a plane figure is to make clear the rotation center, rotation direction and rotation angle. Students who have difficulties can think about it, put it on the table and draw another picture. Question 3: The textbook suggests methods from two aspects, that is, the rotation of a simple figure can be drawn from a line segment; Think about the rotation requirements after painting.
Course: Rotation of Graphics
(1) What to study?
What are the elements of the concept of "rotation"
Concept: In a plane, a figure rotates in a certain direction around a fixed point, which is called the rotation of the figure. This fixed point is called the center of rotation and the rotation angle is called the rotation angle.
Features:
The size and shape of the figure have not changed before and after rotation.
The distance between the corresponding point and the center of rotation is equal.
Every point on the graph has rotated by the same angle in the same direction around the center of rotation.
Learning path: students expect to experience the learning process of thinking and studying problems while learning knowledge;
1, the situation awakens students' existing experience and asks questions to stimulate their learning needs.
2. Describe the rotation in combination with the clock face and crossbar, and realize the three elements of rotation center, rotation direction and rotation angle.
3. Draw the rotation of line segments, compare them in operation, and experience the characteristics of rotation.
4. Deepen understanding and expand application.
How to organize students' learning, promote "deep learning", design reasonable learning paths, and gradually help students learn to describe and understand the characteristics of rotation.
& Experience Awakening-Life Phenomenon-Observation and Perception
& Understand the three elements of rotation-describe the rotation of clock face and gear lever-try to describe and support the operation.
& Deepen the understanding of the three elements, experience the characteristics-drawing the rotation of the line segment-drawing independently, and feedback the discussion.
& Integrate with others, deepen understanding-deepen application-summarize application.
Task-driven learning
Task 1: Draw a line segment after AB rotates 90 clockwise around point B.
Task 2: Draw a line segment after the line segment AB rotates 90.
Introduction to Mathematics Unit as a Whole
Numbers and algebra
Second unit
Understanding of proportion-understanding proportion with rich examples and discovering the laws in proportion.
The application of proportion-solving practical problems, learning solution ratio equation,
Scale-know the scale and understand its application in life.
Zoom in and out of a graph → Zoom in and out of a simple graph with the knowledge of ratio and proportion.
Explanation of specific courses
Understanding of proportion
Question 1: Write the corresponding proportion directly according to the situation of "whether the pictures are alike". .
Through the naughty smile dialogue, the textbook presents two formulas with equal ratio from two angles, which provides an example for understanding and understanding the ratio. Question 2: Reveal the concept and understand the internal and external items. Know that it can be written in fractional form.
Question 3: Expand the range of materials and design the situation of "preparing honey water".
Write the ratio and judge whether the two ratios are equal. There are two angles in the textbook, that is, to judge whether two ratios are equal by calculating the ratio or simplifying the ratio. This is the main method to judge whether two ratios can form a ratio.
The application of proportion "barter" includes the mathematical relationship of exchange according to a certain proportion. Combined with the situation, guide students to solve problems in various ways, realize the diversity of solving methods, list the proportion of unknown quantities in the process of solving problems, and explore the methods of solving ratios independently. Teaching pays more attention to "the application of proportion" and various problem-solving strategies.
Zoom in and out of the figure 1: Create a situation to make students think, "If the ratio of the height of a giant to that of an ordinary person is 4: 1, how to design according to the same ratio?"
The textbook gives hints from the perspectives of classroom height and desk length to help students understand how to design according to the ratio of 4: 1. Question 2: The key to enlarging a rectangle according to the ratio of 4: 1 is to help students understand that "when enlarging a graph, the aspect ratio and width ratio should be equal, that is, the proportion of corresponding line segments before and after enlargement is equal".
Question 3: Understand that "when the figure is reduced, it is only necessary to be equal in proportion to the length of the corresponding line segment".
Positive proportion and inverse proportion
Number of changes-Know the number of changes
Positive proportion and inverse proportion-combining with abundant examples, knowing positive proportion and inverse proportion will draw a positive proportion image. -Determines whether two quantities are directly proportional or inversely proportional.
Explain key issues and cases;
What is the value of letting students learn the knowledge of "variables" in primary schools and experience the thought of function initially? Why should we arrange the lesson of "Variation" before learning the positive-negative ratio formally? We live in a constantly changing world, and studying the relationship between variables from the perspective of mathematics will help people better understand the real world and predict the future.
The development trend of international mathematics curriculum also shows that the exploration and description of the relationship between variables should begin informally in primary school, and the rich experience of functions in the early stage is very important. Infiltrating the idea of function in primary school, analyzing the quantitative relationship of problems by using the viewpoints, sets and corresponding ideas of movement and change can make students realize that everything is constantly changing and interrelated. The number of changes
The purpose is to broaden the knowledge background, so that students can better understand the positive and negative proportions in the knowledge background of "variables" and have rich experience in table representation and image representation of functions.
For primary school students, the concepts of variables and constants are abstract, so this lesson uses a life-like concept "variation" as a topic to help students understand. Teachers can understand the interdependence between variables only by guiding students to describe them in popular languages such as "changing quantity" and "one quantity changes with another quantity".
The number of changes
The textbook presents two specific situations and realizes that there are many interdependent changes in life situations. These two situations are not directly proportional or inversely proportional, but students are expected to understand the amount of change from the general relationship of change, and then gradually understand the relationship of direct ratio and inverse ratio with specific laws.
In the two cases, tables and images are used to show the relationship between variables, so that students can understand the various forms of quantitative relations representing changes.
direct ratio
Question 1: Fill in the form to observe and analyze the changes between the perimeter and the side length, and between the area and the side length of a square.
Question 2: Find out the difference between the changes of two groups of quantities, and find "invariance" from the changes, so as to provide practical support for understanding the meaning of positive proportion.
Question 3: Combine the quantitative relationship of distance, time and speed, enrich the examples, and let students understand the positive ratio. Explain the significance of positive proportion in combination with the situation.
Synthesis and practice
Math is very interesting.
Draw a campus plan.
The floor plan is widely used in our daily life. The textbook designs the activity of "Drawing Campus Plan", which mainly uses the knowledge of "figure and position", "proportion" and "measurement" to draw campus plan. The magical Mobius belt
Mobius belt was discovered by accident by German mathematician Mobius when he was studying the "Four-color Theorem" in 1858. This content is operable, interesting and challenging for students, so the textbook arranges this content as "the fun of mathematics".
Mobius tape has many interesting and wonderful features, such as "only one side", "only one side" and "not two paper tape loops after being cut along the center line, but a big paper tape loop", which will bring some impact to students' thinking (for example, how two sides can become one side), and students will find it a bit difficult to understand and a bit "magical". Let students feel the infinite charm of mathematics through mathematics activities, and further stimulate their curiosity and interest in learning mathematics. Of course, for primary school students, as long as they have a preliminary understanding and experience of the characteristics of * * * *, they do not need to master the knowledge of bilateral surfaces and unilateral surfaces.
In order to help students know Mobius belt and its characteristics, the textbook adopts the method of comparing ordinary paper tape with Mobius belt, and designs a series of practical activities to let students observe, guess, compare, verify, think and discover, intuitively feel the magic of Mobius belt, appreciate the charm of mathematics and expand their mathematical thinking.
The activities of "Cute Kitten" are interesting and fun, which is conducive to the cultivation of students' creative thinking.
When organizing activities, teachers should pay due attention to the requirements of learning. First, the main goal is to let students learn and experience "using the change of number pairs to enlarge and reduce graphics"; Second, students' thinking and calculation activities are all on grid paper marked with coordinates, but students don't need to learn the term "rectangular coordinates", as long as they directly use a specific language such as (2,0) to represent the position of A and (6,2) to represent the position of B.
Always review the basic ideas of writing for 30 class hours.
1. Arranged by field and theme, which is convenient for students to learn and teachers to teach.
2. Ask questions to drive students to organize their knowledge independently, and pay attention to the combination of arrangement and application.
3. Pay attention to the internal connection of spreading knowledge and the infiltration of learning methods.
The function and goal orientation of review course
Review class is to teach knowledge relatively independently at ordinary times, especially by means of reproduction, arrangement and induction, to string together regular knowledge, deepen students' understanding and exchange of knowledge, and make it orderly and systematic. Review class is different from the new teaching practice class, so we should avoid "cold rice and heavy speculation"
New teaching-from thin to thick; Review class-from coarse to fine.
Present situation and problems of review class
Simple repetition; "full house irrigation"; Organization and normalization; Give lectures and comments on exercises; Practice instead of recovery; Maritime tactics. Turn the review class into a "movie class", and students only know how to watch;
Turn the review class into exercise class, and students know how to do it; Turn the review class into a "lecture and evaluation class", and students only know how to listen.
The core task of review class
Knowledge carding: systematize, network and organize the knowledge learned in order to achieve the purpose of comprehensive application.
Check and fill in the gaps: Find the "breakpoints" of students' "knowledge chain" and "thinking chain" and fill in the gaps according to the "breakpoints".
Expand and upgrade: recitation is not a low-level repetition. On the premise of making up the loopholes, we should sublimate our knowledge, improve our ability, and truly realize "reviewing the past and learning the new". Strategies to Improve the Effectiveness of Review Class
(A) a good "review class"
"Reason" and "practice" are the two "cores" for arranging review classes.
There are three different ways to organically combine "reason" and "behavior":
"Management before practice" type
"Management and Practice" Health Assistant
"rational practice" type
Use mind map circle-process knowledge inventory to find out the core knowledge points.
Task-driven, guide students to learn to organize knowledge. There are many forms of organizational knowledge: words, tables, frames and pictures;
Grasp the key, design the whole, carefully design mathematical activities, build a platform suitable for students to organize their knowledge independently, and guide students to review (reproduce) and sort out their knowledge.
O research teaching materials, and classify them appropriately by field and part.
O highlight "learning" and guide students to organize their own knowledge.
Review the characteristics and functions of task design.
Reproduce old knowledge, compare differences, sum up similarities and discover new ideas.
Seek knowledge and seek common development.
Level one, level two, level three.
Strategies to improve the effectiveness of review class 2,
Carefully design exercises to improve their variability, comprehensiveness and pertinence.
O Focus on pertinence, pointing to key points, difficulties and weak links.
O pay attention to variants, integrate them appropriately and improve them effectively.
O ideal: layered practice, layered push practice. Strategies to Improve the Effectiveness of Review Class
3. Do a good job of "commenting on test papers".
O the test paper should be carefully prepared and targeted.
O Pay attention to guiding "methods" when marking papers, and don't just talk about topics.
Teaching suggestions for general review
Make a review plan according to the actual situation of students.
Pay attention to guide students to sort out mathematical knowledge, help students build knowledge structure and communicate the relationship between knowledge.
According to the actual situation of the students in the class, design and select targeted exercises to check for missing parts.
? The key to the diversification of learning forms is pertinence and effectiveness.
Encourage students to ask questions.
Pay attention to giving effective help to students with learning difficulties.
Pay attention to cultivating students' review habits
Add interest and charm, and stimulate students to actively and persistently participate in learning.