I. Design principles
(A) the principle of "design according to standards"
Homework design should comply with the requirements of "Compulsory Education Mathematics Curriculum Standard" on reasonable design and implementation of written homework. First, we should point to the understanding of the essence of mathematics and its rational application in specific situations; second, we should embody the ten core concepts put forward by curriculum standards; third, we should design homework to understand students' learning process.
(B) to improve the quality of the "burden" principle
Homework design should strictly implement and implement the "Opinions on Further Reducing Students' Homework Burden and Off-campus Training Burden" on reducing the total amount and duration of homework in an all-round way and reducing students' excessive homework burden. One is to reduce the total amount of written homework, and the other is to improve the quality of homework. The system design conforms to students' age characteristics and learning rules, and embodies the basic homework oriented by quality education.
consistency
Homework design should match the classroom learning objectives and embody the concept of consistency of "teaching evaluation". Homework design should match the teaching content, and design closely around the teaching key and difficult content. Consolidate the knowledge and skills learned, experience mathematical thinking methods and develop the core literacy of mathematics.
(four) the principle of combining written work with practical work.
The amount of written homework should meet the time requirements of written homework in all grades. There is no written homework in grade one or two, so students can be arranged with some practical homework such as small production, small investigation and small games. Other grades can be assigned a proper amount of written homework, and some practical homework closely related to the learning content can also be appropriately assigned.
(5) The principle of combining hierarchy with interest.
The content of homework should meet the needs of students of all academic levels. Students at all levels have their own homework to avoid "not enough to eat" and "not enough to eat". Pay attention to fun, hierarchy and openness, and the forms of homework should be flexible and diverse, so that students are willing to do homework.
Second, the type of work.
According to the content of homework, homework is divided into three types: basic homework, comprehensive homework and reflective homework.
(1) basic operation
Basic work focuses on consolidating basic knowledge and skills. This kind of homework not only consolidates basic knowledge and skills, but also reflects the process and method of students acquiring basic knowledge and skills, and reflects the occurrence, development and transformation of mathematical knowledge.
(2) Comprehensive management
Comprehensive homework focuses on the comprehensive application of mathematical knowledge, skills and methods in specific situations to explore mathematical problems or solve problems in real life. This kind of homework is an empirical, practical and cooperative homework. It is an important carrier to accumulate experience and cultivate application consciousness in mathematics activities. It can improve the thinking mode of using mathematics, enhance the ability to solve problems, improve the interest in learning mathematics, and enhance the sense of cooperation, innovation and scientific attitude of seeking truth from facts.
(3) reflective homework
Reflective homework focuses on prompting students to actively construct a knowledge system suitable for their own knowledge level. This kind of homework is to let students re-understand and improve their own thinking process and thinking results. It can broaden the vision of mathematics, expand the thinking of mathematics, promote the cultivation of students' autonomous learning ability and evaluation reflection consciousness, and also understand the application value of mathematics.
Third, design strategy.
Homework is an important way to test the achievement of students' classroom learning goals every day. Reasonable design and arrangement of homework is helpful to improve students' mathematics academic performance in an all-round way, feedback the teaching effect in time and improve the teaching quality.
(A) design strategies and examples of basic operations
1. policy.
When designing basic homework, we must accurately grasp the requirements in the course content. Accurately grasp the requirements of "knowing, understanding, mastering and applying" at different levels, pay attention to the understanding of the mathematical essence contained in it, and should dilute the special problem-solving skills to avoid off-topic strange questions. Basic homework design should first grasp the psychological characteristics of students' curiosity, pursue multi-sensory and multi-angle participation in the content and form of homework, and highlight a "live" word. In this way, the designed homework can be changed from "boring" to "interesting", highlighting the interest. Basic homework design should also promote the development of every student, and the differences of students' mathematical knowledge and ability exist objectively. Therefore, we should face up to the individual differences of students, strive to embody "teaching students in accordance with their aptitude" in homework design, and change "unification" into "stratification" to reflect hierarchy.
Example 1: Design the basic homework of "Chicken Eating" (10 addition and subtraction), the first volume of grade one of Beijing Normal University. Go home and play the game of pulling the train with your parents with playing cards. The rule of the game is that as long as two cards can make ten cards, you can take them all away, and there are cards in the middle, and the person with more cards wins in the end.
Description of design intention: The curriculum standard requires you to be proficient in calculating addition and subtraction within 20.
Example 2: The first volume of the third grade of Beijing Normal University "Mixed Operation"
Curriculum standard requirements: know parentheses and be able to perform simple integer elementary arithmetic.
Homework: Use playing cards (1 9 playing cards, which cannot be repeated) to count "24 points" with parents.
Example 3: Division of Fractions, the first volume of the fifth grade of Beijing Normal University.
Curriculum standard requirements: be able to carry out simple fractional division and develop operational ability.
Homework: Fill in, circle and calculate. draw
Example 4: Understanding of Cuboid, Volume II, Grade 5, Beijing Normal University
Curriculum standard requires: through observation and operation, know the cuboid and cube, and know the expansion diagram of cuboid and cube.
You can design the following jobs at different levels:
Required question: Uncle Zhang wants to select five pieces of glass from the following six pieces and splice them directly into an uncovered fish tank (unit: decimeter).
draw
Which piece do you think he chose as the bottom of the fish tank? Which is front, back, left and right? Talk to your partner about your thoughts.
Title: Uncle Zhang's house has the following specifications of wooden boards, and he wants to choose several pieces from them to form a rectangular or cubic wooden box. What choice can he make?
draw
Challenge: If the two rectangles below are two sides of a cuboid, can you imagine the shape of this cuboid? What kind of figure is it on the other side?
draw
Extension problem: What problems can be studied about cuboids? Think, draw, say and calculate.
Example 5: The Circle, the first volume of the sixth grade of Beijing Normal University.
Curriculum standard requirements: through operation, know the ratio of the circumference to the diameter of a circle as a fixed value, master the formula of the circumference of a circle, and solve simple practical problems.
You can design the following jobs at different levels:
Required question: (1) Find the circumference of the following circle, d =10cm; R=2 decimeters. (2) The diameter of the outer wheel of the bicycle is 0.52m.. If you scroll once a second, how many meters can 1 minute walk?
Choose a topic: find out what other round objects are around. Can you find a way to know its circumference?
Challenge: Give you a round glass with broken edges. Can you calculate the original circumference of round glass?
Extension question: Can Uncle Zhang enclose a semicircular vegetable field with a radius of 4 meters with a 20-meter iron wire?
(B) the design strategy of comprehensive homework
When designing comprehensive homework, the materials presenting the content should be close to the students' reality, skillfully and appropriately combined with the teaching content, and reflect the application of mathematics. Open questions should be designed to reflect the diversity of problem-solving strategies. We should pay attention to let students experience the fun of learning mathematics by measuring, collecting data, calculating and drawing, and stimulate students' interest in learning and desire to explore knowledge. The design of comprehensive homework should expand the time and space of students' homework, leave enough thinking space for students from the selection of homework content to the presentation of homework form, change "closed" into "open" and pay attention to openness.
Example 6: How long is a thousand meters? The second grade of Beijing Normal University.
Curriculum standards require: in practice, understand and recognize the length units of kilometers, meters and centimeters, and estimate and measure the length of some objects.
Homework: Go home and measure the height, waist circumference and head circumference of yourself and your family, measure the length of one step, and estimate the distance from home to which landmark building is about one kilometer.
Example 7: The area of rectangle in the third grade of Beijing Normal University.
Curriculum standard requirements: explore and master the area formulas of rectangles and squares, and estimate the area of a given figure.
Homework: "My Home Area"
(1) What is the length and width of your bedroom? How many square meters is the calculated area?
(2) What is the area of your living room? What kind of floor tile is used? How many tablets did you use?
(3) It is estimated that the living room area of your home is several times that of the study? What's the size of the kitchen? What's the size of the bathroom?
Example 8: Scale, the sixth grade of Beijing Normal University.
Curriculum standard requires: knowing the scale, under certain circumstances, the distance on the map and the actual distance will be converted according to a given ratio.
Homework: Draw a plan for my family.
Example 9: The third grade of Beijing Normal University, the second volume "How Heavy" (knowing kilograms)
Curriculum standards require: in real situations, feel and understand grams, kilograms and tons, and can carry out simple unit conversion.
Complete the following investigation assignments after school:
(1) Go to the supermarket to see what items weigh 1 kg?
(2) Record the weight of 1 ham sausage, a pack of instant noodles, a bottle of mineral water, a bag of yellow wine, an egg, etc.
(3) Let's guess with mom and dad how many peanuts are in 1 kg. Then weigh and count.
Example 10: data collation and analysis, the fourth grade of Beijing Normal University, Volume II.
Curriculum standards require: a simple process of collecting, sorting, describing and analyzing data.
Homework: rational housekeeping
Record all the expenses of your family for two weeks, sort out the data (it is best to show the statistical chart), and analyze the expenses of your family. What did you find? Any good suggestions?
Example 1 1: Average Volume 2 of Grade Four of Beijing Normal University.
Curriculum standards require: understand the function of the average, be able to calculate the average, and explain its practical significance in your own language.
Group a
150
168
147
152
158
Group b
162
152
164
150
——
Homework: (1) The following are the scores of two groups of skipping rope competitions per minute (below).
Which group has better grades? Please calculate and explain the reason.
(2) The average depth of a small river is 0.8m, and the height of Xiao Qiang is1.6m.. He can't swim. Is it dangerous for him to wade across the river? Tell me your reasons.
(C) the design strategy of reflective homework
When designing reflective homework, we should strengthen the cultivation of students' autonomous learning ability. Creating opportunities for students to participate actively, and designing some open-ended questions according to their deep understanding of the subject thought and flexible application of the subject method can promote students to think deeply, find problems actively, analyze the reasons, systematically summarize the application conditions, application scope and fields of the subject thought method, and broaden their horizons.
When designing reflective homework, we should stimulate students' awareness of participating in inquiry and arouse their enthusiasm for improving mathematics literacy. When designing reflective homework, students can find ways to organize knowledge, find the connection between knowledge and form a complete knowledge network.
When designing reflective homework, we should pay attention to the cultivation of "transfer" ability. By transferring analogy, we can cultivate students' ability to grasp and discover essence through phenomena. This is an effective way to develop students' core elements.
When designing reflective homework, we should pay attention to the cultivation of reading ability. With the progress of the times, people pay more and more attention to reading ability. Mathematics reading ability is not a simple ability, but a comprehensive ability to think, imagine, operate, analyze and solve problems when reading mathematical materials.
Example 12: data processing, the first volume of Grade 6 of Beijing Normal University.
Curriculum standard requirements: be able to interpret statistical results, make simple judgments and predictions based on the results, and communicate.
Homework: give you two weeks, you can go deep into communities, streets and enterprises to investigate and count the number of cars; You can also visit the traffic police and urban management departments to find out the distribution of parking spaces in your area. You can also collect residents' opinions on the current parking problem and design a multi-functional parking plan by yourself.
Example 13: the area arrangement of plane graphics in the first volume of the fifth grade of Beijing Normal University
Course requirements: Explore and master the area formulas of triangle, parallelogram and trapezoid, and solve simple practical problems.
Homework: Can you draw triangles and parallelograms as high as the trapezoid below? What did you learn after painting?
draw
Example 14: the first volume of the fourth grade of Beijing Normal University, "Three Numbers Times Two Numbers"
Curriculum standard requires that you can calculate the product of three digits and two digits.
Homework: (1) vertically calculate 23×32 and 123×32. (2) Do you dare to challenge 1234×32 and 345×11? Tell me what is calculated at each step. What did you find?
Example 15: Beijing Normal University Edition Grade Four Volume Decimal Multiplication
Curriculum standard requirements: with the help of specific operations, we can explore and discover simple operation rules and develop a sense of numbers.
Homework: Do the math, fill it in and see what you find. Can you give another example to prove your discovery?
2.3x 1.2= 2.3x 1.05=？ 2.3x2. 1= 2.3x 1=
2.3x0.4= 2.3x0.9= 2.3x0.85=？ 2.3x 1. 1=
Example 16: Volume II of Cuboid in Grade Five of Beijing Normal University
Curriculum standard requirements: explore and master the cuboid volume according to the specific situation and solve simple practical problems.
Homework: You can already calculate the volume of a long cube and a cube. Guess whether you can calculate the volume of a cylinder in the same way. Tell me your reasons.
draw
Description of design intention: The curriculum standard requires us to explore and master the cuboid volume according to the specific situation and solve simple practical problems. The volume formulas of long and cube are obtained by multiplying the area by the height. From a dynamic point of view, the bottom surface is "pulled" upward into a body. What kind of ideas can students have after learning the long and cubic volume formulas? Can you generalize the volume formula? This is a problem that teachers should pay attention to. At this time, the design of migration homework not only satisfies the curiosity of primary school students, but also cultivates the concept of space and application consciousness, and also lays the foundation for the later teaching of cylindrical volume.
Example 17: Designing reflective homework for math reading.
Use the holiday time to read Li Yupei's Amazing Digital World, make a math briefing and introduce what you are interested in; You can also record a small video to explain the chapters you are interested in and recommend this book to everyone. Description of design intention: In the process of mathematics reading, guide students to establish the relationship between different mathematical expressions (written language, symbolic language and image language) of the same mathematical object, realize the abstraction of mathematical expressions, realize the logic between the meanings expressed in the context, let students experience the cognitive process of dialogue with the text in reading, and constantly try to assume, imagine, reason and verify. In the process of recommending this book, the evaluation task is embedded, the knowledge of other disciplines is integrated, and the comprehensive ability is developed.
For example, I will read Li Yupei's "Magic Digital World" during my vacation, make a math briefing and introduce my interest. You can also record a small video to explain the chapters you are interested in and recommend this book to everyone.