Three major types of designs for junior high school mathematics homework:
1. Design of knowledge-based mathematics homework
Mathematics courses at the compulsory education stage are designed to promote students’ comprehensive , sustained and harmonious development as its basic starting point. Students are the main subjects of learning. Only through students' own "recreation" activities can all mathematical knowledge be incorporated into the cognitive structure and become effective and useful knowledge. Under this concept, the design of mathematical knowledge inquiry assignments should be based on mathematics textbooks, with the purpose of further understanding the content in the text, and pay attention to the "recreation" of students' knowledge. It is up to the students themselves to discover and "create" what they want to learn. The knowledge acquired in this way can be ingrained in the minds of students.
This type of assignment is often designed after new lectures, using posters, class meetings, knowledge competitions and other means. Feed back the knowledge they have learned through homework, and require students to summarize something from it, such as problem-solving formats, verification ideas, knowledge structure diagrams, or some mathematical history knowledge. The basic process of this kind of homework design is: ask questions - → explore teaching materials - → search for information - → report results - → summarize and evaluate. During the teaching process, we work with students to stimulate students' interest in learning mathematics by focusing on a certain example question in the textbook or an after-school reading question. For example, after finishing the "Pythagorean Theorem", students are divided into groups to look up historical materials about the Pythagorean Theorem from books and the Internet, and then communicate and report in the form of theme class meetings in class meetings, etc. This kind of intellectual inquiry assignment not only overcomes the shortcomings of previous assignments, but also improves students' ability to analyze problems.
2. Design of Mathematics Skills Assignments
Students’ mathematics learning activities should be a lively, active and individual process. Mathematics teaching should be closely connected with students' real life, and acquire knowledge and cultivate abilities through students' autonomy, cooperation and inquiry. During the hands-on operation, students are focused, dedicated, and interested, which enhances their awareness of autonomy and cooperation spirit. Through various forms of inquiry activities such as observation, investigation, hypothesis, and experiment, students put forward their own explanations and motivate students with learning difficulties to learn well. , so that students at each level can have different needs, reflect individual differences, and allow all students to develop lively. It cultivates students' interest in learning mathematics and transforms students from passive "I want to learn" to active "I want to learn".
Skilled homework includes folding, design and hands-on tasks. This type of assignment is designed using extracurricular group activities, allowing students to put forward their own explanations, or design and produce their own works through various forms of inquiry activities such as observation, investigation, hypothesis, experiment, etc.; the basic process is: Ask questions—→ Analyze teaching materials—→Search for information—→Design plan—→Hands-on operation—→Result report—→Summary and evaluation. Let students design exercises with different difficulty levels and form a question bank, so that students at each level can receive appropriate training on exercises, reflect individual differences, and allow all students to develop vividly. When the author taught the lesson "Cut a Geometry", he first asked questions and asked students to take the initiative to use taro to "cut". The students prepared in advance, worked in groups in class, and did hands-on operations. During the operation, one student unexpectedly thought of the right He also conducted the same research on polygons, and he came to a conclusion that no teacher could have imagined! This kind of homework is designed to cultivate students' hands-on production and creative abilities.
Using practical problems as the background, preparing inquiry assignments for inquiry learning can cultivate students' innovative spirit and practical ability. After the author finished teaching "Symmetric Figures", he raised this question: "Four different flowers and plants are planted on a rectangular open space. Now divide this open space into four pieces according to the following requirements: (1) The entire figure after division is Axisymmetric figures. (2) The shapes of the four figures are the same; (3) The areas of the four figures are equal. Please draw more than 4 division methods according to the above requirements. "There are no prescriptive requirements for these questions. Students have rich imagination and can fully complete it by doing it themselves. Many students used the surrounding geometric shapes to place them first and then demonstrate, and achieved great results. This not only cultivates students' hands-on practical ability, but also cultivates students' innovative spirit of daring to break the rules.
3. Design of practical life assignments
“Mathematics comes from life” reflects the basic view of dialectical materialism, while “serving life” reflects the practical value of mathematics .
Modern mathematics pays attention to "mathematics comes from life and serves life". The design of the new teaching materials fully reflects this principle. Teachers should help students design many practical life inquiry assignments, allowing students to choose assignment topics independently, truly enter the big classroom of social life, visit and explore problems in real life, so that their inquiry results can serve the society.
The design of practical life assignments starts from students’ existing knowledge, combines the needs of teaching materials, and uses practical problems as the background to create problem scenarios to stimulate students’ interest in learning and guide students to gradually explore the problems. Form mathematical concepts and develop students' problem-solving abilities. The basic process of designing practical life assignments is: Asking questions - → Life investigation - → Observation and recording - → Explanation and discussion - → Drawing conclusions - → Expressing statements. The design of this kind of inquiry-based assignment can truly reflect the characteristics of students as the main body.