Reflection on Mathematics Teaching and Research Activities Part I During the implementation of the new curriculum, we are delighted to see that the traditional receptive teaching mode has been gradually replaced by lively mathematics activities.
Reflections on Mathematics Teaching in Junior High School
. The classroom is alive, and the students are dynamic: they dare to think, ask, speak, do and argue, and are full of thirst for knowledge and expression. Are you online? Learning as teaching? Today, combining with some specific cases in teaching, it is unique to look at the curriculum reform from the perspective of students' changes.
1. Communication allows students to share happiness and resources.
Students' existing life experience, activity experience and original life background are all good curriculum resources. Are you online? Stereo graphics in life? In this lesson, different students carry out activities according to different life backgrounds, abstract their own graphics and make paper three-dimensional graphics. The communication between them realized their understanding and understanding of the key features of three-dimensional graphics. Everyone * * * shares the happiness of discovery and success * * * enjoys each other's resources.
Second, life-oriented teaching makes students feel the joy of learning.
Are you online? Algebra? In this lesson, we will introduce an exercise in the last lesson to guide students to explore a 5n+2 law, thus leading to the concept of algebra. For example, the teacher pointed out that algebraic expressions are not only useful in mathematics, but also exist in real life. Then the teacher said a few facts, who can use algebra. Can these expressions have other meanings besides what the teacher just said? The students began to get active, and a boy raised his hand. P yuan for a book, how much can 6p represent the price of six books? Inspired, every student is looking for a role model in life, and everyone can deeply feel it from this lesson? Everyone learns useful math? New concept, as Mr. Liu said, algebraic expression in life? .
3. The integration of disciplines makes students feel the charm of modern science and technology and comprehensive learning.
In daily life, people often talk about CT technology and magnetic resonance imaging, but few people can explain the reason clearly. However, did you learn the first volume of the seventh grade? Cut a geometry? In the future, almost all students can realize that the CT technology of modern medicine is actually similar to cutting radish.
Fourth, innovative design makes students think positively.
Under the students' online inquiry, careful design and guidance, it went smoothly? I'm a little designer? Classroom activities: This class is designed according to the homework of the first volume of seventh grade mathematics. Design a picture with squares, circles, triangles and parallelograms, and explain what you want to show. The teacher will assign the content of the topic to the students in advance. Two students are the hosts of this class, and the other students show their works and explain their creativity. Finally, as a special guide, the teacher summarizes the students' geometric design, creativity and speeches, and then the students summarize and reflect on themselves. In the whole class, students have experienced the modern mathematical concept that graphics come from life and serve life, which better embodies the effective learning mode of students' active exploration and exchange learning, and is also an attempt of interdisciplinary comprehensive learning.
5. Cooperative inquiry brings happiness to students' success.
? The choice of statistical chart? In teaching design and teaching, students are required to work in groups of four to investigate and understand various statistical charts applied in all walks of life and disciplines, and to investigate and collect the relevant data of one thing that interests you most in your life. Data must be collected through actual investigation to ensure the accuracy of data sources. Students collect data through newspapers, TV broadcasts and other media, or conduct surveys, interviews or obtain information on issues of interest to them. The collected statistical charts are rich and colorful, involving all walks of life. Let students understand the practical significance of statistical charts in social life, and cultivate the learning quality of being good at observing life and being willing to explore and study, and the consciousness of cooperation and communication with others.
Reflections on Mathematics Teaching and Research Activities Part II Reflections on Junior High School Mathematics Classroom Teaching Liu Yunqing's Thoughts on Studio Junior High School Mathematics Teaching
What is a really good class, how to teach it well, and constantly reflect on teaching in teaching practice and improve it in reflection are important prerequisites to solve the above problems.
First, through examples in life, explain the generation and development of some mathematical knowledge, let students feel that mathematics comes from life, let students really understand their own mathematical thinking methods, and cultivate their own mathematical ability is what we really want to do. And then what? Induction? It is a very important piece of mathematical thinking and mathematical ability. Operational conjecture? This form has played a very good role in cultivating students' inductive thinking and ability. For example, A: B: C = 7: 5: 3. We can set A = 7K, B = 5K and C = 3K, but students don't understand. Let A = 3K and C = 7K. Let me give you an example: father: brother: sister = 7: 5: 3, which is easy to understand.
Second, citing mathematical examples in life, creating situations, stimulating students' learning motivation, guiding students to have good interest and motivation in mathematics, and getting happiness and enjoyment in mathematics learning are our goals. Creating situations through practical problems in life can satisfy students' psychological needs for external novelty and make them feel curious and excited. At the same time, using practical examples in life can make abstract mathematical knowledge and students' thinking process concrete and visual, thus highlighting key points, breaking through difficulties and stimulating students' learning motivation and desire. For example, the inverse proportion function: 80 fish, 2 cats, 40, 4 cats per cat, 20, 8 cats per cat, 10 per cat, X cats eat, and Y is the inverse proportion function of X.
Thirdly, in teaching, we should use mathematical knowledge to explain some common phenomena of human beings and nature, so that students can feel the universality and value of mathematical application. Mathematics learning should be realistic, meaningful and challenging, which is conducive to students' active observation, experiment, guess, verification, reasoning and communication. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. Some examples related to mathematics in life are listed in the compilation of the new textbook. On this basis, teachers can further observe life and collect materials to provide students with some more interesting and valuable examples. Students can explain many phenomena in human social life and nature from the perspective of mathematics, which can make students realize the close relationship between mathematics and nature and human society and understand the value of mathematics, thus enhancing their understanding of mathematics and confidence in learning mathematics well.
Fourthly, in teaching, we should apply the knowledge of mathematics to solve practical problems in life, so that students can further realize the important role of mathematics in human social life, realize the joy of success and the value of mathematics, and understand that knowledge is not only obtained in class, but also obtained in colorful life and social practice, thus breaking the mathematical theorem without feelings, cold mathematical formulas and mathematical symbols without souls. Students can really realize that everyone should learn valuable mathematics and get the necessary mathematics.
Reflections on Mathematics Teaching and Research Activities Part III How does Professor Shulman, a teaching and research expert, view pck? Special integration of teachers' personal teaching experience, teachers' subject content knowledge and pedagogy? , including teachers' knowledge of learners, curriculum knowledge, teaching situation knowledge and teaching methods. How to organize and present specific unit teaching with the integration of professional subject knowledge and pedagogy subject knowledge to meet students' different interests and abilities? . Professor Grossman believes that pck consists of four parts:? Knowledge about the teaching purpose of the subject, students' understanding and misunderstanding of a certain topic, knowledge of courses and teaching materials, teaching strategies and presentation knowledge of specific topics. ? In other words, teachers' subject knowledge (pck) is the core knowledge of teachers' professional knowledge, which can best distinguish subject experts from education experts, and high-level teachers from low-level teachers. Developing subject teaching knowledge is the key to teachers' professional development.
? Curriculum and textbook knowledge? It is an important part of teachers' subject knowledge, and teachers should strive to develop their subject teaching knowledge about learning and using textbooks. As the users of teaching materials, teachers should first study and understand the text of teaching materials in depth. Interpretation? What are the textbooks compiled? Why is the textbook compiled like this? What are the implications for teaching? , so as to clearly think? Teach what? ; Then, the secondary development and selection of teaching materials can guide students to understand and apply mathematics knowledge in simple terms.
First of all, read through the textbook, sort out the basic structure, understand the intention of compiling the textbook, and clarify the basic orientation of teaching.
Understanding teaching materials is the basis of clarifying teaching difficulties, determining teaching objectives and designing teaching plans, and it is also the premise of high-quality teaching design and high-level classroom teaching. To learn a textbook, we can read it through first, grasp the textbook as a whole, understand the intention of compiling the textbook, and make clear the basic content and objectives of teaching. Specifically, you can read through the textbook from the following aspects.
1, depending on the problem.
Since the new round of curriculum reform, textbooks have focused on arousing mathematical problems through thematic situations and developing the teaching process. Only by fully understanding the design intention of the situation can we tap its teaching resources and add value to the problem situation.
(1) Understand the information and relationships presented in the problem situation. What are many problem situations in the new textbook? Scene? The rich connotation of presenting learning materials in a new form sometimes makes it difficult for students to understand and master them. Teachers should be good at analyzing the information contained in the theme situation, such as mathematical information and non-mathematical information, explicit information and implicit information, and study the relationship between information and information, so as to tap the rich learning resources contained in the theme situation of teaching materials.
(2) Understand the knowledge points reflected by the problem situation. The knowledge points of mathematics refer to concepts, formulas, properties, laws, laws and so on. When reading textbooks, we should read the basic knowledge points from the theme situation and think from many angles and aspects, such as the mathematical essence, expression form and formation process of knowledge points.
(3) Understand the unfolding process of the problem situation. The development process of problem situations in reading textbooks, such as what is used in a lot of content now? Create situations, build models, and explain applications? Through the process of textbook presentation, we can understand the knowledge structure of textbooks, think about the enlightenment to teaching methods by the way of textbook presentation, think about the relationship between the presentation structure of textbook content and the logical structure of knowledge, and think about why we should design such a learning process, so as to effectively guide students to experience the process of mathematical modeling in mathematical activities.
(4) Read the tips in the question situation and leave them blank. Textbooks often have ideas and methods worth reminding and marginal notes indicating key knowledge, such as? Observe the formula above. What did you find? The decimal point of quotient should be aligned with the decimal point of dividend to compare the size of surface? These tips or marginal notes provide ideas for students' thinking, point out learning difficulties and guide students to sum up conclusions, methods and laws. There are often some in textbooks? Leave blank? Leave some space for students to study and explore. These tips or? Leave blank? It is not only a guide for students' learning methods, but also a reminder for teachers to highlight key points and disperse difficulties, which needs teachers to ponder carefully.
2. Reading practice
Exercises are an important part of mathematics textbooks. The key to understanding the exercises in the textbook is to understand the content and level of the textbook. First of all, teachers should do all the exercises well, make clear the function and teaching requirements of each exercise, and understand the writing intention of the textbook. Secondly, make clear the levels and internal relations of practice. The exercises in textbooks can generally be divided into three categories. First, the basic questions are completely matched with what students have learned, which mainly plays a role in consolidating new knowledge; The second is variant questions, which change in information presentation and reverse thinking of questions, and promote students to deepen their knowledge understanding; Third, developmental issues, such as exploring practical issues, developing and improving issues, and thinking about developmental issues, can promote students' comprehensive and flexible application of knowledge. Teachers should be clear about the distribution of three types of exercises and their relationship when learning textbooks, such as understanding variant questions? Change? Where is the extension? Expansion? What is it? Wait. And thinking about the use mode and the allocation of class hours, so as to organize students to practice purposefully and orderly, consolidate, understand and internalize knowledge, and improve the effectiveness of practice. Finally, we must ponder the problem-solving strategies and mathematical thinking methods contained in the exercises, and see the learning function of the exercises through the exercise function of the exercises, so as to make full use of the exercises and give full play to their value.
Second, in-depth study, read through the textbook, understand the key and difficult points of the textbook, and grasp the core content of teaching.
After reading through the textbook and mastering the basic content and writing intention of the textbook, teachers should study the textbook in depth and implement it. Interrogation, correlation, multi-angle extension? Read, further understand the essence of mathematical knowledge, clarify the vertical and horizontal connection of knowledge, grasp the important and difficult points of knowledge, and grasp the core content of teaching.
1, carry? Questioning? Study and explore the mathematical essence of core knowledge, and master the implicit learning method and mathematical thinking method of teaching materials.
After reading through the textbook initially, teachers should focus on the core knowledge of the textbook? Questioning? Reading means asking yourself a few questions around the core knowledge of the textbook to promote the understanding of the mathematical nature of knowledge. For example, the connotation and extension of concepts, the establishment conditions and scope of application of formula rules, implicit learning methods and mathematical thinking methods in textbooks, etc.
2. implementation? Contact? Learning, learning textbooks from the perspective of holistic connection, and grasping the stage and continuity of knowledge.
Mathematics is a systematic and logical discipline. All parts of knowledge form a crisscross and closely related knowledge network, and the presentation of a large amount of knowledge is gradual and spiral. When learning textbooks, it is particularly important to read through the whole unit and learn the related units of the same knowledge, which is conducive to students' follow-up study and helps students improve their learning efficiency.
3. implementation? Multi-perspective? Learning is good at grasping teaching materials from the perspective of students and grasping the key and difficult points of teaching.
Teachers should learn to use for reference when studying textbooks in depth? Multi-perspective? Reading, not just from? The teacher taught? From the perspective of interpretation, but also from? Students study? From the perspective of interpretation, sometimes from? The writer made it up? From the perspective of reading, but also from the perspective of textbook comparison. ? Teaching? What is it for? Study? Teachers should be good at studying textbooks from the perspective of students. You can think about several issues.
(1) What is the existing cognitive basis of students? What is the cognitive level? By improving the teaching of this section, what aspects can students develop?
(2) Does the student have any life experience related to the knowledge in this section? What is the life experience of students?
(3) How difficult is it for students to learn this knowledge? What methods are used to help students understand?
(4) What questions do students have when reading this section? What can I learn from self-study? What can be learned from peer discussion? What needs the teacher's guidance or even explanation?
(5) What kind of situations do students like? What kind of learning style do students like? Studying from the perspective of students' learning can correctly grasp the realistic starting point of students, thus determining the starting point of teaching, sorting out the key points and difficulties of teaching and determining the basic strategies of teaching.