The main contents of mathematics in the first semester of senior one are: the quality of numbers, the introduction of counting and four operations. Counting (in kind) is the basis to help children build a sense of number. The quality of numbers and the four operations, in addition to the regular learning purpose, are all metaphors of the profound philosophical and moral connotations behind mathematics through stories and pictures.
There were two classes last semester. In the first class, mathematics planted the seeds of mathematical growth (the seeds of world outlook, morality and spiritual world) in children's hearts through learning and experiencing the quality of numbers. In the second section of mathematics, children can know the abstract+-×÷ operation through stories, and also experience the spiritual connotation behind addition, subtraction, multiplication and division.
When planning, both math parts are placed in four natural weeks. However, due to the influence of holidays, smog and training, the actual teaching days are only about 15 days, so it is actually equivalent to two 3-week math festivals, which also brings no small challenge and appropriately adjusts the teaching expectations.
Because on the one hand, some representative lines (such as circles, polygons, etc. ) introduce numbers into quality teaching, on the other hand, some Chinese characters (such as one, two, three ... days, days, months, etc. ) will naturally spread on the quality teaching of numbers. Therefore, I arranged the first math class after the online painting class and before the Chinese class.
The basic teaching objectives of this part include:
In the above teaching objectives, I did not include the reorganization of numbers. Because the first section focuses on the transmission of "quality", it is easy to dilute the feeling of "quality" and increase more "quantity" under the limited time. The third goal can actually be observed in the teaching process.
This period is called 4 weeks, but actually there are only 15 working days (equivalent to normal 3 weeks), according to the prior arrangement and plan. Completed the introduction of digital literacy from 1 to 10 (the story of 12 has been paved), which runs through digital literacy, physics, rhythm counting and regression in daily songs, rhythms and activities. All these activities will continue to cross and continue in the language section to some extent.
In terms of the quality of numbers, all numbers are introduced in the form of stories (the first day: introduction). After a night's sleep, we review and practice related pictures in the form of pearls, questions and answers, solitaire performances and other words, discuss the form or rhythm of numbers in life and nature, and practice through painting and activities. (the second day: review and artistic practice), and the work in the main textbook (the third day: work). Of course, this is a general rhythm, and there will still be exploration and adjustment in many cases.
The basic form of the main teaching materials is that one page is used to describe pictures with digital quality in nature, and the other page is used to draw related geometric figures. One is the training of pictures and sensibility, and the other is the training of cognition and flexible thinking through non-intellectual ways. With the previous drawing board to learn the accumulation of straight lines and curves, children can basically draw from circles to polygons. The result of work is secondary, and the process of children's work is very important: whether children have enough concentration to listen and work, whether they have enough self-confidence and good self-expectation, and whether they have enough toughness and perseverance to practice and improve constantly. Through these observations, I benefited a lot.
In order to enhance children's sense of counting, we distribute "gems" to children as one of the props for children's physical counting. Children love and cherish their gems very much, put them in jewelry bags, and take them out from time to time to count or put them on the table. In addition to counting gems, physical counting is also integrated into daily activities, including counting fruits or nuts, counting major textbooks of each group, counting wet colored paper, counting color plates, counting the number of leapfrog and so on. In the morning circle, we added more counting-related ballads, clapping ballads, rhythm and finger ballads, and also grew and expanded on the basis of the original rhythm, incorporating more rhythm counting elements.
I integrated all the stories into the background of a medieval kingdom, so in the end, by reviewing these stories, we drew the badges (shield styles) of all the important families in this kingdom.
The initial basic teaching objectives of the second mathematics part are as follows:
Among them, the first four are "knowledge and skill goals", the fifth is "emotional attitude and values goals", and the last is "process and method goals". In fact, I deleted the fourth item "Introduction to understanding numbers", which is still too early. At present, I put it in the process of experience, not to mention the level of consciousness. After deletion, it became:
Some people say that the boundaries of the plates in the lower grades don't need to be too clear, while others advocate that the plates completely "let them sleep" ("make mathematics meaningful") in the interval. Judging from the current situation of myself and my children, on the whole, the plates overlap and transition, and some practical classes and morning circle activities cross-infiltrate.
There is still a remaining task in the second section, which is to complete the digital quality of 1 1, 12. It is also suggested that we can talk about 1 ~ 10 from last semester, and talk about 12 next semester or the second day of junior high school. Personally, it took me a week to transition from Chinese and complete the digital quality. By reviewing and summarizing the nourishing story, I finished the main textbook of the 20th Chinese character, and then gradually changed from drawing, reviewing Arabic numerals and Roman numerals, and adjusting the content proportion of the morning circle to the feeling of mathematics. After the first week, children can't wait to learn addition, subtraction, multiplication and division.
Compared with the first math class, the second math class introduces four operations, but the children are still in the experience stage. If the central task of the last stage is to let children establish the essential connection with mathematics through numbers, then this stage is the initial experience of mathematical expression. Because the leap from physical objects to abstract expressions (arithmetic expressions) is still a big leap for children.
We introduced four gentlemen through The Story of the Master in Maxim's Kingdom. They all have different shapes, personalities and lifestyles, echoing the spiritual connotation behind addition, subtraction, multiplication and division. And use multi-dimensional dictation, physical counting, rhythm counting, multiple counting (2, 5, 3), physical operation, pictures and stories, classroom performance, group activities to let children experience the algorithm and reasoning behind the operation. Through the actual observation of children's state, the quantity and method of intelligence teaching content are adjusted, and only spiral cognition is used to help children consolidate their experience.
The time spent around is roughly as follows:
After reorganizing 7 in the second week, I felt that the knowledge content was a little too fast. In the third week, I resumed the decomposition of numbers, but different from the first round, this round increased the expression of formulas. I intend to deepen in the fourth week, but because of the smog and training, the second round of study only reached 5. But what makes me happy is that in the daily summary and thank-you circle, a child will say that he has learned addition and subtraction ... I believe this is really inhalation and understanding, not technical rote learning.
In the teaching process, constantly remind yourself to think about the problem of "integration of knowledge and practice", and carry out an appropriate degree of practical exploration according to the class situation.
Intuition and generation are the key words of mathematics learning in the whole middle and lower grades. From grade one to grade five, mathematics is developed as an activity closely related to children's life process. It is a development process from the inside out, and concepts and methods are established in the form of pictures. For children, they receive pictures through activities and imitation, then internalize, recall and generate them, and then form usable concepts.
The first section of mathematics, through learning and experiencing the quality of numbers, allows children to plant the seeds of mathematical growth (the seeds of world outlook, morality and spiritual world). In the second section of mathematics, four operations are introduced through the picture of the story, so that children can know the abstract operation symbol+-××× = and experience the spiritual connotation behind addition, subtraction, multiplication and division: every operation has its bright side: diligent collection of addition, willingness to share the wisdom and richness of subtraction and multiplication, and fairness and justice of division. They complement each other and cooperate with each other to become a beautiful ecology. This way may seem ridiculous to adults, but it is a way that children can understand and go deep into their hearts.
The mathematical trauma caused by "too much too fast" is a common problem in mathematics in traditional mainstream education. Mathematics learning is not only the accumulation and memory of technology, but also the content. Some very interesting aspects of mathematics are often overlooked because they are too focused on mastering a long list of skills. Especially when children are too young, too much emphasis on these skills will often lead them to lose sight of the overall situation, understand the concepts behind these problem-solving steps, and lose (or fail to cultivate) their sense of numbers. Math is traumatized as follows: no matter whether your math scores are good or not, you will admit in your heart that you are not good at math and don't like it.
The best way is to step by step in the early stage of school education to ensure that all aspects of the content are covered, so that all students can deeply absorb the content brought to them. After laying this solid foundation, children can really take off in junior and senior high schools.
Of course, we should pay special attention to the phenomenon of mathematics deprivation in some Waldorf schools, that is, we ignore mathematics learning too lightly. Learning requires necessary pressure and effort. There is a vast study area between the comfort zone and the panic zone. Through the teaching activities of rhythm and breathing, we can take into account the development of different children, including cognition and memory.
As a Waldorf school, we should guard against right (mathematical deprivation), but in the context of China, we should mainly guard against left (mathematical trauma). Especially in the lower grades, it is better to have the hatred of leaving pearls than the sadness of trampling. If you haven't learned or mastered it yet, it's not a big problem. If you get old, it's easy to make up for it. But if you are afraid now and lose confidence, it will be difficult to make up for it later. The first grade should be calm and simple, and all children's activities are learning. We see that during the free practice time, children will play games spontaneously and interestingly, and practice with objects and teaching AIDS, which is great. Interest is the best teacher. What I can do is to guide and stimulate children's interest in learning and exploring, and cooperate with parents to remove obstacles to their development.
It may be because of the "mathematical trauma" of the children's parents in those years. Generally speaking, parents will pay more attention to mathematics teaching. Of course, the comparative pressure from public schools sometimes intensifies parents' doubts and worries about Waldorf's "emphasizing art over academics".
This is a good opportunity to establish a healthy, trusting and cooperative parent-teacher relationship. Through parent-teacher conferences, semester interviews, parent-teacher conferences, section reports, etc. , you can establish a two-way interaction mode with parents. On the one hand, it conveys Waldorf's ideas and practice in mathematics teaching, on the other hand, it accumulates trust and builds communication channels.
Because in the process of parents' own education, there is no "quantitative" learning. So many parents are actually confused about the quality of numbers they have studied for several weeks. If this doubt is not resolved in time, it will accumulate into "questioning emotions" and erode the trust foundation of the pro-teacher. Therefore, it is necessary to communicate this information with parents from the beginning. The following is a summary of parent communication in the first section:
Parents' "problems" that are easy to appear during the second quarter are: eager to accept children's mathematics learning results. You will feel anxious when you find that your child does not meet your expectations. Therefore, it is also necessary to communicate in time, so that parents can understand the intention and laws of teaching and reduce the interference to children's teaching.
Of course, how to use the way of thinking or feeling when parents communicate is a process that needs constant exploration. "The beauty of operation lies in one heart."