3 17, our group enjoyed more than 50 people came to Beijing all the way to Lawton, though it is warm spring season, but Beijing has received us with a deep chill these visitors from afar, and then we enjoyed two days of the cold chilly, enjoy in Beijing, we enjoyed eating trot tension and enjoy the stimulation of seats to seize the favorable lectures and enjoy the joy of singing all the way home. However, a careful inventory, so I am most excited about is the spirit with wonderful close and enjoy ... ... Beijing, in the end, what I enjoy? What has left me thinking?
enjoy the articles
a taste of the classroom teacher, to enjoy the
the demonstration activities, a total of eight young teachers doing a demonstration lesson, highlighting the country in Although they are young, but they are from the provinces of the teacher. So let us enjoy the true kung fu master of teaching, from a taste of each teacher's teaching style, deep teaching background, exquisite art of teaching.
1, cleverly cut.
new curriculum, we have been puzzled: how to create a reasonable solution to the problem situation? Please enjoy:
fragment of a, Hongtao teacher
students, March 12 What holiday? (Arbor Day) through tree planting, please raise their hands (really good, there are several) he did not have trees planted trees, but please read other people raise their hands (more than a few) students who had seen the tree, please raise their hands! Tree Planting for? (... ...) If we want to plant trees, what issues need to be considered? (... ...) In this class we're going to plant trees from a mathematical point of view of the problem. Then, to produce courseware for teachers to use the school playground scene map on the side of the playground to plant trees, (only one path, no other mathematical information) and then ask the question: How many tree seedlings need to be prepared? In this real situation, teachers lead students to think, to resolve the number of tree seedlings need to be prepared? What information is also a lack of context? (Planting distance, path length of the ... ...), so the teachers of the above information, with the students embarked on a journey to explore mathematics. We can see that Wang focus on the introduction of links for students to identify problems, such problems from the students, not only to mobilize students to explore interests, and mathematics so that students can view on life issues. A similar cut from real life by the students themselves and ask questions that Zhang Jianhong was also a teacher, Cui Jianzhe the teacher's Then the perspective of the students moved to the classroom by life. In short, these teachers appear to come in handy cut, but let us understand: the classroom, give students real, vivid, challenging learning materials, this situation is effective teaching situation.
fragment II, Wang Wensen teacher,
the teaching demonstration as teachers are teaching in different places, so most teachers are teaching and students before there is interaction, and natural cuts, Wang is uncharacteristically quiet rest he asked his students two minutes Then a simple question: Which number closest to 1? Which two numbers closest to 10? closest to 1000? which the product of two numbers is about 40? which the quotient of two numbers is about 6? how do you think? with What method of estimating? while brainstorming in students, teachers Summary: In fact, the charm lies not only in estimating solutions of these will be questions, but to learn to use. This introduces the application of estimates, and then presented through courseware, simulated scenes of life , so that students on the ground, using the existing experience of estimating experience to solve the problem of happiness, to explore more in the application of strategies and methods of estimation. He made us realize the problems starting point: Do not question the introduction of trade-off, In addition to the existing use of the student life experience, the use of existing knowledge and experience of students turn to explore new knowledge is also excellent, this is teaching us the champions of previous Review ------ bedding. Wei Fang also introduced similar the teacher's Review of the rotation and translation of knowledge, which is more important point is to enable students to understand the transformation strategy. and then the teachers of the phrase: Are you on the conversion of the strategy does not seem layer strangers feel? review have used transformation strategy to solve than what problem? by Tips from the field of space and graphics to the number and algebra field, giving students a huge space of thinking, to further understand the strategies and ideas into. In short, this cut seems bland, but also to We understand that: Mathematics United States on in its thinking, that leads to progressive layers of unknown mathematics classroom full of temptations, and again aroused the desire of students to explore such a simple cut a long absence, let us appreciate the real.
review whether the creation of situations or pave the way, I think the introduction of this class can observe with one word: ingenious! How they are achieving the same,UGG shoes, find a new growth point of knowledge.
2, effective inquiry
curriculum, the teachers all know that the formation of knowledge to enable students to experience the whole process of thinking though in place. But in practice when the results are always unsatisfactory, in the end than the classroom teacher where we clever? Please enjoy:
fragment of a: Hongtao teacher
path length of 100 meters, planted a tree every 5 meters, (both ends of the plant), the number of tree seedlings need to be prepared? Wang read the questions to guide students to understand the mathematical message, let students try to answer This question, and then communicate, arrived at a different solution: (1), 100 ÷ 5 = 20 (trees) (2), 100 ÷ 5 +1 = 21 (trees) (3), 100 ÷ 5 +2 = 22 (trees) then the teacher said: in the three solutions are 100 ÷ 5, then the 100 refers to what? 5 refers to what? results of 20 and mean what? 20 in the end is the interval of a few trees or tree? there is no better way to help us understand? So the introduction of drawing to help solve these problems.
fragment above, teachers can let students self-exploration, and give enough time and space for students to explore, so that teachers learn about children's foundation, but also understand the students practice good or bad, or is incorrect, then Teachers then use these programs generated resources, organization following the teaching, the teachers are willing to put the courage to put. Similarly Zhang Jianhong the teacher's model: the issue of such problems and differences in tree planting and painting music with straight strategy. Wang Lina teacher Enable students to design, how people at a glance which sites repeat ... ... all reflect these lessons so that children to try, and then set to teach teachers to learn.
fragment b, Wei Fang teacher's
independent research by students for students, they found: the approximate area of a circle → rectangular; cylinder approximate volume → the cuboid; parallel → rectangular area of four sides of the line; → parallelogram area of the triangle; decimal multiplication and division Law → integer multiplication and division; different denominator with the denominator of the fraction of fraction addition and subtraction → add and subtract, and so many of these problems. Then teachers joked: Excuse me, we have solved so many problems in the process of solving these problems have in common? (Take advantage of the conversion), how to transform it? (Do not know into the know, that is the unknown into the known), it seems that conversion is a common and important problem-solving strategies, usually used when the transformation strategy? (Complex problems, unknown problems)
more clips, teacher attention in the post-mining methods to explore the things behind it that allow students to explore law ---- ---- conversion strategies, and teachers can not solve the problem of the method as a way , but as a model. Mathematics classroom is, after the divergence of polymerization, and guide students from concrete to abstract, from the emotional to the rational, to enhance the content of thinking. Such examples include the previously mentioned estimates of teaching, students in the learning process, the formation of teachers to help students understand: Why should estimate how estimates (method), flexible application ----- how to use estimates (which is estimated big or small assessment) that a series of strategies and ideas, and not merely to let students use it as a simple calculation. Cui Jianzhe the teacher's ... ... The real lesson we feel: In addition to the students on the main classroom, teachers also have a dominant place, what is What is the role of teachers guide? I believe teachers can see reflected and see the whole picture.
effective inquiry, requires teachers to give students a platform for students to put themselves out there is something to Liang Liang, effective inquiry, students need teachers to the process of drying, to help students to carry things tummy together to form a more rational Summary and Conclusion, continued to form the basis of mathematical thinking ------ strategies.
3, a selection of applications
students methods and strategies for solving problems after the how to consolidate? What training? How to practice? We do!
tree planting problems, teachers provided the following design: the pillars of school buildings problems (feedback exercises), the problem with the tree planting problems similar place? (Post the equivalent of the tree), and if so wish, what life there is such a phenomenon? (... ...) We have to solve several of these issues: street problems, consolidation of training; planting trees seek to tell the distance problem, variant training; bell problem, (development training). In fact, Wang is not only to demonstrate in practice that all teachers are very hard on the selection of topics of great value, and be more profound when the practice of problem solving to enable students to use the newly established mathematical model to solve other problems, and the breakthrough model, variant applications, achieve replicability, the purpose of analogy.
Another example: Wang Wensen final design of the teacher's estimate of such exercises: use estimation methods to solve the following problem:
Commodity Market stores 198 yuan per pair
318 per pair
9 6 discount sales discount sales If teachers want to buy a pair of
the same brand of shoes, where to buy? When students solve problems big and assessment estimated small as two different methods but the results, the teacher said, since the same price, whatever to a can, you say? This design left the subject of thinking of the students time and space, to give room for further development of students so that students feel the estimate is followed by further thought. As the saying goes: into the classroom with a question mark, question mark to leave with more classes, the pace will continue to extend the students to explore.
Second, the classroom experience is not perfect, enjoy the
In fact, teaching is always a regret that the art teacher though, but they left the classroom more or less regret.
Hongtao teacher's class, when he mentioned that there is no good way to know the number of 20 tree planting interval in the end, the students can know that using your fingers, but he ignored the formation of this valuable class , the students of the Si Lula back to the default drawing method, point out the wonderful classroom. We must ask: If a teacher has a strong student body awareness, focused attention to the classroom can not generate the resources? ------ One of the classroom teaching ideas generated concern.
Zhang Jianhong teacher's class, students draw upon a variety of solutions to the problem, when optimized, the teacher saying: I love × species divergence perspective out of the teachers thought only after aggregation, in fact, We want to diversify, but also optimized, but more left to give the children more opportunities for reflection in practice. ------ The second method of teaching thought the pros and cons vary, polymerization is not necessarily unique.
Also in this lesson, the teacher of the scenes from the introduction of the Olympic Games opening ceremony, introducing their favorite characters, the number of Chinese characters, to the Woodland meaning of the word; and then to introduce students to the purist with a mountain stream the Go information. Another lesson for the students play music animation articles This multidisciplinary integration of the classroom not only doubt: how to grasp the subject of a degree of integration? We want to integrate, but not dilute the forty minutes, mathematical literacy training, not waste their fields, kinds of other people's land, and give them work, but it is no benefit. Third ------ integrated teaching ideas for math content services.
Cui Jianzhe teacher's class, although tourism in order to solve mathematical problems, but the teacher leads from the creation of scenarios to mathematical problems, took almost 6 minutes of time, referred to the same question three times, after the students answered correctly Also ask, the results Tuotang 12 minutes, and how control to ensure that classroom time? How to allow students quick access to mathematics learning? The fourth ----- teaching ideas to reduce non-mathematical study time and reduce the mechanical repetition of the time. Qin Xin
class teacher is the time to observe the popular class, because in her problem-solving coaching ------ multiplicative word problems, still clinging to the old materials step by step guide, emphasizing the analysis of step, a solid approach, the classroom teacher pulling too much, a question and answer, 45-minute class, the teacher raised 139 questions per minute of 3.1 issues. What children think about space? The fourth ----- teaching ideas for teachers to manage their mouth.
teachers design teaching in addition to density, class students to think not achieve the desired effect is eager to share the perspective of teachers and students ---- perspective to achieve effective integration; class summary procedures , was concerned only reflect on the learning process, finishing ------ recalled the importance of promoting students to deeper thought is more important ... ...
Third, listen to expert comments and enjoy the
Bo Jiming restore the teacher problem, from small school next issue to come and go cut the line so that children can think of life issues such as wind wind reciprocal feelings, to calculate simple addition and subtraction multiplication and division leads to reduction of the reciprocal issues, to the letter, application, living in sub-sugar problems, library problems, the kind of fill the gap in class to admire all the teachers here ----- all style, worthy of experts. But when she secretly lecture Secret have their students eyed, half of them can not learn, she reflect on their own design, the big step into each issue of small steps, and each section to help students learn to bundling of knowledge, that sort. Let us understand her frankly: Students can not learn, a teacher because, as she put it: more than to find a successful way to find little reason for the failure. In order to mature, close to perfect. Xu Bin, a problem starting from the teacher, changing a series of problems in the classroom, teaching reflects no trace, great with marks. Tells his simple words: to seize the most essential things between knowledge, knowledge is the upper of the things that make the book read more thinner. Li strongly in the teacher's comments ------ Teachers must be willing to retire; Wu Zhengxian ------ teacher reviews the educational value of solving the problem is to allow students to become confident problem solvers; Cuihai Jiang in the teacher's comments - ----- to give the students blank, leaving room for the development of students. Reflections on articles
trip to Beijing to enjoy the harvest of results, could not help but reflect on our teaching: We introduce ------
situation or to go through the motions, do not fully understand and guide the students to find mathematics information, or not the reality of books from the students only use, never creative use of materials, Lenovo plans to start a topic or let it out after a long math problem, or to simply get rid of thematic maps, and replaced the traditional text application questions for students to quickly answer, save
explore the link ------ We often think that students can not learn, simply to listen to you I say, do not waste time; algorithm diverse, we feel that if students do not grasp an algorithm, multi-out time for repeated practice to the benefit, and therefore not willing to children to use their brains to find ways, a waste of breath to the exchange; book, the conclusion is readily available, tell the students to understand, but also what to explore? When the students hands-on, classroom disorder, lost the quiet classroom, or avoid the bar; good news is that some teachers give students enough time and space to explore, but the exchange is only the sake of discussion, look for the questions, this one method, do not know the way there on strategy, then the mathematical model machinery. -------
book to consolidate what part, I practice what, never study materials, not integration exercises, regardless of level, not the extent of student learning for its own design practice.
the last word problems, solve the problem today, in the end a kind of different? I had not learned to find information, think over, how do we solve problems for students to learn a delicious and nutritious mathematical knowledge? How to make lessons From a concept,UGG boots, a formula, an algorithm to see the charm of the whole subject. Think of these, I opened a new one: learning articles, I have recently learned will be extracted bit by bit, and perhaps bring some help to give you, cause more people to solve the problem, more thoughts on teaching.
learning is
Related links: problem solving and the educational value of content
Why should be changed to Why this arrangement? Its educational value is it? Application of the past problems of teaching and problem-solving today What happened?
i
But with time, more and more through the extensive research found that there are many problems in the practical level:
1. Application questions should not be used: the process of teaching the application of title has been immobilized, modeling, application problems in itself and does not reflect the child's life experience, can not reflect some of the important themes of social reality. Anyway, word problems away from the student life experience;
2. Solving Problems single model: the process of teaching word problems into a set of item types, comparing mechanical and rigid;
3. Fixed problem solving answer only: not too much given the conditions, the only definitive conclusion conclusion. In fact the real problem-solving process, as long as a real problem,cheap UGG boots, students are able to solve problems with different ideas and different answers.
4. The presentation of a single issue: the presentation of word problems are relatively simple, with emphasis on the text word problems. Even in education and teaching practice, the formation of a chart with symbols to reflect the thinking process is a relatively low-level approach that can solve the system of a text word problems seems to be a more advanced form. This presentation took the form of word problems restricted to the basic text-level word problems.
for the courses should be pursued, so to solve the problem. The international community is usually called problem solving problem-solving. According to the habit of thinking of our country or the manner of expression, we define it to solve the problem. Abandon the original problem of teaching word problems, inherited a good side.
ii solve the problem with the traditional distinction between the application of title
1. attention to the process of teaching: more emphasis on word problems answer as soon as possible; and a process to solve problems is stressed, is to seek ways and means to solve the problem process. Emphasis on problem-solving process to find solutions to problems and strategies to themselves than to get a more important conclusion.
2. Dependent not only a knowledge point: The question is often combined with the knowledge of a specific point, for example, say today the addition,
is the addition word problems, and tomorrow is the multiplication word problems learning multiplication, word problems are often attached to a certain point in the context of knowledge;
to solve the problem is to emphasize a specific real situation, it is more emphasis on integrated problem-solving process. For example, after the addition finished today, problem-solving scenarios it may not be limited to use addition, subtraction is not limited to use it to mobilize the students have the knowledge to solve problems. It is not only dependent on a certain knowledge point.
3. Analyze specific issues: The problem of teaching the application questions go into class, a class of problems to think about focus, emphasis on speed and skill; and problem-solving emphasis is to analyze specific issues, in other words, in the context of how a new apply the knowledge to solve problems, make the problem more challenging, a problem may be followed by a question. The specific situations faced by different students, the problem is different, students analyze specific issues. To find a solution to this problem, it is more challenging, more innovative.
4. Openness and diversity issues: the application of emphasis on breadth, from the life to come, starting from the existing experience of children, from the current technology, the process of social development, identify problems and refine Wen Ti. The problem itself is its openness and diversity of a very important feature. iii
the educational value of problem-solving
allows students to experience mathematics through problem solving real life with a wide range of human, close and natural connection, to solve the problem by changing the way students learn, according to the specific problem situation, to find strategies for solving problems; in to think independently on the basis of trying to work with others. The core is to promote change in the way students learn. Failed to solve the problem in the following has a positive educational value:
1. Help develop awareness of student problems;
2. Learning through problem solving, access to mathematical knowledge to solve problems using basic strategy;
3. Teaching through problem-solving, so students have access to a wealth of experience in mathematical activities, a wealth of experience will help students understand mathematics, to deepen mathematical knowledge and understanding of the nature of thinking;
4. Teaching through problem-solving, help students understand mathematics in the process of abstraction and a wide range of applications, development of abstract mathematical ability of students;
5. In the process of teaching problem solving, critical thinking, cooperation between students, mathematical communication and expression ... ... the process is very rich in educational value;
In addition, through problem-solving teaching can make students feel that the application of mathematics and value, to arouse the students desire for knowledge, to enhance confidence in learning mathematics.
iv diversity of students in problem-solving strategies
since the new curriculum reform, students in solving problems which appear promising change?
Xuanwu District, Beijing in July 2005 Department of the region for students of all ability to do a test search, the theme is to solve problems. Curriculum reform, the The most fundamental is reflected in the student body changes. Test check in the curriculum and grade were compared with non-curriculum grades, curriculum reform, students are more active thinking, problem-solving approaches more diverse. In other words, their strategy is the strategy level and a stronger sense, this method does not work, he would use other methods to solve.
2008 年 12 月 13 日 -15 days, I have participated in Tai'an, Shandong Province at the Primary Mathematics other expert's report has benefited me quite good. The event is a learning experience.
one, with questions to
before departure, for the solution to the problem of teaching, but also filled with some doubts in mind, we can say, I took my problem to attend the seminar.
My problems are: the creation of what the situation is the most reasonable? Faced with the new curriculum reform, how to handle the relationship between inheritance and innovation, not only train students to solve problems, but also comply with the new curriculum ideas and requests? Analysis, synthesis method and some analysis of the method also used word problems without the teacher say? Line graphs the number of relations and knowledge but also not to speak? Intermediate analysis of the problems mentioned methods, but also do not teach students?
Similarly, the students solve the problem, there are some troubles: A problem I encountered on the halo, do not know where to think about it, the original problem when I do see to see
Second, the full harvest go
by participating in the activities, experts from the theoretical level, the teacher made a very good teaching practice with the interpretation, I pointed out the direction of teaching, so my heart into a question mark exclamation point.
1, leading experts, the report by listening to experts, that I know: (1) To help students Dudong questions, to read three times, over time, find out what it was; Second Bian Reading, screening to capture useful mathematical information between who and who has anything to do. Read three times and told us to resolve any problems. So that only we understand the problem, the problem can be resolved better, reflect on their teaching of the past, when the present example, the used to enable students to read it together again, eager to answer students formulation; also sometimes used to allow students told us briefly answer the question what information, what questions should we ask, and then asked what method of calculation, instead of questions, over time, the students solve the problem, often eager to out-style answers, did not develop the habit of title, are often susceptible to problems caused by ambiguous formulation answer wrong direction on how to analyze the problem is unknown. (2) the value of solving the problem than just access to the solution of specific problems, more students in solving problems is obtained in the course development. One important point is to enable students to learn some basic strategies to solve problems, to experience the diversity of problem-solving strategies, and on this basis in some form their own problem-solving strategies, such as the drawing of the strategy (line graph, tree, set chart, diagram), the list of policy strategies to try to simulate the operation strategy, backstepping strategy, a simplified strategy,UGG boots clearance, reasoning strategies, before I know very little about these strategies, that one problem was solved on the bin down, and ignored method of infiltration. (3) to solve practical problems in the process of transformation to highlight two. The first transformation is from the real problems chaotic to obtain useful information, an abstract mathematical problem into the second transformation is the quantitative relationship between them were analyzed, using mathematical methods to solve or approximate solution, and tested in practice. In teaching, I am the second transformation, often in passing, it is extremely thin, the analysis of the relationship between the number not in place. (4) to good picture of the text word problems situational questions appropriate to the transition, first grade learn some pictures situational questions, you can trigger the interest of students, prompting them to enter the immersive role to understanding the problem. Entering the second grade should be gradual emergence of the mixed graph, or directly with the text description of the application questions in order to develop their abstraction ability. In contrast to my teaching, to situations and scenarios, creating the situation
2, approached the teacher if the expert's guide to clarify my thinking, understanding, improved my theoretical knowledge, then bend the teacher's practice I close a taste of First talk about the symplectic symplectic teach principals around the teacher, the teacher's lesson Pan cognition according to law students continue to cause problems for students to promote the teaching process, according to the laws of the student's cognitive understanding of the carrier to students the way for students to generate and solve problems. The introduction of new courses, it is simple to provide an effective teacher, This is the beginning of wisdom. Verification from the guess, Pan teacher let the students themselves to boldly explore and experience the knowledge of the formation. You have to admire the true teacher Pan, plain, solid classroom teaching characteristics. Pan on the course in the analysis of the teacher, said: material is placed with the matches, because it takes time to put the match too long, and there are limitations (the children think of broken matches, and are not accurate.) So the teacher thought Pan with wire to create a scene. And meals at school the teacher asked the next, the result is the teacher's answer to the teacher Pan. And it was. Pan teacher said he never has the default class, and once he was going to lecture, the results have talked about the teacher ahead of time, teachers would rather not speak Pan, nor speak a default class. This matter, I have been a greater shock, and now many teachers to a preset open class too. Is not a departure from the child's starting point is entirely in the show. As a result, I thought the Is the way teachers are good at Pan psychology students grasp the pulse of humor with passion, care of the students added curiosity and desire to explore. Then there are the first experiments in Jiangsu Suzhou Industrial Park, Xu Bin, teachers teach elementary school Xu, quick thinking, concise language, attention to the development of the child's thinking ability. Xu gave the second grade teacher told the children, He sought to teaching in the classroom
3, professional development through the learning, improved thinking and understanding, broaden the educational perspective, the next step is based on class, bending practice, put into action, and truly learn new ideas, new ideas, new methods applied to their classroom teaching to enhance classroom teaching, and promote professional growth, making an ideal, thoughtful and influential teachers.
the dead of night, hammering the face of the computer, I suddenly think: can the psychological feelings of their own people looked into the benefit of text, need time, need to think, requires insight, which in itself is a species beyond the limited time, limited capacity, I may not get read, people to meet; when I was going to end this feeling, I was still thinking: grade teacher can give us, far from ; word can covers, but also far more than I have mentioned plain win; Next, we can do, to what extent, this is a challenge. But I believe that love of learning and thinking people will succeed, because you pay more than others!, Decorated in the text after this sentence, as mutual encouragement!
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