Teacher Lin Bizhen is a senior teacher, a provincial super teacher and a provincial famous teacher ... She has many titles and has been doing research on "building a classroom full of mathematical ideas".
"Classroom full of mathematical ideas" refers to a classroom that guides students to feel, understand and apply mathematical ideas in a timely, scientific and effective manner in primary school mathematics classroom teaching. This kind of classroom helps students to understand the common sense and laws of mathematics learning by guiding them to understand mathematical thoughts, accumulating experience in activities, and learning to "see with mathematical eyes", "think with mathematical thinking" and "speak with mathematical language". This kind of classroom is not only conducive to cultivating students' mathematical ability, innovative spirit and practical ability, but also can greatly improve the effect of primary school mathematics classroom teaching and truly implement the goal of cultivating mathematics core literacy. This kind of mathematical thought felt in the classroom can affect students' life, really play a long-term role in their future study, life and work, and lay a solid foundation for their lifelong learning and development.
Classroom full of mathematical thoughts is the crystallization of her research for so many years. Many years ago, she put forward the triple realm of teaching, which influenced a group of ethnic minorities. In the first realm of teaching, teachers give students water directly and students gain knowledge; In the second realm of teaching, teachers lead students to find water and students get methods; The third realm of teaching is that teachers guide students from mathematical activities to valuable mathematical thinking and acquire basic mathematical ideas, which is the soul of mathematics teaching.
Teacher Lin has studied the subject for so many years, which fits the concept of the new curriculum standard very well. Knowing that she wants to share this topic, I have more expectations for this lecture.
Teacher Lin made a simple interpretation of the curriculum standards, focusing on the core literacy in the standards. Three will correspond to abstraction, reasoning and modeling. This is what the classroom full of mathematical thoughts pursues.
What kind of classroom is full of mathematical ideas? Teacher Lin didn't talk about this issue, but directly put forward a case of classroom teaching-Mathematical Thinking, the second volume of the sixth grade. Let teachers intuitively feel the classroom full of mathematical ideas.
In this class, Mr. Lin guided students to solve mathematical problems by using the mathematical thought of simplifying the complex through three questions.
With the help of lesson examples, Mr. Lin showed and expounded the "classroom full of mathematical thoughts", that is, teachers combined with the teaching of mathematical textbooks to dig out the mathematical thoughts hidden behind mathematical knowledge, guide students to feel and understand mathematical thoughts properly, scientifically and timely, and make students consciously use mathematical thoughts to solve problems when they encounter new knowledge or problems. This kind of classroom plays an important role in improving learning efficiency, improving students' ability and cultivating subject literacy.
What mathematical thinking methods are suitable for infiltration in primary school mathematics teaching? Teacher Lin shared the following:
Combination of numbers and shapes, set correspondence, classification, symbolization-abstraction, induction, analogy, substitution (substitution), transformation and reduction, limit-reasoning, equation, function, optimization, randomness, statistical thought-modeling.
Combined with the case, the author focuses on sharing the idea of combining numbers with shapes and the idea of transformation.
The combination of numbers and shapes is a thinking strategy that combines numbers and shapes to analyze and solve problems. Numbers and shapes are two main objects of mathematical research. Numbers are inseparable from shapes, and shapes are inseparable from numbers. On the one hand, abstract mathematical concepts and complex quantitative relations are visualized, visualized and simplified through graphics. On the other hand, complex shapes can be expressed by simple quantitative relations.
Regarding the idea of the combination of numbers and shapes, Hua's words gave a high degree of generalization: "A few numbers are not very intuitive, and a few numbers are difficult to be nuanced. The combination of numbers and shapes is good in all aspects and everything is separated. "
Conversion and transformation are common thinking methods to solve mathematical problems. It refers to developing rich associations on the basis of careful observation when facing new problems. In order to arouse the memory of old knowledge, open the door of thinking and successfully use old knowledge and experience to deal with new problems.
There are several types of transformation and transformation ideas:
Vertical regression: the new problems we face are transformed into the old problems that have been solved, and the new problems will be solved after the old problems are solved.
Horizontal regression: turn complex and difficult problems into familiar and simple problems to deal with.
Homologous regression: the new problem is transformed into one or several simple subproblems, and the new problem is also solved by solving subproblems.
Reverse regression: when it is difficult or complicated to think according to the habitual way of thinking, start thinking from the other side of the problem. (reversal, disproof, etc. )
Teacher Lin is very good at deepening students' consciousness by means of material guidance. Like this lecture, she also used some cases to make students feel intuitively, stimulate thinking, and make appropriate explanations to refine and deepen the teaching consciousness of core literacy. From the details of sporadic teaching fragments shared by teacher Lin, we can feel the humor and wisdom of teacher Lin's speech, and we can feel that she inspires students' interest and thinking through language.
I like this case of grounding gas with high theoretical sharing.
A little wanted to think:
The interactive questions set by teacher Lin in sharing are also very good. It just didn't have a good interactive effect. The teachers attending the lectures are basically teachers of the provincial minority associations, and most of them are excellent and researched math teachers in various counties and cities in Fujian Province. Everyone should think and be moved by her problem. It is also a great advantage to be able to communicate directly with teacher Lin face to face. But no one dared to seize such a good opportunity, and no one seized it.
The day before, Mr. You's lecture also designed interactive questions, and everyone's feedback was very enthusiastic and enthusiastic. Moreover, as can be seen from your answers, your understanding of the new curriculum standards and your research on teaching are still in place.
Teacher Lin's interaction is actually more thoughtful and open, and teachers who can participate in the interaction should gain more. What caused such a good welfare that no one took the initiative? What can be done to make this interaction more effective?
Our open class is arranged from 7 pm to 8 pm, during which many teachers are not idle. Some teachers in class are still busy with housework, some may still be eating, and some may be on the way for a walk. Concentration and thinking are not all bows. In the face of relatively simple interaction problems, everyone can participate in time. But in the face of more complicated problems, more time and energy are needed.
The interaction of Lianmai needs an environment and some technical support, as well as some psychological and hardware support.
This kind of interactive problem requires deep participation, can we ask teachers for interaction through the community in advance?
Like students' * * * study, if there are some preliminary preparations, their thinking will be deeper, their thinking and control will be stronger, and their initiative will be better.
Be a math teacher who is good at observing and thinking, be a math teacher who is good at inspiring students to think, and build a thoughtful math classroom. We are on our way.