This makes me have to reflect on my usual teaching activities: every time I ask students to listen, some students don't fully understand the solution to the problem, or understand it, but they don't do it once, and they forget it after a long time. Just like a swimming coach teaching a teacher to swim on the shore, no matter how well he teaches swimming movements and postures, you can't learn to swim without swimming in the swimming pool and drinking a few mouthfuls of water. Everyone understands this truth, but it is so difficult to really implement it in the teacher's classroom. ...
With the gradual deepening of the learning concept of the new curriculum reform, I realize more and more that mathematics is made, and only by letting students do mathematics can they learn mathematics well. The history of mathematical development tells us that the formation and development of every important mathematical concept contains rich experience, such as the discovery of irrational numbers, the proof of Pythagorean theorem and the establishment of plane rectangular coordinate system. All of them are full of deep feelings of human exploration, and people need to rely on existing knowledge and experience to observe, practice, summarize, guess and other rational thinking processes, as well as the courage to pursue the truth unremittingly. That is to say, in the "cold beauty" of formal mathematics, there is a "fiery thinking" of human beings, which has rich life significance in its formation. Then, in mathematics teaching, how to guide students to do and learn mathematics?
First, create a good problem situation, so that students can walk into the problem
Problems are the core of mathematical activities. The formation process of mathematical definition theorems and formulas is transformed into problems with life significance, forming problem situations, so that students can do mathematics and learn mathematics with questions. Therefore, in teaching, the process of knowledge should be transformed into a series of inquiry questions as much as possible, so that relevant materials can truly become the object of students' thinking and mathematics learning can become the inherent needs of students.
Second, guide students to re-create mathematics
Friedenthal, a famous Dutch mathematician, believes that one of the principles of mathematics teaching is the "re-creation" of mathematics. He believes that students and mathematicians should be treated equally and given the same rights, that is, to learn mathematics through re-creation, rather than following and imitating. The theory of "re-creation" holds that teachers don't have to instill various concepts, laws, properties and axioms into students, but should create suitable conditions for students to discover their own mathematical knowledge in practice, just as mathematicians discovered these properties at that time.
For example, when talking about parallelograms in the past, first demonstrate some parallelograms, so that students can master what a parallelogram is, just like telling children what a desk and chair is, and there is no mystery. But now the usual process is that the teacher gives the formal definition of parallelogram, so he skips another hurdle, and students are deprived of the opportunity to create the definition, or even worse, because at this stage, students can't understand the formal definition at all, let alone the purpose and significance of the formal definition. What would a student do if he was allowed to recreate geometry? Give him some parallelograms, and he will find many * * * properties, such as: the opposite sides are parallel, the diagonals are equal, the adjacent angles are complementary, the diagonals are equally divided, the parallelogram can be embedded in a plane, and so on ... Then he will find that one property can be derived from other properties. Maybe different students will choose different basic properties. In this way, students master the basic meaning of formal definition, its relativity and so on ... through this process, students learn to define this mathematical activity instead of imposing the definition on him.
When I talk about the nature of parallelogram, let the students make their own models of parallelogram. Group communication in class: measure the opposite side first and then the opposite side to see what the relationship is. Perhaps it is too deeply bound by traditional thinking. After the measurement, the students replied in unison: "The parallelogram has equal opposite sides and equal diagonal angles." I'm telling you, this measurement actually loses its meaning. Are the angles you measured exactly the same? At this time, students reflect on their own measurement process and tell the real measurement results. One student measured one set of opposite sides as 10.8cm and 10.7cm, and the other set as 5.3cm and 5.4cm respectively. Students all know that this error is caused by measuring tools and is allowed. Then let's guess, what are the properties of the opposite sides of the parallelogram? The student replied: Equality. Then let's try to prove it. Through this operation, students not only re-create the nature of parallelogram, but also further understand the relationship between measurement, conjecture and proof. I said humorously, "everyone in this class has become a mathematician!" " Learning by doing is Freudenthal's main educational thought, and this requirement has been strengthened in the new curriculum standards. In mathematics classroom teaching, whoever provides students with more opportunities and conditions to learn by doing will improve their ability to recreate mathematics. "As soon as I heard that, I forgot. I understood at a glance. I will understand when I do it. " This famous saying highlights the importance of doing.
Third, carry out active and effective mathematical communication.
Effective mathematics learning activities are mainly manifested in independent exploration and cooperative communication, rather than copying and strengthening. Successful and effective mathematical communication is based on active participation, and the characteristics of this kind of mathematical communication are very obvious in students' spontaneous discussion.
The research of educational psychology shows that students can only remember 15% of what they have heard, and only remember 25% of what they have read and 65% of what they have learned while reading. In mathematics teaching, we should try our best to make use of every opportunity for students to practice, do mathematics and learn by doing. Let students experience the process of exploration and research and give full play to their creative potential.