This forces me to reflect on my usual teaching activities: every time I tell 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 knows this truth, but it is so difficult to really implement it in the teacher's classroom ...
With the gradual deepening of the concept of learning 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 experiences, such as the discovery of irrational numbers, the proof of Pythagorean theorem, the establishment of plane rectangular coordinate system, etc., all of which are full of the affection of human exploration, which requires people to rely on existing knowledge and experience to observe, practice, induce, 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 "fiery thinking" of human beings, and there is rich life significance in its formation. Then, in mathematics teaching, how to guide students to do mathematics and learn mathematics?
first, create a good problem situation and bring students into the problem
The problem is the heart of mathematics activities. The formation process of mathematical definition theorems and formulas is transformed into problems with life significance, forming problem situations, thus bringing students into problems, doing mathematics and learning mathematics in the inquiry of problems. Therefore, in teaching, the process of knowledge should be transformed into a series of inquiry questions as far 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 as mathematicians discovered these properties at that time, so that students can discover their own mathematical knowledge in practice.
For example, in the past, when we talked about parallelograms, we first demonstrated some figures of parallelograms, so that students could master what parallelograms are. This is as abstract as telling children what chairs and tables are, and there is no mystery. But now the usual process is that teachers give a formal definition of parallelogram, so another level is skipped, and students are deprived of the opportunity to create a 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 bisected and the parallelograms can be embedded in a plane, etc ... Then he will find that other properties can be derived from one property. Maybe different students will choose different basic properties. Thus, students grasp 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 parallelogram nature, let the students make their own parallelogram model first. Communicate in groups in class: first measure the opposite side and then the opposite side, and see what the relationship is. Perhaps it is too deeply bound by traditional thinking. After measuring, the students replied in unison: "Parallelogram has equal opposite sides and equal diagonal angles." I tell you, this kind of measurement actually loses its meaning. Are the corners you measured exactly the same? At this time, students reflect on their own measurement process and tell the real measurement results. A student measured that one set of opposite sides was 1.8cm and 1.7cm respectively, and the other set was 5.3cm and 5.4cm respectively. Students all know that this kind of error is caused by measuring tools and is allowed. Then let's guess, what are the properties of the parallelogram on the opposite side? The students replied: equal. Then let's try to prove it. Through this operation, students not only re-create the parallelogram nature, but also further understand the relationship between measurement, conjecture and proof. I said humorously, "Everyone became a mathematician in this class!" Learning by doing is Freudenthal's main educational thought, and this requirement is strengthened in the new curriculum standard. In mathematics classroom teaching, whoever provides students with more opportunities and conditions to learn by doing will improve their ability to recreate mathematics. "When I heard about it, I forgot. When I saw it, I understood it. When I did it, I understood it." This famous saying highlights the importance of doing.
Third, carry out active and effective mathematical communication
Effective mathematical 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 this feature of mathematical communication is very obvious in students' spontaneous discussion.
Educational psychology research shows that students can only remember 15% of what they have heard if they only listen to the teacher and don't read books, 25% of what they have seen if they only read books and don't listen to lectures, and 65% of what they have learned if they watch and listen. In mathematics teaching, we should try our best to make use of every opportunity to let students practice, do mathematics and learn by doing. Let students experience the process of exploration and research, and give full play to their creative potential.