Suhomlinski said: In people's hearts, there is a deep-rooted need to be a discoverer, researcher and explorer. In teaching, we should give priority to improving students' conscious learning ability and let them learn to explore. Treat students' mistakes correctly, so that students can study in a democratic atmosphere, think positively and be brave in guessing. In mathematics teaching, teachers should always consciously use heuristic teaching to guide students to make bold guesses, stimulate students' strong inner needs, and let students feel the power of guessing and enjoy the joy of guessing.
3. Stimulate students' desire for mathematical conjecture through hands-on experiments and operations.
Psychologist Piaget pointed out: "Activity is the basis of cognition, and wisdom begins with action." Hands-on operation is an inquiry process of learning knowledge. Hands-on operation promotes thinking and mobilizes students' various senses to participate in learning. Through experimental activities, find out the law and put forward a guess. For example, when teaching the trilateral relationship of triangle, students are required to prepare some small sticks with different lengths, such as: if the length is 6, 8, 8, 14, 20 (unit centimeter), choose three sticks to make a triangle, 1, and how many ways to choose from; 2. Which sticks can be made into triangles and which can't be made into triangles. 3. What quantitative relationships do you think small sticks can form triangles? Let the students guess for themselves.
4. Pay attention to cultivating students' inductive ability in teaching, so that students can learn to guess in induction.
Induction is a special to general way of thinking. It includes incomplete induction and complete induction. Inductive conjecture refers to the conjecture activity of using incomplete induction to observe and analyze the research object or problem from a certain number of cases and special circumstances, so as to put forward new mathematical propositions or methods. Attention should be paid to the cultivation of students' inductive ability in teaching. Teachers can guide students to sum up the similarities and differences of things by observing and synthesizing special cases of things, reveal the essence of things, and make general guesses about things according to their essential characteristics. Through this inductive conjecture, students can draw some mathematical conclusions. For example, the sum of the internal angles of a triangle is180o =1*180o, the sum of the internal angles of a quadrilateral is 360o=2* 180o, and the sum of the internal angles of a pentagon is 540o = 3 * 180o.
5. Pay attention to cultivating students' analogy ability in teaching and guide guessing through analogy.
By observing and comparing the similarities and differences between two similar mathematical research objects, the analogy discovery method infers the similar nature of another research object from the similar nature of one studied and known object. Laplace, a famous mathematician, pointed out that in mathematics, the main tools for discovering truth are induction and analogy. Deepen the understanding of knowledge categories by analogy conjecture. Because things often have the same or similar attributes, when two problems are similar in a certain way, we can guess the possible attributes of another problem from the known attributes of one problem. The general idea of using analogy conjecture is: observation-association-analogy-conjecture. For example, the algorithm of teaching real numbers, the algorithm of sequential analogy combined with numbers and series, the nature of the two bottom angles of an isosceles triangle is similar to that of an isosceles trapezoid with the same base.
In a word, the cultivation of students' guessing ability is not a one-off event, and it needs to be cultivated consciously and purposefully in the teaching process. Cultivating students' guessing ability is the mission entrusted to our teachers by the times, and it is also an inevitable trend to further deepen quality education.