"Mathematics Curriculum Standard" expounds the reasoning ability in how to cultivate the reasoning ability of primary school students in teaching: "Mathematical conjecture can be obtained by observation, experiment, induction, analogy and other methods, and can be further verified, proved or given counterexamples; Be able to express your thinking process clearly and methodically, and be reasonable and well-founded; In the process of communicating with others, I can discuss and ask questions logically in mathematical language. " The online teaching strategy of cultivating students' reasoning ability in primary school mathematics has benefited me a lot. Now, combined with my own learning experience and teaching practice, I will talk about how to cultivate pupils' reasoning ability in teaching.
First, demonstrate and teach students the correct reasoning methods.
Pupils learn to imitate, so how to reason needs examples, and then students can learn to reason. Many mathematical conclusions in primary school mathematics are drawn by inductive reasoning, so we should consciously demonstrate how to make correct reasoning by combining mathematical content in teaching.
Second, from the special to the general, cultivate students' inductive reasoning ability
Taking the law of individual things in a certain kind of things as the universal law of this kind of things, the reasoning from special to general in this thinking process is called inductive reasoning or induction. This is a means of seeking truth and discovering truth from individual to general, from experimental facts to theory. Inductive reasoning is often used in the teaching of rules, laws, formulas, conclusions and problem solving, and incomplete induction is generally used. The conclusion of incomplete induction is not necessarily correct and needs strict proof. The incomplete induction method is more suitable for the age characteristics of primary school students and easy to accept. Therefore, this form of reasoning is often used in primary school mathematics teaching.
Third, develop students' analogical reasoning ability from special to special.
Analogical reasoning is based on the similarity or similarity of two different objects in some aspects (such as characteristics, attributes, relationships, etc.). ), and deduce their thinking forms that may be the same or similar in other aspects. It is the reasoning from special to special in the process of thinking. This is also a basic and important means to seek and discover the truth.
In mathematical thinking activities, analogy has many forms. Generally, it can be divided into simple analogy and complex analogy. Simple analogy is formal analogy. For example, from "in the division formula, the divisor can't be zero", the denominator of the fraction can't be zero and the last term of the ratio can't be zero are deduced analogically. Complex analogy is a real analogy, which can broaden students' knowledge, guide students to explore the hidden internal relationship between quantity and grasp the law of change that quantity may cause.
Fourthly, from association to verification, develop students' mathematical guessing ability.
Newton said, "Without bold speculation, there will be no great discovery." Conjecture is the most common and important rational reasoning, and both induction and analogy contain conjecture. Paulia believes: "To put it bluntly, reasonable reasoning is conjecture." Traditional teaching leaves too little content and time for students' thinking activities, which not only weakens students' cognitive process, but also leads to students' thinking imprisonment, and they dare not or will not guess. This is contrary to the requirements of the times to cultivate students' innovative ability. In order to develop students' creative thinking, teachers should teach students thinking methods, encourage students to analyze specific problems and specific teaching materials, and make guesses through observation, experiment, analogy and induction. In this way, students can not only master mathematics knowledge and satisfy their thirst for knowledge, but also learn how to explore knowledge.
In short, in the future teaching, I should pay attention to cultivating students' reasoning ability, let students actively participate in mathematical activities, experience the formation process of mathematical knowledge, let students experience the method and efficiency of reasoning, improve students' reasoning ability and achieve ideal teaching results.