Psychologist Bruner said: "Learners should not be passive recipients of information, but active participants in the process of knowledge acquisition." How to make students actively explore and discover new knowledge in teaching? In the teaching of new knowledge, teachers should consciously create problem situations for students, and through instruction, inspiration and guidance, promote students' positive thinking, let them explore and put forward valuable mathematical problems independently, make them have a strong desire for knowledge and cultivate their awareness of finding problems. Teachers should always encourage students to operate, try, communicate, discuss, question, dispel doubts and obtain independently, give students the right to ask questions, the opportunity to speak and the process of doing, and give students as much time and space as possible to study independently and creatively, thus forming a lively learning situation. In the process of inquiry, teachers should use a variety of evaluation strategies to inspire students with their own demeanor, movements and language, so as to maintain students' enthusiasm for inquiry, stimulate students' emotions in classroom learning, and promote students' active and automatic participation in the activities of exploring mathematical knowledge. The following is a teaching situation I created when I was teaching "Logarithmic Arithmetic".
Logarithmic function is an important elementary function, so we should use the knowledge of the learned function to learn it. Logarithmic operation is the basis and tool for learning logarithmic function and studying its properties, so it is the focus and difficulty of teaching. In the process of practice, I consciously designed the "logarithmic algorithm" as the inquiry topic and conducted a "mathematical experiment": let students set the values of m and n with a calculator and explore lgM, lgN, lgM+lgN, lgM-lgN, lgMlgN, lgM/lgN, lg(MN) and LG (Mn) independently. The practice results show that students are not only interested in "mathematical experiments", but also discover the operational nature of logarithm through calculation, observation and induction, experience the process of mathematical discovery and creation, and develop innovative consciousness, which not only develops cognitive structure, but also develops body, mind and quality. As the students themselves said: "Careful, rigorous, patient, realistic, dare to guess, dare to experiment", "The knowledge gained through their own thinking and practice is more interesting and more solid. Everything must be taken seriously, you can't follow the trend, you have to explore it yourself before you can draw a conclusion. "
Creating classroom teaching situation through the above-mentioned independent exploration fully mobilized students' initiative in learning and exploring, stimulated students' interest in learning logarithmic algorithm, and thus improved students' desire to learn mathematics.
Second, the use of scientific events to create classroom teaching situations
Creating classroom teaching situations with scientific events is easy to attract students' attention and stimulate their interest in learning. The following is a teaching situation I created when I was teaching "Exponential Function".
When teaching "Exponential Function", it can be introduced from a news report: On July 14, 2002, archaeologists from China discovered the ancient body of Han Dynasty in Lianyungang, Jiangsu Province, which aroused great concern. Archaeologists can detect a 1,000-year-old body discovered in the Han Dynasty without historical verification. How do archaeologists determine the age of the discovered body? The introduction of this situation aroused students' curiosity and interest. In fact, this is based on the decay rate of a radioactive element "carbon-14" contained in the human body (0.014 in the human body decays into "nitrogen-14" every year) and the "carbon-/kloc" in the corpse. That is, the problem is solved by the mathematical model of radioactive element decay, m=moe-λt, where t represents the elapsed time, m0 represents the initial mass, the attenuation mass is m, and λ=0.0 12% is a normal number. By introducing such a situation, students' interest and desire in learning "exponential function" can be stimulated, so as to improve students' initiative in learning and exploring, greatly improve classroom efficiency and achieve twice the result with half the effort.
Third, the use of mathematical stories to create classroom teaching situations
The form of storytelling is very attractive to middle school students, and it is easy to attract students' attention, thus stimulating their interest in learning. The following is the teaching situation I created when I was teaching Sequence.
When teaching "Sum Formula of Arithmetic Series", we can tell the story of German "Math Prince" Gauss who solved a math problem in elementary school. Namely: "1+2+3+…+ 100=?" As soon as the teacher finished reading the topic, Gauss wrote the answer on the blackboard: 5050. At this time, other students are still adding one by one. So how did Gauss calculate so fast? At this time, students will have a strong interest and a strong desire to explore, which leads to arithmetic progression's summation method-inverse addition.
Creating classroom teaching situations through the above mathematicians' stories has stimulated students' interest and desire to explore mathematics actively, and enabled them to participate in mathematics learning more actively.
Creating classroom teaching situations through the above three ways has greatly mobilized students' initiative and enthusiasm for exploring mathematics, improved students' efficiency in learning mathematics, made mathematics lively and interesting, and stimulated students' interest and desire in learning mathematics.