Class One: Mathematics for Grade 11
Environment: A bright and clean classroom with approximately 24 students. The desks are arranged vertically. Students will discuss with the students next door. Some charts of key points of mathematical formulas are pasted on the walls. Teaching AIDS is placed in one corner of the classroom.
The instructor who teaches this course has over 20 years of teaching experience and emphasizes a student-centered teaching model. She very much hopes that her students will ask her more questions.
Teaching content: Equations about polynomials.
In her class, during the sharing session among peers, the students in the class would listen quietly to their speeches. During the sharing session among students, there were often several students looking down at their exercise books. At this time, the teacher would pause the teaching and remind the other students to listen to how they shared and how they solved the problems. Students also help each other in group projects and then complete the assignments as quickly as possible. I think this is particularly good because every student’s idea can basically be respected. When a student proposes to solve the problem using the method learned in the last class, the teacher would answer, “This is a method we learned before; let’s see if we can use it in this problem.” No student’s idea was rejected, but introverted students seldom spoke up voluntarily. Moreover, when the teachers are doing group assignments, they will also walk around the classroom to help students solve problems. In her class, most of the students will answer the questions given by the teacher very actively. When students are not sure whether their answers are correct, teachers will also actively encourage them to express their thoughts. ​​When students are distracted, teachers will promptly remind them to focus on the class and quickly get them back into it.
Class Two: Grade 9 Mathematics
Environment: A typical classroom with approximately 28 students. Desks are arranged in six rows. The classroom projector displays slides for the lesson, and posters of student group projects are displayed on the walls.
Teacher: Has nearly 10 years of teaching experience; During the group activities, he would also constantly walk around the classroom, record the ideas proposed by the students in a notebook, and then help the students solve some problems.
Teaching content: About solving single-variable linear equations.
The students’ listening state is not very active. When studying in pairs, if 2 to 3 groups of students talk about topics unrelated to mathematics, the teacher needs to intervene several times before the students can refocus on their studies. Peer support among students is quite limited and not particularly frequent. When a student asks a question, his/her partner will simply provide the answer without offering any further explanation. Sometimes students’ ideas are rejected. When a student suggests solving a problem in another way, it will be rejected by other students in the group. Other members in the group will say, “We need a more efficient method to solve the problem as soon as possible.” These words prevented the student from continuing the subsequent group discussion, and during the discussion, he/she did not express his/her own thoughts either. During classroom group discussions, the teacher observes the class and selects some students to speak. However, some students do not participate in the discussion. This requires teachers to frequently speak to remind students and keep them focused on their classes. Only in this way can students’ participation be enhanced.
Class Three: Grade 10 Mathematics
Environment: A comfortable classroom with about 20 students. The desks consist of four tables pushed together to facilitate group discussions. The walls are covered with posters about geometry projects made by students themselves.
Teacher: Has 10 years of teaching experience; She would bring up some interesting topics in class and then get the distracted students back into the interaction.
Teaching content: About geometric figures.
In the classroom, the students’ performance in listening was extremely excellent. The teacher will actively invite students to speak, and other students will all gather over to listen carefully, making all students actively participate in the class. When students share their problem-solving ideas, the whole class will gently applaud to encourage the speaker. The mutual assistance among students is very proactive. When studying with partners, students will record their partners’ viewpoints on key point charts. But when students don’t know how to solve problems, partners in the group will also help each other and learn from one another. Students’ ideas are always respected. No matter what methods students use to complete the problems given by the teacher, they can always get the teacher’s approval and the applause and encouragement of their classmates.
In these three classes, all students can receive respect from their teachers. Moreover, in these three classrooms, both the classroom environment and the learning atmosphere are very suitable for students to study mathematics. Every teacher will use their own unique teaching style and some interesting questions to make the math class less boring and make the whole class very interesting. At the same time, every teacher is doing their best to ensure that all students can concentrate on listening to the lecture, study diligently, and actively discuss with their group members. Through this observation, I learned a lot, but I also realized one thing: if students are truly unwilling to learn, then the teacher’s help and persuasion will be completely ineffective.. At present, I don’t know how to solve this problem.