Alternative Classroom: Math Edition

Author: Xu Bin / Country: Mainland China
Publisher:
Publish Date: 2006-01-01
Features: Analysis of Eight Common Misunderstandings in Classroom Teaching – Reflections on Current Alternative Teaching Practices in Classrooms
Author: Xu Bin, Suzhou Industrial Park No. 2 Primary School, Jiangsu Province
The brand-new concepts brought by the new curriculum reform have led to a brand-new life in classroom education, with teachers' educational concepts, teaching methods, and students' learning methods all undergoing encouraging changes. However, as the experimental implementation of the new curriculum reform gradually deepens, some deep-seated issues have also emerged. Below are several common misconceptions in primary school mathematics classroom teaching, each analyzed separately to seek solutions.
Mistake 1: Creating Contexts Just for the Sake of Contexts
The Full-Time Compulsory Education Mathematics Curriculum Standards (Experimental Version) (hereinafter referred to as the Mathematics Curriculum Standards) states that it is necessary to "allow students to personally experience the process of abstracting real-world problems into mathematical models and applying and explaining them," and proposes that "students should learn mathematics in vivid and concrete contexts." Indeed, creating effective mathematical contexts can stimulate students' interest in learning and provide them with a good learning environment. Recently, the author attended a lesson on "Recognizing Multiplication." At the beginning of the class, the teacher presented a fascinating animated scene—"A Corner of the Zoo." The teacher asked the students to observe the scene and asked, "What did you discover?" After observing, the students eagerly shared their findings.
Student 1: I think it’s so fun here! There are small animals, houses, trees, clouds, rivers, and bridges.
Student 2: I noticed the water in the river is still flowing!
Student 3: I saw fish swimming in the river!
Student 4: I saw the rabbits jumping happily!
Student 5: I noticed the chicken’s head is moving—Are they pecking at grain, or are they eating insects?
Student 6: I saw two white rabbits on the bridge—Are they coming to this side, or are they crossing the bridge?
Student 7: There are two houses there—Which one is the chicken’s, and which one is the rabbit’s?
Student 8: The clouds in the distance are drifting, as if welcoming us!
By this point, over ten minutes had passed, and the students kept making new discoveries. The teacher kept asking, "Did you find anything else?" And the students kept making new discoveries.
Reflection: At this point, the author cannot help but ask: What is the purpose of creating contexts? Is this a mathematics lesson or a picture description lesson? Although the atmosphere was lively, the nature of the lesson seemed to have changed. In fact, after presenting the scene, the teacher could simply ask: "How many types of animals are there in the picture?" (Two: chickens and rabbits) "How many of each are there together?" (Rabbits are in groups of two, chickens in groups of three) Then, guide the students to count the rabbits in pairs and the chickens in threes. Next, ask the students to figure out how many rabbits and chickens there are in total. In this way, students can effectively capture mathematical information in the problem context, gain an initial understanding of the "several groups of several" concept in real life, and prepare for the upcoming multiplication lesson.
We know that the driving force behind the development of mathematics comes from two aspects: first, the needs of the external real-world society for mathematics; second, the internal contradictions of mathematics itself, i.e., the need for mathematics to develop. Constructivism holds that learning is always connected to a certain social background, or "context," and learning in real contexts is beneficial for meaning construction. However, creating contexts should not only aim for superficial liveliness and should not allow excessive non-mathematical information to interfere with or weaken the learning of mathematical knowledge and skills, as well as the development of mathematical thinking. The creation of contexts in mathematics lessons should serve students' learning of mathematics, help them use a mathematical perspective to observe real life, provide support for their learning of mathematical knowledge and skills, and create fertile ground for the development of mathematical thinking.
On the other hand, before teaching new content, should students still be reviewed? In fact, the main purpose of reviewing before teaching new content is twofold: first, to activate existing related prior knowledge in students' minds through reproduction or re-recognition, and second, to ease the difficulties of learning new knowledge. The former, if necessary, is perfectly reasonable. The issue lies in the latter, where teachers often design transitional or suggestive questions to ensure smooth teaching, or even artificially set a narrow channel of thinking, making it unnecessary for students to explore or requiring only minimal effort to reach conclusions. This so-called "preparation" of chewing knowledge and feeding it to students is not conducive to developing students' ability to actively acquire knowledge.
It is clear that creating contexts and reviewing preparation are not contradictory. Not all teaching content needs to find prototypes in life. The choice of introduction method depends on the characteristics of the content itself and students' starting points.
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