The following is a problem from 1956 Tokyo University STEM major's 1st test Comprehension I part. We have translated and uploaded it for people interested in math, education, and history. Please take a look and comment or post your own solutions. * CLA note : There is a long way to solve this problem and also a short, quick way. It is very important to be able to solve this problem in both ways.
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5-2. Internet/media classrooms
This may be the ultimate in having as many students as possible for a single instructor. The session can vary from recorded lectures to live chatroom sessions where students will submit their questions publicly and the instructor will publicly answer them as they come. The main benefit is that this removes restrictions in time and space for everyone, including the students. They can seek out more convenient time and place for study, a benefit which cannot be ignored. The student can also look at questions, comments, and answers from a large number of people, and he may find some that are very useful. A good on-line instructor can guide students in a carefully paced path of discovery that can greatly enhance understanding of everyone viewing the process. The drawbacks are pretty obvious as well. There are many limitations to student and instructor interaction, and the time-delay may confuse people in certain situations. The instructor has very little control over what the student is doing, and there is great potential for students to cheat on their attendance, homework, or exams in these setting. Some of the very fine details related to the subject content may be impossible to convey over the internet/media as well; thus many people will leave these classes with incomplete knowledge. Still, for students who are just getting started, or need only a few tips, this can be a great venue. These classes are great for getting one’s feet wet with the subject matter, often are free or very cheap, and offer immense flexibility to a student’s schedule. It also lets people separated by great distance interact with each other. As long as what the student needs isn’t intense exploration into minute details concerning the subject, which requires close proximity of the instructor or some one-to-one attention, there are many ways these setups can be used productively. Conclusion Great variety exists in student-to-instructor ratios in a class, and they all have their uses, advantages, and disadvantages. Even within a single subject course, people may encounter different classroom setups that will have different student-to-instructor ratios. Instead of proclaiming one student-to- instructor ratio as ideal, it is much better to study its strengths and weaknesses, find ways to reduce its weaknesses and enhance its strengths, then properly formulate a ratio according to the needs of the students and restrictions imposed by the situations. As technology advances, there will be more ways to work and study in these setups, cover up some of their weaknesses, and bring about new methods. It is important to flexibly adapt these classroom setups to best accommodate the needs of the students and the society in which they live, remembering that all the setups can be made to be useful and productive. 5-1. Large Classroom of Ten or more students to one instructor: Sad Reality or Factory?
In most school classrooms around the world, any time in history, this is the typical setup. This setup is often born out of scarcity in various resources; thus people don’t have any choice to be in a different setup when it comes to student-instructor ratio. Still, this setup actually does have some unique advantages that make it useful in certain cases. The most obvious disadvantage of this setup is that the instruction can’t be individualized. It is hard to elicit active participation from the students, and such a session has the chance of diverging into unrelated topics or dwelling upon unimportant materials. Students can easily lose interest and forget any information from class instructions. Homework and tests become the primary tool to facilitate students actively learning or practicing the contents; thus it is possible to overburden students. If the instructor misjudges the general state of understanding or makes mistakes in planning the lesson, this can lead to large number of people wasting the whole classroom period, as it is harder to adjust with so many people present. For these reasons and other potential problems, it is understandable that most educational institutes publicly say they don’t like this setup, even though most of the larger institutes conduct the majority of the classes with this student-to-teacher ratio. For the educational institute, this setup is the very profitable. With this student-to-teacher ratio, it can reduce the instructor’s pay, costs associated with maintaining the classroom, and other expenses and overheads per each student. Since the profit margin becomes larger as the number of students per instructor grows, there is strong financial motivation for the institutes to create these settings. One extreme example would be a core subject class in a large public university, where as many as 2000 students may be listening to one professor’s lecture (note: in these setups, the true ratio isn’t 2000 to one, as there are sub-professors and teaching assistants present for many “smaller” group activities, making the ratio more like 2000 students to 50 instructors, which would make the ratio closer to 40 to one). Despite these problems, there are cases where it may be in student’s best interest to take classes with such a ratio. The most obvious case would be when the student already knows most of the material and just needs a little refresher and introduction to the newest developments in the subject. All he really needs is to see someone work through the whole material once, and he can have that for a price much cheaper than tutoring or in smaller class setups. He also is free to concentrate on the material he needs or wants, and ignore other things he already knows. This is why these setups can remind people of large academic conference where learned scholars showcase the latest discoveries. Another situation is when the student only needs to do some practice with some homework and practice tests. The instructor will begin the class by giving students a very brief lecture, followed by some problems on which to work. Students will do the problems, and then the instructor can explain why certain answers are right or wrong, occasionally answering questions. Since the student already is capable of answering the majority of questions correctly, he is free to divert some of his time into thinking more about problems on which he really needs to work, and be able to request help with certain specific problems. Another case where this setting can be useful is when the instructor needs to give a general overview of the whole subject to people who understand very little of it. Since people don’t know enough to even ask questions, it sometimes is better to give them the whole thing before breaking it down to smaller chunks to investigate in detail. In these general introductory settings, most of the class would benefit from simply listening and watching the whole subject matter be unfolded by a good instructor. After they receive their exposure, they can now be separated into smaller classes to gain deeper understanding of the fine details. In situations when much time and resources may be wasted by trying active/collaborative learning techniques, it is more productive to go through one of these large-class passive learning phases to prepare the students for more active/collaborative sessions. These larger classrooms also offers students more chance to meet different people and encounter different ideas and perspectives. Therefore, it is better to properly utilize these large classrooms, instead of trying to eliminate them completely. |
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