It has today become possible to install teleconferencing systems in classrooms and use communication circuits to enable classes in remote locations to together in "distance leaning" sessions Distance learning experiments are being conducted mainly in the U.S., but there have not as large as 30 or so pupils, of the kind that are common in Japan. We have developed a distance learning system linking remote points which is suited to the circumstances found in Japan, and have christened it the "CCV(computer, communication, visual) Education System." In the previous issue we reported on distance leaning lessons held in late June and early July. In this report, we describe distance learning sessions conducted in September with the theme "making embroidered pictures" (instruction in curves).
The lesson contents described in the previous issue were an improved version of the material long appearing in textbooks. However, In the present lessons(held on Sept.26 and 27 and Oct. 14),the material of the textbook was further extended, and entirely new material was developed and prepared for use in lessons. Let us now explain briefly why instruction curves was given.
Traditional school educ ation centers on the straight line and the circle, and there is no instruction on curves in general. One reason something given for the absence of instruction on curves is the difficulty faced in trying to quantify the properties of curves. The length of a curve cannot be measured in a simple manner as in the case of straight lines, nor can the bending of the curve be easily expressed numerically. Taken as an entirely qualitative entity, curves have little use in subsequent arithmetic studies, and so, it seems, they are omitted from the curriculum until the students begin to study the differential and integral calculus.
When infants reach the age of one year, they are given crayons and pencils and allowed to draw circles and other shapes freely on drawing paper. At the age of two, the nature and features of the objects drawn become clear\for instance, the eyes, nose, mouth, hair and other features of the mother's face. At three years of age, curves are used to express the outlines of the face and body. At the age of five, children start to draw pictures with a sense of depth, filling up the drawing paper, and human figures have finer and more functional movements. The bending of the body, the curves in arms and legs, and other features begin to be more realistic.
In the background of this growth in artistic ability is the development of activities to recognize objects being drawn. In order to further heighten these attempts at recognition, qualitative instruction on the properties of curves, followed by quantitative instruction, is needed elementary school . more specifically, the notions of curvature and rate of twist should be covered beginning in elementary school.
The general order of instruction for different grade is as follows. In the lower grades, the pupils study qualitative aspects: "It's bent in this way\it's pointed," as a means of making them aware of the type of bending or curving. In intermediate grades, children lean about the ratio of a circle's diameter to its circumference(about 3.1 or so), calculating the length of an arc(actual calculations are done using electronic calculators), drawing using perpendicular bisecting segments, and approximating curves by arcs of circles, and in these ways lean to quantify curves. In higher grades, students learn about secants and tangents, and learn to grasp changes in the type of curvature.
@@ This curriculum was used in distance learning sessions conducted between 37 four-graders at the elementary school attached to Yamanashi Univ.(hereafter simply "Yamanashi") and eight fourth-graders in the third & fourth grade class at the elementary school attached to Yamagata Univ.("Yamagata"). A series of lesson comprises distance learning, and lessons in which CCV educational system equipment is actually used in communication are called interactive lessons. In distance learning, ordinary lessons are held in alternation with interactive lessons.
In distance learning lessons on "making embroidered pictures," the pupils create embroidered pictures while learning about straight lines, polygons, circles, pie shapes and curves. The pictures illustrate regional folk tales or depict the landscapes or culture of the area. The main emphasis is on arithmetic, but with elements of drawing, language and social studies.
In the fourth grade, pupils normally learn about measurement of angles, drawing, decimal numbers and integers. In addition, the classes participating in the CCV sessions also learned about pi(approx. 3.1), the length of the circumference of a circle, pie shapes, subtending angle, and the length of arcs.
The pupils learn that circles are symmetric about diameter lines; they also learn to draw two chords connecting three points on a circle, and construct perpendicular bisecting lines for the two chords using a bisecting ruler made from a transparent plastic sheet. They learn that the intersection of these two perpendicular bisectors is the center of the circle. They then create embroidered pictures using figures already studied containing smooth curves (everywhere-differentiable curves).
The smooth curves are partitioned, assuming them to be connected arcs. The portion of a curve in each partition is regarded as an arc, three points on this arc are chosen and used to find the center of the circle. By then measuring the radius and the subtending angle, they can calculate the length of the arc.
In the way , the length of one section of a curve can be found. By repeating the process and summing the length, the total length of a smooth curve can be determined.
The children mainly study the bending or curvature of curves. A "circular ruler" consisting of concentric circles draw on transparent plastic sheet is held against the curves of various objects in the immediate surroundings, and circle coinciding with fixed sections of circles. Following this, they create embroidered pictures based on figures already studied containing pointed curves as in curves with a non-differentiable point. The circular ruler is placed against the paper and used to determine the initial curvature of a design is created. As a result, the curves used in this task are, from the beginning, continuations of arcs. A circular ruler is used to draw curves, and so the radius and the circle center are already known. By measuring each subtending angle of the pie shapes and finding the lengths of the arcs, the lengths of each curve can be determined.
The distance learning lesson begins with the children showing each other the embroidered pictures they have made. The are made to notice the differences in the types of curves used, and exchange information about the curves. The Yamanashi children learn about the circular ruler, types of curving, and pointed curves. The Yamagata pupils learn hoe to determine the center of a circle using a bisecting ruler, and learn about smooth curves.
The children in both classes will become able to point to a part of a curve and characterize it: "This is a curve with radius xx‡p and of length yy‡p." The exchange between the classes will result in a more advanced ability to deal with curves.
In addition, the children will learn from the designs about features of the other school's geographical area, thus promoting exchange on the cultural level as well.
In the Yamagata class room, the interactive lessons were led by instructor Satoshi Seiki, with the equipment operated by Instructor Kazuhiko Komatsu; in Yamanashi, the lessons were led by Okuyama, with Instructor Takashi Moriki operating the equipment. In normal lessons, the respective classes were led by Instructors Seiki and Okuyama alone.
Three interactive lessons were conducted.
photo1.A Yamanashi child discussing the features of a Yamagata picture (taken
at Yamagata)
Photo 2:Presenting the picture "Kenzaburo the flute-player"(taken at Yamagata)
Photo3:Yamagata child practicing using a bisecting ruler white communi cation is interrupted
The children twice created embroidered pictures, but the pictures were bolder and with more beautiful lines. The first time, it was all they could do to learn the use of the tools and method of calculations. But the second time they were more consciously trying to create attractive designs.
In viewing the shadow-pictures and Gernica, both groups became more animated in identifying pointed and smooth curves. It was clear that the children's awareness of curves was heightened trough the distance learning sessions.
In lessons, a complete hour was not devote to communication between the classes; rather, communication was interrupted and each class began their own activities, so that the children did not become bored. This is especially important in classes of first-graders.
Photo4:A Yamagata child explaining the features of a Yamanashi picture(taken at Yamagata)
Photo 5:Introducing works created by Yamagata children(taken at Yamagata)
In this lesson, a "touch panel child specifier device" was introduced. The positions of children were input in advance, and after the instructor specifies a child by name, simply touching the panel causes the camera to be trained on the child specified. This device brings us another step closer to a set up in which lessons can be conducted by a single instructor.
Photo6:Yiewing Picasso'sGernica.The children are leaning forward in rapt attention (taken at Yamagata)
Some time is also required for arrangements between instructors so that interactive lessons can be conducted smoothly; and more than one-half years are required to pr epare the contents of a lesson for distance learning. However, the creation of embroidered pictures involves art, literature and regional culture as well as exchanges in arithmetic and general culture, and so overall made a large contribution to the children's well-being. The development of such comprehensive educational content has great significance. Hereafter the development of educational materials which facilitate and are premised on distance learning will grow in importance.
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