Top-down And Bottom-up Along The Christmas Tree
High School of Mathematics "Baba Tonka"
Ivan Vazov str.20, 7000 Rouse, Bulgaria,
1 Structural Programming as a Purpose.
One of the things that teachers try to acknowledge the students with in the process of working in Logo environment is the modular approach in programming. As a whole, top-down and bottom-up programming is quite a difficult thing for the children to understand, so it is usually introduced by the implementation of easier tasks, in which it is illustrated . The first tries along these lines are connected with the building of towers, rosettes and wallpapers. The teacher directs the students to them, having already created procedures for a square and a triangle, and knowing that they can be used repeatedly and in different combinations. The children easily get used to that way of bottom-up programming and most of them succeed to understand its advantages and make use of them in their work.
The next step in the rationalization of the modular programming by the students is performed by the teachers through giving the children the ready figure and providing to them the chance to look for the basic building element on their own. Every student may find a different one, which when combined in a particular way leads to the desired rosette. There are not few cases in which the children find an element, with which they cannot build the preliminarily desired figure but some approximation of it. The children usually dont realize that in such activities they use top-down programming in seeking for a solution to the task and bottom-up programming in its realization.
2 The "Christmas" Project.
The projects in which theres not a pre-defined final look of a figure, but only an idea of what it has to resemble make a particular interest. These projects are developed with a definite topic and idea. I have gone into a project of the kind in Comenius Logo with 11-year-old students. It was connected with the Christmas holidays in Bulgaria which have two basic elements: a decorated Christmas tree and a sourvaknica - a decorated twig used for wishing people good health by tapping them on the back. The topical project, which we took up, together with the students, required a christmas tree and a sourvaknica to be displayed and to become decorated when the user clicked with the mouse on them.
3 In search of basic (building) elements in the project.
In the beginning we started with the building of a christmas tree. Every student had a well-formulated idea of that kind of a tree. Thus we easily deduced its basic outward characteristic features, which could help us in building it up on the screen:
4 An Old Element in a New Figure.
The second basic stage of our project was connected with the building of a sourvaknica. The students ideas of it differed, because its appearance is usually a product of some personal creative decision. As a whole, there are elements in it that are easily distinguished and lend the characteristic features to the sourvaknica: it is made of a cornel twig; theres a main stick, around which circles are hung; the circles are wrapped up with stripes of cloth, so as not to hurt you when you are tapped.
A closer scrutiny in a stylize image of the sourvaknica revealed that the appearance of the circles looked much alike the branches of the Christmas tree. This suggested to the students the idea of using the previously discovered basic element.
5 The New Informatic Devices as a Necessity.
The next stage of the topical project was related to the decoration of the Christmas tree and the sourvaknica. Every child created its own set of toys, which was going to be used. But a problem arose: to create such a procedure, that when clicking with the left button of the mouse the turtle should go to the position of the mouse pointer.Thus there appeared the necessity of introducing the conditional operator, ASCII-code of a symbol and its reading, co-ordinates and positions of the mouse pointer, placing the turtle in a given position and recursion. The explanation of every one of these notions was a motivating process for the students and this mobilized them for repeated experimenting on them until they attained a considerable stage of rationalization of the new informatic devices .
6 The Important.
As a whole in the realization of the project we mustnt ignore the way, walked to the arrival at the solution. The work was set with tries and errors. In most cases the very errors gave the students the possibility to execute self-control over their own work and to look for a better solution to the problem . The students didnt give up their idea of realization on arriving at a not quite satisfactory result, but became eager to improve it. This lead them to repeated walks from down to top in the creation of the objects. Whats more, sometimes the necessity of introducing a new primitive (which had to fulfil some particular conditions and to be applicable in the specific cases) appeared. If there wasnt such, they looked for a way to combine the familiar ones, to attain the desired result.