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Once upon a time, when I worked as a teacher and been not related to the world of training programs, I was extremely skeptical about programs. Well, any problem the program can solve - I can as well. To write down a theorem, to group examples and so on - I can do all these things as well. You have to spend time to understand how to work with a program, while the benefit for your professional activity is zero.
Due to various reasons, I had to engage in development of educational software, and my attitude to the training programs began to change. Better to say I changed my attitude. The following pivotal question arises: what functions of the training program make it a good assistant of the teacher? I still firmly believe that at present no program can replace a teacher. However, I am sure now that the computer can help a lot, and some functions of the teacher can be "delegated" to the machine:
- Development of task-books and other methodical materials
- Assistance in everything related with the word "to learn"
- Building up various knowledge, abilities and skills necessary in studying mathematics
- Formation of various knowledge and skills of general educational character
- Analysis of educational work
- Assistance in organization of "differentiated" approach in teaching
Testing the level of knowledge, abilities and skills
Now let us go point by point:
The methodical materials
Did you never spent half a night in preparation of tests and variants of control works for the class? I am almost sure that you did not escape these pleasures, let alone fascinating search for appropriate examples and problems in preparation for everyday lessons. Moreover, you have to solve all these examples, haven't you? With the help of the program, this work can be done in minutes! If you are interested in finding out how, look at the article "Development of methodical materials".
To learn
This article is intended for professionals, thus I shall not explain that before all formulas and definitions are learnt, the student cannot solve problems. The time allocated for learning the formulations is tight and, to tell the truth, it is a pity to spend time for such boring work. Who of you never thought: "Jesus, how many times more should I repeat this for this guy?!" Do not forget however that, firstly, the teachers "repeat" this information the whole life. Secondly, everyone needs to repeat anything his own number of times to learn it. The question should be posed differently - is it possible that each student has his own tutor? The tutor that asks questions, gives hints, offers tests - and does not get angry after the hundredth error is made at the same place.
The computer is just born for these purposes. For more detail please read the article "The theory in the training programs in math" or load the free-of-charge version "EM Formula Light". You do not really need it, as you learnt all formulas long ago, but you can easily evaluate the quality of the tool and its potentials. As professionals, you will immediately see how to use this program in your "personal" interest.
Building up various knowledge, abilities and skills necessary in studying mathematics
Page "Techniques" lists training potentials of the programs and shows tables relating training potentials with methodical schemes realized in the programs. The same info can be found in the window "Settings" of the program "EM Mentor". The purpose of the tables is extremely simple: to establish a correspondence between a concrete knowledge, ability or skill and a system of methodical exercises realized in the programs of the complex. Try methodical schemes in work to evaluate their effectiveness.
The number of methodical schemes is intentionally excessive. The purpose was to make the program as flexible as possible and useful for as many users as possible. Every teacher has his own set of exercises to build up a particular skill. In practice, the choice of these exercises depends on what a particular student knows and what he can do.
With this in mind, we did not attempt to construct any "universal" set of exercises. Our objective was to give a wide spectrum of exercises, so that any teacher can choose a suitable portion of methodical exercises.
Each exercise needs to be prepared and worked out by the teacher. In the case that the exercise is ready for you, what does it mean that the exercise is worked out? This means that the program puts questions, gives hints if necessary, analyses student's performance, repeats the same exercise if necessary. You need only to choose exercises and to control their fulfillment "by the edge of an eye". The attention can be switched to the other student.
Formation of various knowledge and skills of general educational character
One of tasks all teachers face is to teach students to obtain knowledge independently, on their own. This task is solved only at universities, but the schoolteachers lay down the basis. Such skill of self-education, if present, facilitates the teaching work and increases its quality. In other words, if a student is accustomed to work with the book, then he is on midway. A necessary condition for self-education is building up abilities and skills related to organization of control and self-control in carrying out the educational work.
The basis for development of this skill is the analysis of educational work and the following methodical conclusions. In the simplified form, the scheme works as follows: If such errors or mistakes are made, then these exercises should be executed to eliminate the errors.
In pedagogical practice, you can hardly spend time on development of such skills, as you have to teach to subtract and to divide.
It goes faster if you do the exercise yourself and give out the recommendation: do an exercise number N on page M. To make the detailed analysis you need a lot of time whereas the result is not guaranteed.
One small remark about the results. In my pedagogical practice, I was rather frequently forced to make the detailed analysis of educational work. I was developing the experimental educational plan and therefore many bureaucrats were involved; well, you cannot argue with such people, you just do what they ask.
The tables "Analysis and synthesis" were developed by myself, but they were filled in by my students. An unexpected "effects" of students' work appeared a bit later. Firstly, the students began to study much better; secondly, they were much more effective in working with books. I did not trace these "effects" since the bureaucrats left me eventually alone.
An obstacle for the use of the described resource is the hard question that will do the analysis. In our program the analysis is done "automatically", all mistakes are revealed and it remains to ask the question: what should be done to correct them? If after some time the student will formulate this question to himself, then a part of knowledge necessary for self-education is laid down.
Another common objection: it is not a good idea to overload students with excessive knowledge from pedagogics. To my opinion, however, there is no excessive knowledge, and besides, the pedagogics is not a thing in itself that intended for the teachers only. If something from pedagogics is useful for students in their study then this something should be taught.
The analysis of educational work
The analysis of educational work is a necessary "every minute" component of teaching work. The forms and purposes of the analysis can differ. In the development of the programs, we were interested in typical mistakes of students in performing educational tasks. Having the list of mistakes, the teacher can easily conclude what type of exercise should be performed to eliminate a cause of these mistakes. If you use the program for working out a certain type of exercises, you can get the list of mistakes at the end of exercise or in the course of performance. With this information in hands, you can easily make appropriate conclusions.
Differentiated approach
I hope that I do not need to explain that this is one of the most difficult forms of lesson, but also the most productive. Besides, if the class is strongly stratified by the level of knowledge, abilities and skills, then, probably, this form of teaching is the only possible if you intend to teach the whole class not just a group of students. Below I try to show the potential of the computer use at such lessons. The major difficulties are:
- Preparation of methodical materials for different groups of students.
- Switching of your activity between groups
- Check on performance of the students and evaluation of their activity.
With switching of your activity between the groups, no program can help - this is a question of your creativity. For the rest the computer can help significantly.
Materials for different groups can be prepared in two forms: in paper and in electronic form. What does it mean electronic form? This means you have to choose examples or formulas intended for studying, to select the suitable technique (such as: to compare, to evaluate, to solve independently etc., about 60 techniques in total), to choose the hint system and the size of the list of multiple answers. That's all. Your work is completed at this point. The program will ask questions, will give hints, will evaluate the answers, will do the analysis of mistakes and will give methodical recommendations. If you do not believe in this, try the free-of-charge version "EM Mentor Light" and satisfy yourself.
Now let us speak about the dark sides of the ideal picture described above.
- You are not familiar with electronic approach. However, nobody can escape the computer era, computers will perforate into the educational process in various forms, thus eventually you have to get used to computer anyway.
- The math teachers do not like technical innovations. They need only a piece of chalk and the blackboard, that's all. Still, look at the subject sensibly: if computer can facilitate your work - why not to try?
- The bustling period of adaptation to the new technique. This refers mostly to the question how good you are in observing the discipline at your lessons.
- You and your students have to spend time to master the program. The testing shows that it takes 10-15 min to get used to the standard program. Well, try, play, evaluate and maybe the pluses will compensate for the efforts applied.
Check on the level of knowledge, abilities and skills
How one can use the program for these purposes is written above. Here I want to make a small remark. The best check is, certainly, the control work. A sheet of paper, a pen, and a complete freedom for creativity. Unfortunately, this cannot be done with the computer. The reason is extremely simple: math record has very complicated structure.
While the input tool is the mouse and keyboard, the problem of fast and simple input of mathematical text cannot be solved. We have to limit ourselves by the test approach. Note however that any test contains a half of answer. Let us consider control works. You have composed variants, printed them and held a control work. Now you have to check them, meaning, first of all, to solve the variants. Surely, it is easier to press the button and to print all solutions than to spend time to solve problems on your own.
Another remark: did you ever trust your best students to check the results of the tests? In the case that the course of solution is written in detail, they do this job marvelously; they pull out all mistakes that a teacher can overlook. I do not speak about the "epochal" control works, these you should check yourself. There are however a lot of normal current tests which should be done, but as you think about checking them, you loose all your optimism.
An obstacle to using the students in checks is the necessity to write the detailed solution, which takes time. With EMMentor, the machine solves and prints! One more aspect: it is good for students to check somebody else’s work. You do not have to ask them to do this systematically, just sometimes for their own advantage, and well, you can breathe freely.
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