Dr. Rodolpho Caniato
Universidade Federal Rural do Rio de Janeiro
UNDER SUPERVISION: DR. DAVID LAYTON
UNIVERSITY OF LEEDS, UK.
UNESCO : 7, place de Fontenoy, 75352 Paris 07 SP
Teacher Training Projects Grounded on Researches on Teachers´ Misconceptions
Dr. Rodolpho Caniato
Universidade Federal Rural do Rio de Janeiro
1. Research with teachers.
The wealth of the collection of all the teachers’ misconceptions throughout years of research makes it impossible to deal with the subject within the scope of one short work. Therefore, we must confine ourselves to only a few outstanding and most frequent types of misconceptions. We will also mention important aspects of the teaching-learning process verified during the Physics Teacher Training Courses.
Here are some examples of important concepts for the understanding of many others that proved confusing.
*The concept of acceleration was confusing even among those who knew all the definitions and formulas.
*The understanding of the first law of motion went rarely beyond the literal definition.
*The understanding of the second law of motion – second Newton Law (F=m.a) – even though it is the most used equation, it is one of the least understood.
*”To go into orbit” – most frequently means “balance between two forces; that of the gravity, which pulls inwards and that of the centrifugal force, which pulls outwards.”
*”Satellites go into orbits when they leave the gravitational field.”
*”Satellites go into orbits when they leave the atmosphere and enter in the vacuum.”
*Ignorance of the law of areas: “a law of planets.”
1.2. Non-applicability of concepts.
Some concepts are difficult to be recognized or applied to a specific situation. Here are some examples:
*All teachers often use the Newton as a unit of power. However, a few teachers were capable of giving any idea that could suggest the size of the force, even among those who managed to say that 1 kg (f) = 9.8 N.
*Angle slope coefficient and angle tangent. It is one of the most common mistakes disseminated by the schools that prepare students to enter the university.
*Measures of angles. Frequent difficult imaging and measuring an angle in degrees without protractor, a table or a calculator.
*Small angles. Sometimes it is advisable, in Physics or other subjects, to substitute x for sen x, “as long as x is small”. What is then a small angle? – One degree? – Thus instead of sen 1, can you use 1 degree? (It is not a question of “limit”).
1.3. Ignorance of any basic principles of celestial sphere and its simplest relationships with everyday life.
Here are some examples:
*Ignorance of how to determine the points of the compass (North, South, East and West).
*Ignorance of how to measure the time and how to set a clock (not mentioning atomic clocks).
*The meaning of and how to measure, even roughly, the latitude and the longitude.
*How to determine the movements of the Earth, phases of the moon, etc…
1.4. Lack of initiative.
Generalized difficulty using the hands. Even greater difficulty using the hands and thinking about Physics altogether. Difficulty taking the initiative in situations that require ACTION. For example:
Perplexity over a situation to check the second Law of Newton, a kit is offered: a small cart with low friction, a smooth and horizontal table or rail, a rubber band (dynamometer), a ruler and a clock.
1.5. Difficulties of different aspects revealed during the discussion.
*Difficulty of understanding the texts.
*Difficulty of arguing.
*Difficulty of verbalizing one’s own idea.
*Difficulty stopping talking to listen to other people’s argumentation.
1.6. “High level” myths.
Great concern about the “high level” appears in different types of myths, such as:
*Physics is for those who want to pursue a scientific career.
*The more difficult the presentation of the topic the higher the level of the course. High levels of algebra frequently hide great conceptual limitations and poor contents.
*Massive failing (flunking) is also taken as a sign of “high level”.
Prejudices are those simple, wrong concepts – probably from elementary school – which curious – by outlast the higher education (sometimes called higher just because they were put “above”).
Here are some examples:
*The points of the compass are marked from the East, when the Sun rises.
*At midday the Sun is at (high noon) Zenith.
*The seasons of the year (winter, spring, summer and fall) are derived from the elliptical orbit of the Earth round the Sun. When the Earth is near the Sun, it´s summer; when it is far from the Sun, it´s winter.
*Belief in the horoscope as a factor that influences life.
Most teachers, beside their voice, only use a piece of chalk and the blackboard. The students keep quiet while listening and/or taking notes. Practical exercises are restricted to solving written exercises.
In such a process the teacher is the source of knowledge; the students the recipients to be filled up. Everyday teachers exert an authoritarian attitude on their students while students undergo a passive behavior for years and years. They train much more their “sitting” skills. Both teacher and students are the victim of an impoverishing routine process. Without any motivation from discussions, the teacher’s knowledge becomes crystallized or even fossilized, after years of repeating the same things.
2. First draft of the project
The outline of the problem, according to the survey carried out, would establish the sketch or draft of the project. At first, the project would aim at being the “negative” of the outline of the problem. Thus, the first lines of the project were:
2.1. To include, in the directions of the project, the conceptually fundamental questions detected among the trainee teacher deficiencies.
2.2. To put into practice the theoretical concepts. To help the trainee teachers so that they use the concepts learned in specific situations.
2.3. To offer elements of astronomy, starting from principles of celestial sphere and other approaches of astronomy subjects.
2.4. To foster the trainee teachers and students initiative always, mainly including handmade work.
2.5. To centralize the discussions in all situations, mainly the following exercises.
*Verbalization of ideas.
*Being silent to listen to others.
2.6. To help the teacher’s task so that he can easily beat the “high level” myths.
2.7. To help make clear some prejudices related to science, specially knowledge taken for granted.
3. First project
My first project started in Dec 1970 and since then it has been subjected to different trials. In Dec 1973, a summary of the researches and the methodological proposal were assembled in a PhD Thesis (1), accompanied by two volumes with the texts and activities. In one of them, Physics is tackled through Astronomy (1). In other (2), the subject resembles what is traditionally called Mechanics.
3.1. Work centered in the discussion.
One of the basic assumptions is that the learner, even if he/she is a trainee teacher, must be the main agent in the building of his/her own knowledge. Most work must be performed by the learner guided by the teacher and backers by his/her will, his/her senses and his/her intelligence. The work must be developed in groups (six at the most), with the use of five verbs, which are fundamental for the project. The students must act. These actions will be observed and required from the participants.
Reading is done in a loud voice within each group. Each peer reads a piece. The first reading is done without interruption. Each participant ticks the point he wants to discuss or the points he has something to say about or even the point he wants to add something to. It is very important that all students have the text so that they can take the chance to improve their reading skill (word articulation, visual reading and listening comprehension), mainly among teenagers.
During the second reading, the groups discuss the content, oriented by the teacher. After the discussion of the text the learners must perform the activity that follows.
3.1.3. Doing (also with the hands).
All the texts are accompanied by activities including the hands. These activities are not more suggestions; they are an inseparable part of the text and must stimulate new discussions and not cut them off.
3.1.4. Adding (contributing).
The participants must be motivated to give their contributions, which can be ideas, information and questions. Questions are very important to build knowledge.
The participants must be stimulated to be cooperative in all aspects. Instead of competing for grades, the students must share difficulties and knowledge. This helps to lower the affective filter and promotes an atmosphere of sympathy and relaxation.
3.2. Three levels.
In this work, the participants are not divided into “the good” and “the bad”. People have interest and different abilities. Students are not supposed to learn the same ways each has his/her own characteristics. Many texts have three levels. There is a level which is common to all texts with growing difficulties. For those who want and are able, something more is offered: “if you want to know a little more.” For those who want to go a little further: “a little much more.”
3.3. The Teacher’s role.
The teacher’s role is not that of repeating things, which the text does much more effectively. He is spared to more important things: guide, detect difficulties, help and make sure that the students overcome the difficulties. After the topic has been chosen, the teacher must show its relevance briefly. The first time (using this method), he show the difference. The participants are no going “to watch” the game, they are going “to play” it. Everybody must know the “rules” of the “game”. The rules are in the books. The participants most know what they are expected to do: ACTION (five verbs). Their overall performance will be observed and registered on a sheet called “Registro de Desempenho” – “Progress Report” (evaluation). The teacher starts the activity, choosing who reads first and making sure everybody reads. He also helps in the discussions without giving answers, which must arise within each group. The teacher should also motivate the shy ones and attract them to the discussions. Challenging questions are also very stimulating. Sometimes, when appropriate, a micro speech is rewarding and it serves to show the teacher’s characteristics.
Therefore, the teacher gets less tired and guides the students better. Through the discussions in each session, the teacher gets more and more experienced. Consequently, he can observe the students better and detect their difficulties and misunderstandings much more easily. Thus, he can make sure the students will overcome this process.
3.4. Apparatus developed for the project.
A lot of concerns were taken into account when developing the ACTIVITIES. Besides the purpose of the activity itself the material should be of very low cost and easy to obtain. Almost all activities have an original aspect. Two examples will illustrate the present work because it would be impossible to describe all of them.
The “planetarium of the poor”.
For the study of the celestial sphere, beside the texts (1), we will use a spherical distillation flask (1.000 ml), easily found in chemical labs. Fill the flask with water, colored with blue aniline, so that it reaches the half of the flask, the neck of which is upside down. The flask must be supported by a tripod. The neck of the flask must pass through the opening of the tripod shaped ring, so that it can be moved from a vertical to a horizontal position. Moreover, the neck of the flask will serve as a handle to manipulate the “planetarium” (number 1 in the photo).
The spherical part of the flask resembles the celestial sphere which can rotate with any inclination. This inclination will determine the geographical latitude of the place whose sky one whishes to reproduce. The water represents the horizon. The observer must be imagined in the center of the horizon, that is, in the center of the surface of the water. This model represents, with fidelity, the vault of heaven and the horizon, as if we were in the middle of the ocean.
This apparatus can be used in different levels. It can be used purely in a qualitative manner to reproduce the movement of the sky as we see it. It can be used, with its geometrical elements, to show how we determine the latitude and longitude. In this case, it is possible to forecast and measure how the day will be in any place on Earth, for any date, without leaving the table.
For architects it serves to simulate the isolation of the projects in any place of Earth.
In Philosophy of science, it serves to explore the concepts of theories and models in science.
After these photographies were taken for the project, there was need for another project. They required the development of a special technique, not only for production but for use. They were very cheap. Even the clock used in some of the photographs is home-made. The main goal of the collection (around 50 photos) is to offer real “frozen” movements. Most of mechanics can be studied with them. The movements range from the most simple, such as the rectilinear uniform motion, to more complex ones. In each of the photos the time intervals are equal. Besides permitting a qualitative study, a lot of them also allow a quantitative assessment. For that in some pictures the clock and a scale in centimeters were photographed. The photos are also used to show how little on can do with a lot of traditional kinematics. Ideal problems, which rarely occur in practice, are created just for the sake of using the kinematics formulae taught. On the other hand, a simple concept, for instance vectors, in a short while would serve to more general and real situations.
Try observing the photograph on page 12. Could you use any kinematics formulae usually taught in high school? In what point of the path do you think the highest acceleration occurs? What do you think this experiment is? What do you know that the law of areas could be used here? Does that help? How?
These questions aim at exemplifying other concrete situations in which the participants are challenged to apply all their knowledge and argumentation.
Some samples of the equipment used are showed in the photo on page …. and are identified by numbers.
1 – The planetarium described above.
2 – A multiple purpose apparatus: variable scale accelerometer, balance (dynamometer balance), law of Hooke, introduction to the simple harmonic motion.
3 – Wood telemeter.
4 – Original equipment for the study of gases, completely dismountable, in sizes normal and “mini”.
5 – Collection of cheap low frictions carts, with interchangeable mass relation, to produce a number of types of frontal collisions. Grooves in the wheels allow the use on iron rails.
6 – Plastic tube for experiments with gases.
3.5. Structure in parallel.
In parallel here means that the topics do not have to be treated one after the other. They are almost independent from another. That allows a free choice on the part of the teacher and students, according to their preference. Each text with its activity is almost a small project. Since the teacher is enough prepared, different groups can discuss different topics in the same room.
The participants will have an evaluation founded on easily observable ACTIONS expressed by the five basic verbs. The teacher will use the Progress Report sheet like the one below:
Did the Activity
The participants will have to know the “rules of the game” and therefore what is basically expected from them – that they READ, PERFORM THE ACTIVITY, DISCUSS, ADD and COOPERATE in the group work. In the Progress Report there is also a column for “remarks” for the teacher to fill out when appropriate. This kind of evaluation allows the students to build their progress in a continuous and smooth work. It also avoids that such factors as luck or misfortune determine the student’s promotion or failing. In a short while the teacher will have the student’s progress in hand and will be able to know his students better.
3.7. Other features.
The teacher must be alert so that the reading is synchronized within each group. While a student reads, the others follow in their text. The synchronized reading allows difficulties and inadequate understandings to arouse. Therefore, knowledge would be strengthened and difficulties would be lessened. If somebody has a question, somebody else in the group will certainly be able to answer it. If the reading is unbalanced, some students’ difficulties may be the same and remain unnoticed. The peers must be required to show their difficulties, which are one of the most important elements in knowledge building.
The teacher must stimulate and promote a working atmosphere, as well as relaxation and even happiness. Building knowledge this way can offer a chance of enjoying the PLEASURE and the FUN to discover how the world functions.
It´s not advisable that the teacher use any form of coercion or threat, not even low grades. Although opinions may vary within a group, group work serves as an exercise of living together in which the peers share knowledge and friendship (cordiality). Here the session serves also as a daily practice of citizenship.
3.8. Perspectives and difficulties.
Since the formalization of the proposal, around fifty training courses for Physics teacher were given, with an average of twenty-five participants in each. There were five editions (2.000 books each editions), until year ago. Since last year an outstanding publisher has been commercializing them. Even though most of the participants of the training courses feel enthusiasm about the “new” experience, there has been a poorer diffusion of the proposal that one would expect.
The main difficulties for a greater diffusion and acceptance of the project are the following:
a) The teacher fear that their limitations be exposed when they get involved in open discussions, sometimes of unforeseeable courses.
b) Resistance on the part of schools and directors to allow anything out of the traditional. Sometimes, even the physical environment impairs new experiences, for instance the traditional seating arrangement: parallel rows of desks stuck to the floor facing the board.
c) Resistance on part of parents and also students in doing such works that do not guarantee success in the examinations to enter the university.
4. Searching roots.
With the spread of courses, besides the misunderstandings already detected, a new series of conceptual problems seems to become more visible. These misconceptions have to do with the topics treated in the introduction to themes related to Astronomy. In the beginning these subjects appear casually, as a consequence of the open discussions. For examples, the discussions about Kepler’s laws ended up involving topics such as the Earth, the Sun, the motions of the Earth, the days and nights, the seasons, the points of the compass…
Because of some ideas appeared more frequently, they called our attention. Therefore, it was possible to treat these questions more accurately. Some of the questions would surprise us for the ingenuity and inconsistence.
For the objectives of this work, we are going to mention but a few questions which we decide to devote special care to.
All teachers knew the points of the compass: North, South, East and West. All of them knew that they were as a reference for orientation. When asked how to determine these points, most of teachers mentioned the East as the one in which the Sun rises and the West the one in which the Sun sets. Some teachers knew that the rising point of the Sun changes in the course of the year; some had never thought about it.
Almost all of them knew that it´s midday when the Sun is at high noon (zenith). But most of them did not know that the Sun at high noon is rare, even in a tropical country like Brazil. Nobody knew that in most of the Brazilian territory the Sun has never been nor will never be at the high noon. Nobody knew that being tropical is being able to have the Sun at high noon.
All of them knew about seasons: winter, spring, summer and fall. Almost all of them thought that the elliptical orbit of the Earth around the Sun would cause the seasons.
In an ellipsis, the Earth approaches and moves away from the Sun. Summer would be the period when the Earth is near and winter when the Earth is far from the Sun. The fall and spring would occur at intermediate distances.
These questions deserve a special discussion. First of all, neither high school nor higher education programs present these subjects. They are mandatorily present in elementary school programs. Therefore, it was assumed that these subjects would have been taught to the future teachers in elementary school.
Consequently, the following questions are open to discussion:
- Are these topics still taught today?
- If they are, are they taught that way?
- If they were taught to teachers today, could this equivocal knowledge have resisted or survived the higher levels?
In some cases, people remember learning like this in elementary school. These traces were not enough. Because they were taught like this in the past, which does not mean that they will be taught like this now. And, if someone taught like this today, would it be possible to generalize, or at least, to know if this is very frequent?
These questions motivated a new research that would be done in elementary school. This research gave rise to another project, which was addressed to elementary school teachers and ended up being longer than the project that originated the research.
5. A new research and training project.
The results above had shown a need for a research on elementary school teaching. This was possible in a project oriented by the author and coordinated by Professor Yacy A. Leitão at the “Universidade Federal Rural do Rio de Janeiro” (Rural Federal University of Rio de Janeiro), from 1977 on.
In 1978 the first trial took place with thirty-five elementary school teachers. The main goal was to verify if those mistakes detected among Physics teachers were still taught and how they were taught. We were also interested in the whole conception of the world, of science which concerned the teacher’s practice.
Only after hours of discussion was it possible to set up a trusting atmosphere among the teachers. They were obviously afraid of exposing their limitations; but in the end they gave in and got convinced that we wanted to help them.
The results were surprising. All of them, without exception, taught those subjects, which we had detected and were still obligatory in the programs in use, in a completely equivocal way. All teachers confirmed having learned this way. One of the teachers said that she had been teaching those topics for fifteen years.
Our work was to set up a naïve argumentation with which a child could refute all the science he had learned/been taught. From these dialogues a story was born (the story of “Joãozinho da Maré”) which circulates in one of the author’s books (5) (another version exists to be played in three acts, and after that a debate). Argumentations were obviously naïve, those of a child who watches and wants to understand.
A child living in a slum and waking up everyday with the sunshine on his face is able to know that in the course of the year the Sun rises in different points on the horizon. It is a great difference, at least 47 degrees, and it calls one’s attention. The very child wanted to see and check the Sun at high noon, when he left the class at about twelve noon. He could notice with his own eyes that, even at midday, the shadows of the poles were large. Casually, he could have seen, at the end of year in Rio, the day when the shadows of the poles disappeared; and it was not midday. Any child, even in slums, watch television. While this very child is living in an intense heat of forty degrees, the television is showing live an intense winter in countries of the north Hemisphere. Besides Christmas, with a shivering Santa Claus in a “carioca” setting of breathtaking heat. The argument over the approximation and the receding of the Earth in relation to the Sun do not resist a naïve argumentation either. If the Earth came exceptionally near the Sun, in summer the Sun would seem much bigger. The children know that planes, for example, appear much bigger when they come closer and smaller when they move away from them. The Sun appears to be the same size always. A perceptible increase in the size of the Sun would bring about panic on everybody.
After realizing that the science they taught yielded to a child´s arguments, the teachers got prostrate, chiefly the one who said in public that she had been teaching these subjects for more than fifteen years.
The next step on the part of the teachers was to compel us to give them the “right” answers. If we did so, we would go against the character of our proposal. In this case, as in many others, what counts is that the answer may be right or wrong.
Prostrate by their clear-cut mistakes, the teachers begged for help. This reinforced and hastened the elaboration of what would be a new project, specially designed for elementary school teaching. Right after that we started the making of new texts and activities, which should include all those topics and questions already mentioned. These texts and activities are assembled in a book (4), which has been used; a second volume has not been published yet; even though it has been used.
In 1979 the first teacher training course for elementary school was given. Since then, around hundred courses took place, with an average of thirty-five elementary school teachers.
In every course we could enlarge the research on the misunderstandings and mistakes “learned” and “taught” in elementary schools. It is amazing the extent and the depth of the problem: it is not a question of misconceptions or mistakes; most of the teachers have a magic conception of the operation of the world.
This project of elementary school teacher training comprises most of our work. The teaching of Physics is imperative for a citizen of a world whose problems will not be solved without science. Nevertheless, most urgent should be the improvement and reform of the methods used in elementary school teaching, since they seem to influence some factors that condition not only the conception of the world but the initiative into changing it. An elementary school that constrains children to sit for hours and hours, to passively listen to a boring and uninteresting science, will not distort only the scientific conception but will distort and impair one’s initiative; therefore, it will impair the exercise of citizenship (5).
(RELATED TO BOTH PROJECTS)
(1) CANIATO, R. 1973. Um Projeto Brasileiro para o Ensino da Física. Campinas. Unicamp.
(2) CANIATO, R. 1990. O céu. São Paulo. Editora Ática.
(3) CANIATO, R. 1990. Linguagens da Física. Editora Ática.
(4) CANIATO, R. 1990. A Terra em que vivemos. Papirus Editora.
(5) CANIATO, R. 1989. Com Ciência na Educação. Campinas. Papirus Editora.
(6) CANIATO, R. 1987. Que é Astronomia. São Paulo. Editora Brasiliense.
(RELATED TO BOTH PROJECTS)
(1) CANIATO, R. 1973. A Brazilian Project for Physics Teaching. Campinas. Unicamp.
(2) CANIATO, R. 1990. The Sky. São Paulo. Editora Ática.
(3) CANIATO, R. 1990. Languages of Physics. Editora Ática.
(4) CANIATO, R. 1990. The Earth on which we live. Papirus Editora.
(5) CANIATO, R. 1989. Conscience in Education (in Portuguese “com ciência” is a pun; it means with science and also conscience). Campinas. Papirus Editora.
(6) CANIATO, R. 1987. What is Astronomy. São Paulo. Editora Brasiliense.
Quem sou eu
- Rodolpho Caniato
- Campinas, São Paulo, Brazil
- Rio de Janeiro em 1929. Bacharelado e Licenciatura em Matemática(PUC Rio, USP e PUCCAMP,1956).Cursos no exterior:”Advanced Topics”, Universidad Nacional de Chile,1964, “Vibrations and Waves”, Reed College, Oregon,USA,1965. Cursos no Brasil:Curso “Phywe” para professores de Física na AEC(Rio,1958), PSSCC Physics com os autores(1962).Doutorado (Física UNESP,1974) com a tese “Um Projeto Brasileiro para o Ensino de Física”,orientador Prof.J.Goldemberg, grau máximo. Ex-professor da PUCCAMP(1957-69),UNESP(1979—74),USP(visitante,197678),UNICAMP(1972-76), UFRRJ,Rio(1976,aposentado 1993). Autor dos livros: “O céu” e “As linguagens da Física” da Atica,”Com(ns)Ciência da Educação”(Papirus), “A Terra em que vivemos” da Atomo, “O que é Astronomia”da Brasiliense e “(Re)Descobrindo a Astronomia” da Atomo. Docência de cursos sobre os próprios livros em muitos países da América Latina(1974-1988), além de todas regiões do Brasil.