Val Voroshilov
Teaching Labs Tech Coordinator,
Physics Department, BU
590 Comm. Ave, #B31
Boston, MA 02215
617-353-2602
www.beaplus.com
 
During my previous life I have had a rich experience of working with school and college students and teachers.
As a teacher and researcher, I see the next possible direction for my potential educational work:

	The action	The idea
1	Training a group of students to Math/Physics competitions	Developing of an experience of solving nontraditional Math/Physics problems
2	Training a group of students to Math/Physics problem-solving strategies	Developing specific Math/Physics style of thinking/reasoning
3	Working on Integrated Math/Physics curricula	Considering Math as a language of Physics and Physics as an applied Math, study Math and Physics cooperatively
4	Working with the group of high school teachers developing the themes 1 - 3	Building the channel for systematic implementation of new educational resources into the teaching practice

 
During the teaching work the further research could be proceeded:
1.Classification of common mistakes and misunderstandings of students during problem solving in Math/Physics.
2.Classification of common reasons of common mistakes and misunderstandings of students.
3.Developing set of learning aids to help students to overcome difficulties during problem solving in Math/Physics.
 
The research can be understood as parts of two complex long-running projects:
1. Study of the influence of teaching methods on the developing of students’ brain (see App. 1). I believe, the cooperation with physiologist and neurologists could be very helpful for this project.
2. Developing Integrated Open Online Math/Physics course (see App. 2).
The last project can include as a part a developing the Virtual Physics Teaching Laboratory (see App. 3).

App. 1

I find as one of the most interesting problems of educational science is the problem of the influence of training methods on the functioning of a student’s brain. I will use an analogy. Let us assume that students have been doing for years one type of physical exercises only - squats. Then in the end of education, they can squat many times without any difficulties. However, all the muscles have not been involved in the exercise would be not developed. Students would not be able to do other exercises. A brain works the same way. If for years the majority of lessons were based on memorizing and reproduction, other kinds of intellectual activities would be difficult for students to produce. I believe that any school subject should work at the first place as a tool for “brainbuilding” and then as a tool for “knowledgebuilding”.

It is obvious that there is dependence, a link, a relationships, a bind, a connection between a brain and intelligence. In particular, we can observe the consequences of that dependence in a variety of human behavior.

We have two supplemental questions:

1. How dose the brain control behavior?

2. How dose behavior influence on the brain?

I would suggest that those questions are two parts of the next one: How dose the brain know/learn how to behave?

Talking abut how dose behavior influence on the brain, let’s start from the simple assumption.

Let’s say, the brain is like a muscle, from a birth it has some starting structure, shape, level of development, but further physiological development of the brain is possible under loading, under exercises only. To develop different “sub-muscles” of the brain different exercises are needed.

It seems obvious that the physiological base of the developed intelligence must be the developed brain. Intelligence is an ability of creating (not just finding/searching) solutions of problems. The more difficult problem can be solved, the more developed intelligence has the problem solver.

The common, natural, ordinary way/mechanism of finding/constructing (i.e. finding as building, not as searching) any solution is making links, connections, ties, relationships, bonds between facts, phenomena, thoughts, rules, laws, interpretations, feelings, visions etc. Any sentences, arguments, logical conclusions are created from words, signs, symbols, sounds which are stored into a memory. The logical or emotional links, relationships between words, signs are based on chemical-electrical connections, bonds between some neurons or other structural parts of the brain. So, any logical chain or chain of behavioral actions is a reflection of some electrochemical chain of signals through the brain. Hence, the ability of the brain for making chains of electrochemical signals is the physiological base of the ability for making logical or behavioral chains. The electrochemical structure of the brain is the physiological base of the thinking, reasoning, etc.

Reasoning, conclusions, points of view, opinions are just the network of words/signs connected by a their meanings (and escorted by emotions). Such a kind of connections can be easily visualized. For example, in Physics, we can represent the main logical connections between the terms (mostly physical quantities) as a vertex-edge graph. A vertex represents a term and an edge represents a connection (in Physics, usually an algebraic connection) between two terms.

The picture below is an example of a possible visualization (Fig. 1).

For example, here the vertex # 8 represents displacement DS, the vertex # 16 represents time Dt taken for that displacement, the vertex # 17 represents the average velocity v_av. The edges (segments) 8 - 16, 8 - 17 and 16 – 17 all are represent the same connection/equation v_av = DS/Dt, etc (see details on SOCC; also this graph can be used also to calculating the difficultness of Physics problems).

Any logical reasoning (and even non-logical) can be represented as a journey throughout such a graph/map of sense-vertexes and operation-edges (there are interesting questions such as what is the dimension of the logical space the map of which is just two-dimensional, or what is a topology of the graph, also we can use the graph to determine the level of difficulty of the reasoning/problem/solution by calculating the vertexes and edges involved in them).

Fig. 1

There is an obvious consequent from this point of view on the reasoning. There are no “naked” words in the language of any human being (the term was taken from physics, for example “a naked electron”). We can write and pronounce the combination of sounds “hleb”, but it will be not a word for us, it dose not make any sense. However, If you were a Russian, you would get a lot of associations when you herd it, but for getting the same associations you have to hear the combination of sounds “a bread”. The accompanied associations actually make the meaning of the word, they make this combination of sounds be a word. So, “naked word” is just an abstract, any word is a word just because of links/connections with other words or objects, pictures, signs, emotions, visions etc. Any word is always a cluster.

We can describe the process of constructing of the solution of a problem as a process of constructing the vertex-edge chains, which represent the logical structure of the solution. The process of constructing of electrochemical chains in the brain is the base of the former process. By some reasons the first word/cluster have got activated (the problem was proposed to the owner of the brain). This simple model assumes that a physiological carrier of a word/term/sense has just to possible states: active and inactive. Same is correct for the physiological carriers of a connections (edges represent them). First the set of certain memory elements is getting activated. Then the activity transfers (by the activated connections) to the memory elements in the vicinity of the originally activated (there is no acting in a distance). I believe (I took it from my teaching experience, from my empiric observation and from law of conservation of energy) the every certain brain (i.e. a person) at any certain moment of time has a certain finite/limited/fixed “activating energy”. That means the brain cannot keep in active state more active memory elements and connections then it is given/defined by its nature (genetic basis) and by the history of training/developing (educational basis).

If a person has a well-trained brain he or she can keep in active state a lot of memory elements and connections for a long time, hence be able to construct the long-leading logical (and sub-logical) chains or construct heave-weighted clusters of associates.

For example, a chess player can make a long-leading mental calculations of the further moves (the long-leading chain), or the composer can hear in the brain the dozens of musical instruments plying.

Initially activated memory elements can activate the neighbors, the neighbors can activate their neighbors and so on. But the total number of elements can be in active state is limited. So, to main configurations can be created by the active elements.

The first one is a long-leading chain (Fig. 2)

Fig. 2

There is a spine of primary activated elements and the secondary activated elements.

The second one is a cluster (Fig. 3).

Fig. 3

There is the primary activated element and the circle of secondary activated elements (and thirdly, etc).

The real brain is operating by a mixture of that kind of objects.

The longer the long–leading chain, the thinner it is, and versus versa.

The total number of possibly activated elements and connections is fixed, it is a constant for the certain moment of time, but this constant could be developed by exercises.

Today we do not study the influence of teaching methods on that brain constant. But I think this problem very soon will be the # 1 problem in educational psychology. I believe the special theory and practice (brain-building) will be very helpful to construct new education.

Every school subject can be researched in that point of view. Physics and Math are very good for brain development. But theater is too (because of the necessity of controlling arms and legs and a body and the voice and etc), music is as well (it is uneasy governing of ten fingers and a foot plying a piano).

Plus a special subject can be developed. Brain-muscle must being developing as often as just regular muscles. The simple analogy: the regular school subjects for students are like a regular exercises for a basketball player, and the specifically designed “brainbuilding” is like a training of special moves.

And again, it is important to repeat; the earlier the “brainbuilding” starts, the more developed will be the brain. The children have a so syncretic brain that connects everything with everything. Elders have troubles making new connections. If we reverse the time axis, we have to say that the brain of unborn or just born baby is the most flexible brain ever. In that period of life the brain is constructing the basis of its action-reaction functions (sort of imprinting). During this period of time the brain is finding the most interesting/in-a-future-important signals (regions of signals) and reactions on the signals (future skills in music, math, maybe even sexuality, for example, when a father is kissing and touching his son or a mother is kissing and touching her daughter).

App. 2

Let's carry out a mental experiment. Let us assume, hypothetically, that we created a group of the best designers/inventors of car wheels and gave them out everything that they have asked for to do their job. Then we have separately formed a group of the best designers of car engines. Plus, we have independently formed a group of the best cars’ body designers, etc. The groups have invented the best wheels in the world, the best engine in the world, the best auto body in the world, etc. Now ask yourself, what will turn out, if we try to put all these best auto parts together? The obvious answer - nothing! They will not match to each other.

Absolutely the same situation we can observe now in education. Someone writes fine textbooks for middle school students. Other persons independently write a collection of problems for the high school students. A third person creates an electronic encyclopedia for students at the college level, and etc. Each didactic tool can be helpful for students of a certain grade, but they do not match to each other.

From this point of view, probably, one of the most effective tools for developing a system of education is an Open-On-Line-School, which allows getting a high quality on-line education for millions of students (at least high school students). I am sure that a creation of an Internet based educational complexes will raise the quality of education to the next level (at least because of making harder a competition on the educational field). Such an educational complex should include the full curriculum of a subject from an initial level of studying up to graduate level, and also a full set of electronic textbooks, sets of tasks/problems, training and testing computer programs and other didactic tools which are necessary to help ANY student to master a subject (in ideal situation – without any help of a teacher; which is impossible, however can be keeping in a mind as a horizon of research). Publishing this materials on Internet leads automatically to necessity of making the materials adjusted to any possible kind of a student, hence the integrity of the materials must by very high.

One of the most interesting problems, which should be solved to create such an educational complex, is a modeling of mental processes, which are “boiling” in a student’s head during a problem solving situation. Today’s computer based teaching software cannot compete a teacher in this teaching/learning situation, because the software do not have a possibility of adjusting on a students’ strangeness and weaknesses.

App. 3

We can find a lot of computer based simulations today, but there is no still a real virtual lab. The real virtual physics lab must allow student, for example, do the all actions necessary to prepare a lab and to take a dates. Student has to go first in the virtual stockroom, take from virtual shelves virtual devices, power supplies, wires and etc., put together the setup and try to get dates (if the setup was put up correctly, in the other case a student can try rearrange the setup) and than try to analyze the dates. Plus, this kind of software has to be open to allow to anybody to put a new virtual device on the virtual shelf.