© Grigori TOMSKI, UNESCO/FIDJIP, 1997
1. Introduction
The JIPTO system is a series of methods used succesfully in Siberia to stimulate creativity through education games ('Jeux Intellectuels de poursuite de Tomski'). There are more and more JIPTO enthusiasts in Europe and the United States. The main components of this education system are:
1) early exposure of children (aged 4 to 6) to intellectual sport through 'Sonor' and other JIPTOs;
2) making the pieces and board using local craft traditions;
3) introduction to technical creativity by making pieces and boards both mechanical and electronic;
4) taking part in the organization of competitions to improve organizochanal and public speaking skills.
5) performance analysis to improve players' standards;
6) analysis of game positions and strategies by elementary mathematical methods.
It is fascinating to create a new game, to launch and to watch its theoty develop. True JIPTO specialists and enthusiasts choose the game for the elegance and intelligibility of its theory. That game then becames one of their favorite pastimes.
During the International Forum on Scientific and Technological Literacy for All held in July 1993 at UNESCO Headquarters, specialists and enthusiasts of the JIPTO system decided to set up the Fédération internationale du Système JIPTO (FIDJIP).
In this article, we shall explain how that federation can take part in the development of scientific
and technological literacy for all.
2. Birthplace of JIPTOs
Virtually unremitting warfare in the Turkish-Mongol region compelled several groups to move out in search of a more peaceful place to live. We still do not know today, however, when and how the first horse-riding people speaking Turkic and Mongoloid dialects found the extensive pastures in the Lena and Viluy valleys, so far away from the Southern Siberian steppes.
The indigenous population, who lived by hunting and reindeer-bree- ding in the taiga, the tundra and the mountains, allowed the newcomers to settle in the wide fields that they did not need. They traded furs for crafts and metal work. Well before the arrival of the Russians in the seventeenth century, the descendants of these Turkic and Mongoloid groups and part of the Tungusic and Paleo-Asiatic tribes had formed a new people, the Sakha. So my people was born, better known hitherto by the corrupt form of the name, Yakuts, who today number more than 400,000 and occupy a vast area more than 3,000,000 km² in North-West Siberia.
For a long time, the land of the Sakha (Yakutiya) was a 'fortress without walls' for the Sakha and the other indigenous peoples who lived there, mainly because of its extremely harsh climate. Temperature can plummet to -70°C in winter and soar 40°C in summer. The Sakha were cut off from other Turkic and Mongoloid peoples before the latter embraced the Muslim and Buddhist religions.
In this isolation, the Sakha people's cultural and intellectual develop- ment was to take a highly distinctive course, preserving very ancient traditions that have long disappeared from Central Asia and Mongolia.The epic Sakha poems often have tens of thousands of lines and are full of scenes of the chase. The verses were recited and the words of the characters chanted over several evenings. This activity was a powerful source of joy and comfort in the long, cold darkness of the Arctic night. Small wonder, then, that the Sakha greet the arrival of summer and the blossoming of nature with extraordinary festivities.
The festival (Yassyakh), which lasts for several days during the second half of June, is, in my opinion, the expression of those 'ceremonial games' that, to quote Roger Caillois 'are a feature of nearly all great civilizations'. Being long untouched by outside word and retaining the patterns of development of the ancient South Siberian civilizations, the Sakha culture treated this annual
event with great solemnity. The festival starts with a traditional ceremony conducted by Tangra priests (white shamans). At one time, Tangarism was a religion that spread as far as the Balkans.
All sorts of competitions are then held. Archery, two or three types of wrestling, three types of jumping, horse racing and competitions of leaders of round-dances can last
several days.
Games inspired by the Great Summer Festivals are occasionally held in nursery and primary schools in winter. Because of climatic conditions, people regularly play mentally challenging games. Draughts, known to the Turkic and Mongoloid peoples since time immemorial, is very popular.
I often used to devote my free time to the invention of intellectual games in which I endeavoured to combine the Sakha's passion for games of pursuit with my scientific and educational activites.
My favorite JIPTO, 'Sonor', very quickly became popular in our Repablic, whose population is scattered over an area six times the size of France. The Ministry of Education of the Sakha Republic decided to introduce JIPs in all nersery schools. The Ministry of Youth and Sport set up the 'Sonor' Federation. Public opinion and the press in our Republic recognized that 'Sonor' had
become the national educational game of the Sakha and a feature of our modern culture.
3. The board and the pieces
Anyone can make a cloth or paper 'Sonor' board (mat) and pieces (draughts pieces may be used initially).
Draw a 30 x 40 cm rectangle.
Mark the starting-point of the 'pursuer' in the middle of the ghort right-hand of the rectangle.
Mark the starting-points of the five 'fugitives' on the left-hand side of the rectangle.
Draw tree lines, 1 cm, 10 cm and 19 cm away from the rigth-hand side of the rectangle.
There must be six pieces for the 'fugitive' (one held in reserve) and two pieces for the 'pursuer'(one held in reserve).
The base of the pieces must be round: it is used as a means of measurement when the pieces are moved. They can move in any direction (no squares are drawn on the board). The recommended diameter is 2 cm.
You can start to play by marking out the board on paper or cardboard, using neutral pieces, but above all, do not forget that an attractive board and pieces relevant to dally life (cottage industry, family history) constitute one aspect of the game's interest for children's hands and eyes. In Siberia, the pieces used represent characters or animals from legends or well-known children's stories.
For France the theme of the fox and hens would strike a chord with children, or a wolf ond five Red Riding Hoolds, a Pied Piper of Hamelin and childrin, five wild horses and a trainer trying to get close to them.
It is useful to have several sets of pieces available: the child chooses the set that strikes its fancy
at a particular moment.
Sakha pieces are crafted locally of carved wood, mammouth ivory, reinder antlers, cut stone, etc.
A board that is pleasing to the eye and touch could be made of cloth with embroidered lines or areas marked off by strips of cloth of different colours (patchwork), painted wood, coloured leather, etc.
4. Basic rules
Aim of the game. The 'fugitivs' try to reach the other side of the board without being touched by the 'pursuer': the latter tries to capture the 'figitives' as far away as possible from its own side, i.e. before they cross lines III, II and even, if possible, I.
Moves. A move is made in one or more consecutive steps. A step is made as follows: press the piece to be moved so that it is immobilized on the board; put the reserve piece next to and
touching it, facing the chosen direction; then remove the first piece, wich in turn becomes the 'reserve' for the next move. At the beginning of the game, each 'fugitive' takes a step or stays still. Next, the 'pursuer' maker one move consisting of two steps. Then comes the turn of the 'fugitives' again, and so on.
In the version described above, the pieces used are same size, wich means that the 'pursuer' moves at twice the speed of 'fugitives'. The 'pursuer' is often as big as the 'fugitives', in which case the players make moves consisting of the same number of steps.
Capture. A 'fugitive' which prevents the 'pursuer' from moving foward or touches
it after the latter has moved forward is captured and removed from the play area.
Points. Each 'fugitive' which manages to touch line I, II or III before being captured, scores a point for each line reached (in other words, if it reaches line I, it scores 1 point, if it reaches line II, it scores 2 points and if it reaches line III, it scores 3 points).
After the first half of the game, the players exchange pieces and play the second half. The winner is determined by comparing the scores of the 'fugitives' in these two halves of the game. If there is a draw, the winner is the one who has moved the most 'fugitives' up to the line III. If this rule does not suffice, other conditions may be introduced.
5. Practical advice
At the beginning of a game, it is preferable to speed up the movement of the pieces a little. The 'fugitives' may be allowed to make moves of a few steps; the 'pursuer' will then be entitled to respond by twice as many steps as any 'fugitive'. The procedure is as follows: before playing, the 'fugitives' state the maximum number of steps desired; the 'pursuer' may then either accept
that proposal ar set the maximum number of steps at a lower figure. This decision is final - none of the 'fugitives' is entitled to overstep this set maximum number of steps, while the 'pursuer' cannot make more than twice that number of steps.
This procedure speeds up the beginning of the game considerably. Very soon, the 'fugitives' are moving in single steps as the time comes to make shrewd manoeuvres.
To shorten a game, two halves may be played simultaneously on two boards. The player who moves 'fugitives' forward on one board must of course move the 'pursuer' forword on
the other.
Many families have a visually attractive version of the 'Sonor' game, which is a real luxury item and an ornament to the home. Children aged 3 to 4 who see adults and older children
playing, enjpy handling the pieces, which often represent animals.
They often ask adult to play xith them. Small children do not, of course, start to play immediately according to the rules set out above, but they are gtadually drawn into the game.
It is enough to show a 5- or 6-yeard old the game two or three times and to play with him or her occasionally.
One may start off with only two 'fugitives'. First, the child learns about the movement of the pieces, then the purpose of the game, and then he or she starts to think about improving performance.
The game described above is something like draughts, except that in JIPTO a piece may be moved in any direction (in draughts, movement is possible in two derections only). Whereas
the number of games in chess or draughts is very large but finite, in JIPTO, with very simple rules, the number of games is infinite. This explains the rich strategic potential of JIPTOs.
6. The JIPTO system
The JIP system encompasses all the different methods of stimulating children's creativity through JIPTO games. Uere is how it is played by enthusiasts.
Nursery and primary-school children. Early exposure of children (aged 4 to 6) to intellectual sport by means of the 'Sonor' and other JIPTO games. The chid plays 'Sonor' at early age finds it easy to learn to play chess and other intellectual games.
From their first contact with the game, small children learn the appropriate verses, songs and riddles for the characters whom the pieces in the game represent. Through the game, children discover their surroundings and native culture and begin to develop language skills. The game
also helps them to learn number and geometry.
Secondary-school children. Development of a centre of interest for the child. It has been very
often shown that play, closely linked to exploratory behaviour and curiosity, is the driving force of learning and discovery. Children who have experience of these games and the exploration that they entail are capable of finding many things interesting in traditional educational curricula, in their environment and the media. This centre of interest, being sufficienly multi-faceted and varied, often enables them to put acquired knowledge to immediate use.
Then comes the time when the child starts to analyse the games played to improve his or her standart of play. This is the phase of analytical activity and metal gymnastics; this is already research: observation of games, analysis of different situations, conjecture, and formulation of ever more sophisticated strategies. JIP games can even be played with a pen and transparent
perforated ruler and a record kept on paper. JIP enthusiasts can work out mathematical rules for optimum moves in certain game situations. This kind of research encourages children to deepen and broaden the knowledge they gain at school more effectively than does the mere
repetition of ordinary lessons. A good grouding in mathematics is acquired through such research, even in the even of failure to demonstrate the hypothesis formulated or even if the hypothesis is false.
The infinite world of JIPs also affronds many opportunities for basic learning about computer programming.
Artistic and manual creativity. It is important for children to make the pieces and the boards, because they like to play with games that they have made themselves. It is an opportnuty to co-operate with others, to design and complete projects and the experiment; they produce games based on an idea of their own, of several children or of the family; parents may intervence to provide guidance, to help them to think things through or to point out problems. This manual
activity brings children into contact with different types of materials, develops their sensory capacities and gives their imagination free rein.
7. Conclusion
FIDJIP was organized on the initiative of l'UNESCO and its Project 2000+ Secretariat for the devlopment of scientific and technological literacy for all with a view to promoting
JIPTO games that draw on elementary mathematical theory.
This theory forms a unique branch of modern mathematics that is within the grasp of secondary-school teachers and pupils. Accordingly, elements of that theory are beginning to be included in mathematics syllabuses in specialized secondary schools.
Traditional intellectual games that have been played for centuries are unfortunately based on abstract patterns. That prevents those children from being introduced to them at a very young age. Even the grand masters, for example, admit that they started playing chess around the age 11. Several new games also rely on potential pattern. It is important, however, to expose children to intellectual games as early as possible.
JIPTO games are perfectly suited to that purpose because they model real or invented activities of pursuit.
Advanced JIPTO players can use mathematics to work out optimum action rules for specific game situations. If a given proposition based on analysis of games played or a specially
directed experiment has not been formulated before, research into ways of demonstating it is one of the most interesting and difficult forms of scientific activity.
Competitions by correspondence may be organized in ten or more stages, using the Olimpic method, with many participants from different countries taking part in JIPTO games with a small number of moves? That will facilitate the rapid spread of these games, bonding among players and axchanges of experience. The fees paid by participants in these competitions will normally provide the necessary resources for holding ordinary competitions for more gifted JIPTO players - 'JIPTO artists and masters'.
FIDJIP would also like to hold an international competition on solving elementary theory of pursuit of pursuit problems. Wide dissemination of JIPTOs result in the devlopement of the elementary theory of pursuit by the most active JIP enthusiasts, mathematics teachers, and particularly gifted students and pupils. We might then call this new phenomenon 'popular mathematics".
1. Introduction
The JIPTO system is a series of methods used succesfully in Siberia to stimulate creativity through education games ('Jeux Intellectuels de poursuite de Tomski'). There are more and more JIPTO enthusiasts in Europe and the United States. The main components of this education system are:
1) early exposure of children (aged 4 to 6) to intellectual sport through 'Sonor' and other JIPTOs;
2) making the pieces and board using local craft traditions;
3) introduction to technical creativity by making pieces and boards both mechanical and electronic;
4) taking part in the organization of competitions to improve organizochanal and public speaking skills.
5) performance analysis to improve players' standards;
6) analysis of game positions and strategies by elementary mathematical methods.
It is fascinating to create a new game, to launch and to watch its theoty develop. True JIPTO specialists and enthusiasts choose the game for the elegance and intelligibility of its theory. That game then becames one of their favorite pastimes.
During the International Forum on Scientific and Technological Literacy for All held in July 1993 at UNESCO Headquarters, specialists and enthusiasts of the JIPTO system decided to set up the Fédération internationale du Système JIPTO (FIDJIP).
In this article, we shall explain how that federation can take part in the development of scientific
and technological literacy for all.
2. Birthplace of JIPTOs
Virtually unremitting warfare in the Turkish-Mongol region compelled several groups to move out in search of a more peaceful place to live. We still do not know today, however, when and how the first horse-riding people speaking Turkic and Mongoloid dialects found the extensive pastures in the Lena and Viluy valleys, so far away from the Southern Siberian steppes.
The indigenous population, who lived by hunting and reindeer-bree- ding in the taiga, the tundra and the mountains, allowed the newcomers to settle in the wide fields that they did not need. They traded furs for crafts and metal work. Well before the arrival of the Russians in the seventeenth century, the descendants of these Turkic and Mongoloid groups and part of the Tungusic and Paleo-Asiatic tribes had formed a new people, the Sakha. So my people was born, better known hitherto by the corrupt form of the name, Yakuts, who today number more than 400,000 and occupy a vast area more than 3,000,000 km² in North-West Siberia.
For a long time, the land of the Sakha (Yakutiya) was a 'fortress without walls' for the Sakha and the other indigenous peoples who lived there, mainly because of its extremely harsh climate. Temperature can plummet to -70°C in winter and soar 40°C in summer. The Sakha were cut off from other Turkic and Mongoloid peoples before the latter embraced the Muslim and Buddhist religions.
In this isolation, the Sakha people's cultural and intellectual develop- ment was to take a highly distinctive course, preserving very ancient traditions that have long disappeared from Central Asia and Mongolia.The epic Sakha poems often have tens of thousands of lines and are full of scenes of the chase. The verses were recited and the words of the characters chanted over several evenings. This activity was a powerful source of joy and comfort in the long, cold darkness of the Arctic night. Small wonder, then, that the Sakha greet the arrival of summer and the blossoming of nature with extraordinary festivities.
The festival (Yassyakh), which lasts for several days during the second half of June, is, in my opinion, the expression of those 'ceremonial games' that, to quote Roger Caillois 'are a feature of nearly all great civilizations'. Being long untouched by outside word and retaining the patterns of development of the ancient South Siberian civilizations, the Sakha culture treated this annual
event with great solemnity. The festival starts with a traditional ceremony conducted by Tangra priests (white shamans). At one time, Tangarism was a religion that spread as far as the Balkans.
All sorts of competitions are then held. Archery, two or three types of wrestling, three types of jumping, horse racing and competitions of leaders of round-dances can last
several days.
Games inspired by the Great Summer Festivals are occasionally held in nursery and primary schools in winter. Because of climatic conditions, people regularly play mentally challenging games. Draughts, known to the Turkic and Mongoloid peoples since time immemorial, is very popular.
I often used to devote my free time to the invention of intellectual games in which I endeavoured to combine the Sakha's passion for games of pursuit with my scientific and educational activites.
My favorite JIPTO, 'Sonor', very quickly became popular in our Repablic, whose population is scattered over an area six times the size of France. The Ministry of Education of the Sakha Republic decided to introduce JIPs in all nersery schools. The Ministry of Youth and Sport set up the 'Sonor' Federation. Public opinion and the press in our Republic recognized that 'Sonor' had
become the national educational game of the Sakha and a feature of our modern culture.
3. The board and the pieces
Anyone can make a cloth or paper 'Sonor' board (mat) and pieces (draughts pieces may be used initially).
Draw a 30 x 40 cm rectangle.
Mark the starting-point of the 'pursuer' in the middle of the ghort right-hand of the rectangle.
Mark the starting-points of the five 'fugitives' on the left-hand side of the rectangle.
Draw tree lines, 1 cm, 10 cm and 19 cm away from the rigth-hand side of the rectangle.
There must be six pieces for the 'fugitive' (one held in reserve) and two pieces for the 'pursuer'(one held in reserve).
The base of the pieces must be round: it is used as a means of measurement when the pieces are moved. They can move in any direction (no squares are drawn on the board). The recommended diameter is 2 cm.
You can start to play by marking out the board on paper or cardboard, using neutral pieces, but above all, do not forget that an attractive board and pieces relevant to dally life (cottage industry, family history) constitute one aspect of the game's interest for children's hands and eyes. In Siberia, the pieces used represent characters or animals from legends or well-known children's stories.
For France the theme of the fox and hens would strike a chord with children, or a wolf ond five Red Riding Hoolds, a Pied Piper of Hamelin and childrin, five wild horses and a trainer trying to get close to them.
It is useful to have several sets of pieces available: the child chooses the set that strikes its fancy
at a particular moment.
Sakha pieces are crafted locally of carved wood, mammouth ivory, reinder antlers, cut stone, etc.
A board that is pleasing to the eye and touch could be made of cloth with embroidered lines or areas marked off by strips of cloth of different colours (patchwork), painted wood, coloured leather, etc.
4. Basic rules
Aim of the game. The 'fugitivs' try to reach the other side of the board without being touched by the 'pursuer': the latter tries to capture the 'figitives' as far away as possible from its own side, i.e. before they cross lines III, II and even, if possible, I.
Moves. A move is made in one or more consecutive steps. A step is made as follows: press the piece to be moved so that it is immobilized on the board; put the reserve piece next to and
touching it, facing the chosen direction; then remove the first piece, wich in turn becomes the 'reserve' for the next move. At the beginning of the game, each 'fugitive' takes a step or stays still. Next, the 'pursuer' maker one move consisting of two steps. Then comes the turn of the 'fugitives' again, and so on.
In the version described above, the pieces used are same size, wich means that the 'pursuer' moves at twice the speed of 'fugitives'. The 'pursuer' is often as big as the 'fugitives', in which case the players make moves consisting of the same number of steps.
Capture. A 'fugitive' which prevents the 'pursuer' from moving foward or touches
it after the latter has moved forward is captured and removed from the play area.
Points. Each 'fugitive' which manages to touch line I, II or III before being captured, scores a point for each line reached (in other words, if it reaches line I, it scores 1 point, if it reaches line II, it scores 2 points and if it reaches line III, it scores 3 points).
After the first half of the game, the players exchange pieces and play the second half. The winner is determined by comparing the scores of the 'fugitives' in these two halves of the game. If there is a draw, the winner is the one who has moved the most 'fugitives' up to the line III. If this rule does not suffice, other conditions may be introduced.
5. Practical advice
At the beginning of a game, it is preferable to speed up the movement of the pieces a little. The 'fugitives' may be allowed to make moves of a few steps; the 'pursuer' will then be entitled to respond by twice as many steps as any 'fugitive'. The procedure is as follows: before playing, the 'fugitives' state the maximum number of steps desired; the 'pursuer' may then either accept
that proposal ar set the maximum number of steps at a lower figure. This decision is final - none of the 'fugitives' is entitled to overstep this set maximum number of steps, while the 'pursuer' cannot make more than twice that number of steps.
This procedure speeds up the beginning of the game considerably. Very soon, the 'fugitives' are moving in single steps as the time comes to make shrewd manoeuvres.
To shorten a game, two halves may be played simultaneously on two boards. The player who moves 'fugitives' forward on one board must of course move the 'pursuer' forword on
the other.
Many families have a visually attractive version of the 'Sonor' game, which is a real luxury item and an ornament to the home. Children aged 3 to 4 who see adults and older children
playing, enjpy handling the pieces, which often represent animals.
They often ask adult to play xith them. Small children do not, of course, start to play immediately according to the rules set out above, but they are gtadually drawn into the game.
It is enough to show a 5- or 6-yeard old the game two or three times and to play with him or her occasionally.
One may start off with only two 'fugitives'. First, the child learns about the movement of the pieces, then the purpose of the game, and then he or she starts to think about improving performance.
The game described above is something like draughts, except that in JIPTO a piece may be moved in any direction (in draughts, movement is possible in two derections only). Whereas
the number of games in chess or draughts is very large but finite, in JIPTO, with very simple rules, the number of games is infinite. This explains the rich strategic potential of JIPTOs.
6. The JIPTO system
The JIP system encompasses all the different methods of stimulating children's creativity through JIPTO games. Uere is how it is played by enthusiasts.
Nursery and primary-school children. Early exposure of children (aged 4 to 6) to intellectual sport by means of the 'Sonor' and other JIPTO games. The chid plays 'Sonor' at early age finds it easy to learn to play chess and other intellectual games.
From their first contact with the game, small children learn the appropriate verses, songs and riddles for the characters whom the pieces in the game represent. Through the game, children discover their surroundings and native culture and begin to develop language skills. The game
also helps them to learn number and geometry.
Secondary-school children. Development of a centre of interest for the child. It has been very
often shown that play, closely linked to exploratory behaviour and curiosity, is the driving force of learning and discovery. Children who have experience of these games and the exploration that they entail are capable of finding many things interesting in traditional educational curricula, in their environment and the media. This centre of interest, being sufficienly multi-faceted and varied, often enables them to put acquired knowledge to immediate use.
Then comes the time when the child starts to analyse the games played to improve his or her standart of play. This is the phase of analytical activity and metal gymnastics; this is already research: observation of games, analysis of different situations, conjecture, and formulation of ever more sophisticated strategies. JIP games can even be played with a pen and transparent
perforated ruler and a record kept on paper. JIP enthusiasts can work out mathematical rules for optimum moves in certain game situations. This kind of research encourages children to deepen and broaden the knowledge they gain at school more effectively than does the mere
repetition of ordinary lessons. A good grouding in mathematics is acquired through such research, even in the even of failure to demonstrate the hypothesis formulated or even if the hypothesis is false.
The infinite world of JIPs also affronds many opportunities for basic learning about computer programming.
Artistic and manual creativity. It is important for children to make the pieces and the boards, because they like to play with games that they have made themselves. It is an opportnuty to co-operate with others, to design and complete projects and the experiment; they produce games based on an idea of their own, of several children or of the family; parents may intervence to provide guidance, to help them to think things through or to point out problems. This manual
activity brings children into contact with different types of materials, develops their sensory capacities and gives their imagination free rein.
7. Conclusion
FIDJIP was organized on the initiative of l'UNESCO and its Project 2000+ Secretariat for the devlopment of scientific and technological literacy for all with a view to promoting
JIPTO games that draw on elementary mathematical theory.
This theory forms a unique branch of modern mathematics that is within the grasp of secondary-school teachers and pupils. Accordingly, elements of that theory are beginning to be included in mathematics syllabuses in specialized secondary schools.
Traditional intellectual games that have been played for centuries are unfortunately based on abstract patterns. That prevents those children from being introduced to them at a very young age. Even the grand masters, for example, admit that they started playing chess around the age 11. Several new games also rely on potential pattern. It is important, however, to expose children to intellectual games as early as possible.
JIPTO games are perfectly suited to that purpose because they model real or invented activities of pursuit.
Advanced JIPTO players can use mathematics to work out optimum action rules for specific game situations. If a given proposition based on analysis of games played or a specially
directed experiment has not been formulated before, research into ways of demonstating it is one of the most interesting and difficult forms of scientific activity.
Competitions by correspondence may be organized in ten or more stages, using the Olimpic method, with many participants from different countries taking part in JIPTO games with a small number of moves? That will facilitate the rapid spread of these games, bonding among players and axchanges of experience. The fees paid by participants in these competitions will normally provide the necessary resources for holding ordinary competitions for more gifted JIPTO players - 'JIPTO artists and masters'.
FIDJIP would also like to hold an international competition on solving elementary theory of pursuit of pursuit problems. Wide dissemination of JIPTOs result in the devlopement of the elementary theory of pursuit by the most active JIP enthusiasts, mathematics teachers, and particularly gifted students and pupils. We might then call this new phenomenon 'popular mathematics".
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