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Memoirs of a Maverick Mathematician Chapter 1: Papua New Guinea

© 1999, Zoltan P. Dienes. All rights reserved.


“How would you like to have a look at one of our schools?”, said the Director of Education of the then Territory of Papua New Guinea, as he was sitting comfortably in his air conditioned office.

“Sure thing”, I replied “I suppose this is what the Minister for Territories sent me here to do”

Port Moresby was then a straggling “town”, or rather a large village, built along the South coast of Papua. There were not many roads that radiated from Port Moresby, and those that existed came to abrupt ends in the most unlikely places. If you wanted to go anywhere, you had to go by plane, walk or get a ride in a native canoe! The director and I drove along the dusty roads for a short distance from his offices and pulled up outside a very modern building, which the director assured me was one of their schools. I was duly introduced to the Headmaster and some of the teaching staff and taken round the school. Everything seemed to work like clockwork, children marching in and out of classroom to the sound of stirring martial music, all the children wearing smart but identical uniforms, all looking very serious, not one of them giving us a smile! We looked in on one or two of the classes, in which the teaching was being done in well established traditional ways, with the teacher up front, and most of the time the children mechanically repeating everything the teacher said. As we were ushered from one classroom to the next I just managed to whisper to the director:

“I am sure not all your schools are like this! Couldn’t we go and see one of your more usual schools?”

“I am sure we can show you some”, said the director, “we shall excuse ourselves from here as soon it is politely possible!”

I met the director the next morning who introduced me to a number of inspectors, who were to accompany us. I had brought some mathematics materials with me, mainly attribute blocks, so that if the occasion allowed it, I could actually work with the children to test out the terrain a little.

We made our way to a small school, on the periphery of Port Moresby. The building was just a shack, there were not even walls all round, but the roof managed to keep out the rain! I asked the director if he would like me to do something with the children. He told me to help myself, and explained to the teacher in charge that I would take over the class for the next little while. I put several sets of attribute blocks on the floor and arranged the children in groups around the blocks and told them to do what they liked with the blocks. Not one child stirred. They all sat still, waiting for commands.

Well, I thought, Rome was not built in a day, so I got them to form a semicircle and placed one lot of blocks centrally on the floor. I began by asking one child to pick up any two blocks and asking him how they were alike and how they were different. This led to a “pairing game” in which blocks had to be paired, so that in each pair the two blocks were different from each other in exactly the same way and they were like each other in exactly the same way. This began to motivate them and they began to argue with each other as to the rights and wrongs of individual pairs of blocks. Before long I was able to put them back into groups, and got them to “play this game”, followed by a number of other games. I began to get smiles, as the children were beginning to enjoy the freedom of thinking the problems out for themselves.

When the bell went, the children did not want to stop “playing”. But of course the bell meant that something else was about to happen according to the routine, so they had to stop. “What do you think all that was about?” said one of the inspectors who had been watching all the aforementioned developments. They had a brief discussion amongst themselves, to the effect that it was not really desirable to allow children to play, when more serious things ought to be taught to them. They were totally unaware of the incipient logical thinking that was involved in the games and they thought the whole thing would be extremely bad for discipline. The director did not join in this discussion, but gave me an occasional meaningful look, as much as to say that we would talk later. When we found ourselves alone in the directors office, the inspectors having retired to the local hotel no doubt with a view to consuming some appropriate beverages, I said to the director:

“Do you not have any schools where inspectors do not inspect?”

“Do you mean you REALLY want to do some work? The lesson you showed us was most interesting and if you like I can show you some schools where inspectors are never likely to go, if you really are anxious to do something here. You see, most people that the Minister for Territories sends us up here, enjoy the first class flight on the plane, a few days of looking around, perhaps a trip to Manus, Goroka or Mount Hagen. Then they utter some platitudes, pocket a good consulting fee and go home and tell hair raising stories about our stone age natives! I assumed you were one of the usual run of “official” visitors!”

Mr. Barnes, the Minister,”I replied,” had told me on the phone before I came that the mathematics education was so bad here, that if I threw it up in the air and let it fall down, it would be probably be an improvement! I told him I had never done anything like this before, but he still encouraged me to come, after having sent some observers to our experimental schools in Adelaide, who gave him a glowing report. So I am here and I should like to see what can be done, and then do it, if I can!”

“That sounds most interesting”, replied the director, “I’ll tell you what we’ll do! Be ready about 5 a. m. tomorrow morning, have some of your material to take with you, and a jeep will come to the hotel and take you to a school”

On this cordial note we parted, I was run back to the only decent (and air conditioned! ) hotel in Port Moresby, where I was wined and dined and went to bed early, asking for a wake up call at 4. 40 a. m. At 5. a. m. the next morning I loaded the jeep with a large box of mathematics materials, and sat in by the native driver, who was detailed to take me to the school. We soon left Port Moresby behind, the road rapidly deteriorated into a dusty track, and soon we found ourselves driving along the beach. It was a beautiful morning, just getting light, the sky getting redder and redder by the minute. The sea was as calm as a duck pond. All of a sudden the driver brought the jeep to a stop. On our right was the ocean, in front of us flowed a sizeable river, somewhat muddy looking, but still looking quite majestic, as its waters continued to empty into the ocean. I said to the driver:

“Where is the school?”

“Over river, two mile”, replied the driver.

“How do we cross the river?”, I asked

“Walk”, was the laconic reply

“All right then”. I said, “let’s go “

“I no go”, said the driver “you go”

I must say I was a little taken aback. I thought the jeep was going to take me to a school. There was not a soul in sight, no sign of any habitation, only a mangrove swamp on our left, the ocean on our right and the river in front of us.

“Why don’t you cross the river? This material is very heavy for me to carry for two miles!”, I said to him.

“Crocodiles”, said the driver.

Suddenly everything had become clear to me. I had asked the director of education to let me work in a school where inspectors never went! I realised just why they would not do so! The driver helped me with the material down to the bank of the river, said goodbye, went back to his jeep, turned round on the sand and drove away. Of course there was nothing else to do but to wade across the river. It did not seem very deep, it would probably come up to my waist, but of course I could not be sure. There seemed no suspicious looking objects floating down the river, so I heaved the box of materials on to my head and proceeded to wade. It only took a minute to cross, but it was one of the longest minutes I had lived up to that point! I rested a bit, the sun had risen and it was getting warmer, so it did not seem to matter that all my clothes were wet. So I put my burden on my head again and started off on my two mile hike, following the coast. The driver had been about right, because after about three quarters of an hour I came across some houses, in fact I soon found myself in the middle of a native village. Some of the houses were built on stilts in the lagoon, and some were a little away from the seashore.

It was not hard to find the school as it was the only building that obviously was not built by the natives, and had a corrugated iron roof. I could hear the noise of the children, from which I assumed that school had not yet started, but was about to start. I put down my box, and sighed a sigh of relief, then entered the school building. What I saw surprised me a little; a small boy was lying on the floor, and a teacher, a European, was administering something to him.

“Good morning”, I said “the director of education has sent me”

“You’d better just stay where you are for the moment, and watch me. This child has malaria, and if I don’t give him a large dose of nivequin, he won’t be here much longer”, said the teacher, while he was trying to get the child to swallow the said dose of nivequin.

That reminded me that I had not taken mine, so I promptly took a pill out of my pocket and swallowed it. All visitors to New Guinea take such quinine based medication as a prophylactic against malaria. The boy on the floor was taken back to his parents by one of the native teachers. As it happens he did survive. Having done his morning life saving chores, the teacher said to me:

“How good to see another European face! I am the only one in the village, all my teachers are natives. So what can I do for you?”

This was the start of the New Guinea Mathematics Project, on which I continued to work for more than two years, trying to devise meaningful ways of teaching native children mathematics, using as much local material as possible, and trying to make it relevant to their environment. How the project developed, I will relate in another Chapter. Now I should like to tell the reader how it happened that I came to be asked to do the job of bringing mathematics to the stone age society of New Guinea. I shall have to go back to the years of the first world war in the Hungarian city of Budapest, where as a child I had looked at a bird flying across the sky and exclaimed “Look, it’s just like an aeroplane!”