Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called 'Logo' adapted to objectify an enduring framework of mathematical experimentation.

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vegetation, that a uniform and high temperature is maintained throughout the night. Because of this fact, in the radiometric observations of tropical regions the boundaries between water and land, hence parts of the outlines of continents, cannot be distinguished.Comparison of a radiation picture of the Siberian tundra on 5 September 1964 (Fig. 16) and hydrometeorological data for the same date provides an example of very close equilibrium between soil and air temperatures. In Fig. 16 a band of clouds, indicating a cold front, lies across western Siberia near 60?N. The skies to the north and south are cloudless; this is indicated by the clearly visible lakes and rivers on both sides of the front. Blackbody temperatures, however, are markedly different on the two sides. To the south of the front the temperatures range from 277? to about 280?K, while to the northwest they are about 287?. Surface-air data provided by the Hydrometeorological Service of the U.S.S.R. show that surface-air temperatures in the southern region were about 279 K, while in the northwest they ranged from 283? to 288?K. This agreement with the satellite-measured soil temperatures suggests a complete equilibrium between air and soil temperatures in this region. Other radiometer observations were obtained vegetation, that a uniform and high temperature is maintained throughout the night. Because of this fact, in the radiometric observations of tropical regions the boundaries between water and land, hence parts of the outlines of continents, cannot be distinguished.Comparison of a radiation picture of the Siberian tundra on 5 September 1964 (Fig. 16) and hydrometeorological data for the same date provides an example of very close equilibrium between soil and air temperatures. In Fig. 16 a band of clouds, indicating a cold front, lies across western Siberia near 60?N. The skies to the north and south are cloudless; this is indicated by the clearly visible lakes and rivers on both sides of the front. Blackbody temperatures, however, are markedly different on the two sides. To the south of the front the temperatures range from 277? to about 280?K, while to the northwest they are about 287?. Surface-air data provided by the Hydrometeorological Service of the U.S.S.R. show that surface-air temperatures in the southern region were about 279 K, while in the northwest they ranged from 283? to 288?K. This agreement with the satellite-measured soil temperatures suggests a complete equilibrium between air and soil temperatures in this region. Other radiometer observations were obtained The authors are associated with Bolt Beranek

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