Treutlein P. (1845-1912), who was an active mathematics teacher at secondary schools in Germany and developed a new geometry curriculum for secondary schools, gave a great deal of influence on geometry teaching in Japan. His book, Die geometrische Anschauungsunterricht als Unterstufe eines zweistufi gen goemetrischen Unterrichts an unseren hoheren Schulen (1911) was translated into Japanese in 1920 and accepted as a new model of geometry teaching curriculum in Japan. Treutlein called his own geometry curriculum 'der geometische Anschauungsunterricht' (the geometrical intuitive instruction), which was the geometry teaching for lower levels of secondary schools at that time. The main goal of his 'der geometische Anschauungsunterricht' was to develop 'das raumliche Anschauungsvermogen (spatial imagination)' of pupils through verious geometrical tasks: cutting solids in mind, making their models, making new figures with some pieces of another figures, estimations and measuring of lengths and eares, construction and so on. The purpose of this paper is to consider the question what the meaning of `das raumliche Anschauungsvermogen' is. In order to interpretate his verious tasks in his geometry teaching and to make clear the histrical process of the development of the geometry teaching in Japan, it is very important to consider the qustion. The analysis of his own statements about geometry teaching and some tasks in 'der geometische Anschauungsunterricht' in this paper made it clear that 'das raumliche Anschauungsvermogen' was the ability to imagine and manipulate figures in mind, and that the figures meant both plane and solid figures. Although it seems that spatial imagination is usually only about solids in these days, spatial imagination for his geometry teaching means the ability to imagine and mamipulate figures both in plane and in space.