Experimental Tests Of Mathematical Ability And Their Prognostic Value PDF Download

From the beginning of the first chapter. The decision of every question of moment in education depends upon both psychological and sociological considerations. As regards the latter, investigation is greatly complicated at the present time by the far-reaching character of the changes that are taking place in our industrial and social life. So rapid and so complex are these changes that recommendations based upon yesterday's situation may prove ill-adapted to that of to-day. In this respect the psychologist has a considerable advantage over the sociologist, where educational guidance is concerned; for, however variable and elusive it may be, the original nature of man is a more stable thing than the environment to which it is exposed. The task of discovering what can be known of the innate abilities of the individual presents fewer obstacles to the scientific investigator and once attained it will remain a permanent possession and unfailing fingerpost for the educator. In no sphere is this knowledge more desirable and necessary at the present time than in the high school subjects and particularly in mathematics. Reforms of a far-reaching character are already planned or in process and it is important that such psychological considerations as bear upon a satisfactory scheme should be ascertained. In our present comparative ignorance of the abilities involved in mathematical work, we lack one important means of estimating the significance of the reconstructions proposed in this field. This study is a partial contribution towards supplying this need. Its purpose is to make an analysis of the abilities involved in high school mathematics, to determine their efficiency and status, their interrelations and also their connection with certain other forms of mental capacity. Primarily it is directed to discover dynamic and quantitative relations between mathematical abilities rather than to show how we think in mathematics from the standpoint of analytic or structural psychology. It is to be distinguished, therefore, from the work on the thought processes of the Wurzburg School, since it does not attempt to analyze the content of thought in mathematical thinking, while it seeks to determine the functional relations between mathematical abilities and their connection or lack of connection with certain other mental abilities. It is not concerned with the development of ideas of number or space in the child, which recent writers on the Psychology of Mathematics have considered at some length l and which has importance for the elementary school teacher....