CONCEPT LEARNING AND RETENTION IN MATHEMATICS
RECENTLY many experiments have been con ducted in order to investigate the different ways by which children learn mathematical concepts. There is a growing concern as to what methods of instruc tion are most appropriate for children of all levels of mathematical and academic ability. Questions of what can be and what should be taught at the differ ent levels of mathematics education have been raised, and there now seems to be some agreement that children are capable of mastering more mathe matics and more complex mathematics, than was previously possible. One has only to review the findings'of a researcher such as Suppes, and read the reports of well-known mathematicians, psychol ogists, and educators such as those who composed the Cambridge Report, in order to learn of recent advancements and proposals for the future. Some of the recent experiments have been con cerned with how children employ newly learned con cepts in a problem-solving situation. This area of mathematics education is beginning to undergo much experimentation, but as yet, there is not much that can be put together in the form of well-defined pro cedures and widely accepted ideas. Many psychologists and mathematics educators, considering the above concern, have investigated the effectiveness of the use of programed materi als as a means of testing various instructional theo ries. One can find opposing views as to the effec tiveness of such materials in an instructional situ ation, but the least that can be said is that pro gramed materials allow the researcher to more nearly duplicate the normal teaching situations than did the classical laboratory methods.