An Empirical Study On The Implicit Learning Of Mathematic Mapping Maxims At Elementary School Level

The proposal of tacit knowledge and subsequent research on implicit memory stimulate innovative reevaluation on contemporary theories of cognition and learning. In 1967, Reber, an American psychologist, verified in his empirical study that human, even without sensing potential schema of environmental stimulus, can comprehend the schema and make proper responses with it. On this basis, he proposed the concept and theoretical framework of implicit learning, and established the essential approach in implicit learning study—artificial grammar learning pattern.According to Reber, implicit learning is a process of unconsciously attaining complex maxims in environmental stimulus. Human can apply two essentially different learning modes to complicated learning tasks. One is explicit learning mode that is under the control of consciousness and that needs attention. The other is implicit learning mode. In recent forty years, implicit learning has become a focus of psychological study. Various researches have been made on the features, psychological mechanism and application of implicit learning. Implicit learning is characterized by: implicity (unconsciousness information processing, an essential feature of implicit learning), efficiency (high efficiency in information transfer and knowledge attainment, featured by freedom from psychological abnormity and brain damage and longer term of knowledge store than explicit learning) and intensity (much higher capacity in information processing and store than explicit learning). Researches reveal that besides these dominant features, implicit has other features like anti-interference, material-sensitivity and advantage effect. Findings of implicit learning research have been widely applied in different fields like education, man-machine communication interface design and social behavior learning, and have made some significant contributions.So far, a large quantity of research has been conducted on mathematic concepts and maxims in the field of learning psychology, educational psychology, cognitive psychology and cultural psychology, due to their great importance. As a result, some achievements have been acquired. However, almost all these studies concern explicitlearning, focusing on the formation and mastery of mathematic concepts and maxims intentionally and consciously. Virtually, numerous implicit learning takes place in the process of mathematic learning. It is demonstrated in some studies that implicit learning effects exists in pupil's learning of the function concepts in mathematics. However, it is universally acknowledged that implicit learning effect is not generated in the process of mathematics learning about the concepts and laws. The present study attempts to extend an experimental study in this field on the basis of the defects of the previous studies.Taking pupils of fourth grade as subjects, simple mathematic mapping maxims with a certain degree of complexity as learning material and Raven's Standard Progressive Matrices (SPM) , the present study carried out an empirical study on the mathematic mapping maxims of pupils. The research findings shows:1. Autonomous and apparent in dominance effect, implicit learning does exist during simple mathematic maxim learning of school children.2. Both implicit and explicit learning can be separated effectively through instruction.3. Implicit learning of simple mathematic mapping maxims among elementary students is related with their capacity for understanding.4. No significant gender difference is found in implicit learning of simple mathematic mapping maxims among elementary students.5. Pupils' implicit learning of simple mathematic mapping maxims is not subject to the influence of pupils' IQ.6. In mathematic learning, implicit learning is easier to occur when students are exposed to learning materials with medium difficulty and complicated structure.The findings also suggested pupils' implicit learning was sensitive to the difficulty and structure of learning materials. Generally speaking, pupils' explicit learning of mathematic mapping rules was superior to implicit learning in terms of learning efficiency.The implications of the present study are as following: Since the study on implicit learning reveals a store of mathematic knowledge will lead to accumulative effect, adequate importance should be attached to the role of mechanical memory. Implicit learning also implies that sufficient attention should be given to accumulative effect in implementing innovative education. In addition, enough attention should also be paid to the role of implicit learning, which is of great help to the achievement of the implicit...