A Study On The 10～(th) Graders' Cognitive Barriers Of Learning Abstract Function

Function is one of the fundamental and basic knowledge in Middle and High school mathematics and its structure contains two clues, one called "explicit clue" and the other "implicit clue". If functions appear in concrete function expressions and they are analyzed in the way that connects the algebra and geometry figures, then to students, there are relatively fewer cognitive barriers in understanding and mastering. So we call "explicit clue" in such situation.However, as far as "implicit clue" concerned, it refers to the understanding and recognizing of function y = f(x) as such without the concrete function expression. And during the High School mathematics teaching, such functions mentioned above are named abstract function. Speaking in detail, the abstract function has not the concrete function expression, but it possesses functions' basic properties such as parity, monotonic and periodic property.Abstract function is the difficulty of the function part in Middle and High school mathematics. Teachers could recognize deeply that students have trouble in learning abstract function and they are not able to accept and understand such function. This study investigated the 10th graders' cognitive barriers of learning abstract function through questionnaire, test and interview. The findings shows that there are about 10 aspects of students' cognitive barriers involved having not any the solution clues, being unable to understand the problems and use the problem conditions, confusing the relationship between function values and variables, being unable to evaluate variables, neglecting domains, being unable to understanding the function properties, being lack of relevant knowledge, drawing the wrong figures, attitudes and affect. Finally, according to the analysis of barriers, this study gives some relevant suggestions.