A Study On Mathematical Explanation Of Mid-school Students

With the coming of knowledge-economy age, more and more people come to realize that only by acquiring knowledge with understanding, can they apply that knowledge to learn new topics and to solve new or unfamiliar problems. Now teaching mathematics for understanding has become one of the main issues in today' world. In our nation the long existing influence of "Examination-Oriented Education" results in the decline in students' mathematical understanding level. The students' ability to practice and create has long been the focus of people's attention. This dissertation is based on the findings of the most up-to-date philosophical hermeneutics and psychology about understanding and explanation. The main purposes of the study on mathematical explanation of mid-school student are to provide a way of improving students' mathematical understanding, to present a new instrument for assessing the students' understanding, and to provide reasons and suggestions for teaching and learning mathematics and curriculum reform with understanding.The dissertation consists of four parts, including the introduction, the empirical study, the theoretical study, suggestions to realize teaching mathematics for understanding.The introduction is based on the analysis of research from philosophical hermeneutics and psychology about understanding and explanation and PME on mathematical understanding. It illuminates the significance of study mid-school students' mathematical explanation, and briefly introduces research questions and research methods.Part two is an empirical study, including two chapters. Chapter Two is "mathematical explanation study as understanding performance form" and Chapter Three is "mathematical explanation study as a tool promoting understanding".Chapter Two mainly uses qualitative research method, and exploits SOLO theory as an instrument, according to the content of middle school students' explanation to mathematical concepts, mathematical theorem and problem solving. The primary conclusion is that the mid-school students in our nation as a wholehave a low level of conceptual understanding in mathematics. The research discovers elements such as meaningful representation, essential conceptual image, elaborated schema and problem-solving strategy are the essential parts of building available mental model to solve problems successfully. But the level of conceptual understanding in mathematics is low, especially the shortage of dynamic image is the root cause of the students' weak ability to solve real problems and irregular mathematical problems. Meanwhile, internal factors and external factors that influence the students' conceptual understanding are explored.Chapter Three includes case study of improving mathematical understanding by eliciting student's mathematical explanation and an experimental research of improving mathematical understanding by eliciting self-explanations to study worked-example. The findings not only show that eliciting mathematical explanation is really helpful to construct declarative knowledge and procedural knowledge, to integrate new and old knowledge, and to generate self-inference and repair students' mental model, but also show that if the teacher provides appropriate intervention, it may have a critical influence on fostering students' understanding.Part three is a theoretical study, namely Chapter Four is "the teaching function of students' mathematical explanation"Chapter Four is coherent with the research conclusions in Part two, I primarily induced that the students' mathematical explanation has functions of teaching, which are elicitation, diagnosis and assessment.Part Four gives us some suggestions in teaching mathematics for understanding, which is the end point of this dissertation. Based on the whole research and our present teaching condition, it states that we should strongly advocate promoting students' explanation in teaching mathematics, besides analyzes the limitation of variation practice and advocates integrating variation practice, proble...