Study On The Prospective Teachers' Mathematical Knowledge For Teaching

Seeing effective ways to improve the quality of prospective teachers andprofessional development of teachers in educational research are the currently hotissues. Research on the knowledge of teacher is one of important research fields. Thestudy belongs to the research of the knowing base of teaching. Specifically, this studywas to consider the mathematical knowledge for teaching. Since the 1980's, this issuehas attracted the concern of many researchers in the area of teacher education. Due tothe different perspectives, the results from different studies differ obviously.The research focuses on the following works.Firstly, this study adopts a unique perspective, which is the genesis and de-velopment of history, based on the historical- genetic--principle.Secondly, in reference to the relevant literature and related researches, this paperformed a theoretical framework to analysis mathematical knowledge for teaching(MKT). Mathematical knowledge for teaching is made up of the subject matterknowledge and the pedagogical knowledge. From the perspective of the the genesisand development of mathematics, subject matter knowledge is the knowledge of theresearch problem and the back motive which promote the development of a researchtopic and the knowledge of the research methods which solve the research problemand the knowledge to explain and apply the final results of the research. Theknowledge of curriculum is knowledge about the genesis and development of specifictopic and its orientation in textbooks and the logic system structure and the knowledgeof its horizontal linkages with other subjects. The knowledge of content and studentmainly refers to the knowledge about the difficulties and confusion that students maybe subjected in a particular topic, the knowledge about the causes of cognition errorsand the cognitive style. In order to meet the demand of the educational aims andteaching objectives, the knowledge of content and teaching includes knowledge abouthow to select and organize the teaching contents, to determine an effective metaphor,representation, interpretation and sample, to select an effective way to design teachingand learning activities and to arrange the order of teaching. The above two kinds of knowledge is the knowledge of learning and teaching.Thirdly, on the basis of analysis framework of mathematics understanding leveland cognitive level, the research's analysis framework is constructed which has fourlevels to analyse mathematics knowledge for teaching. From the view of the genesisand development of history, the research analyses the prospective teachers' level ofmathematics knowledge for teaching and its reasons. The procedure is named as"fourlevels and two problems".Based on the above analysis framework, this paper focuses the qualitativeanalysis of 6 prospective teachers. The research whose carrier is trigonometry uses aquestionnaire, an interview and other research tools to collect data.With the aboveframework, the results can be summarized as follows:(1) The prospective teachers' understanding of mathematical knowledge is underthe methodology-exploring level.(2) The prospective teachers' understanding of textbooks stays at the level ofconcepts and problem-solving. The learning of higher mathematics does not raisetheir level of processing textbooks.The reason is that they have no idea of thehistorical-genetic knowledge and they were not conscious of the communication ofdifferent knowledge.(3) The prospective teachers' knowledge of students' learning difficulties cann'tpredict precisely difficulties students may encounter. Some prospective teachersdeveloped some knowledge about students, but, in general, their knowledge for"diagnosing"and"predicting"students' learning difficulties is very limited.Mathematics historical-genetic knowledge is an important factor influencing theprospective teachers to"diagnosis"and"predict"students' learning difficulties.(4) Generally speaking, the prospective teachers' mathematics knowledge forteaching of the prospective teachers distributes the first three levels. This result is inconsistent with the other results. The prospective teachers of understanding ofmathematics can't reach methodology-exploring, and the level of understanding oftextbook reserve at the level of concepts and problem-solving.They can't"diagnose"and"predict"students' learning difficulties. At the same time, they lack of experience. All of these factors affect the prospective teachers' understanding of the learning andteaching to a low level. From the classroom instruction of the prospective teachers,the knowledge of the genesis and development of mathematics is an important factorthat affects the levels of instruction.Finally, this study puts forward a model for the prospective teacher education:paying attention to the genesis and development of knowledge, and payingtransforming subject matter knowledge for the aim of education.