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A Study On The Ability Of Error Analysis For Mathematics Teachers Of Junior High School

Posted on:2008-12-15Degree:DoctorType:Dissertation
Country:ChinaCandidate:A H PengFull Text:PDF
GTID:1117360215465472Subject:Curriculum and pedagogy
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With the education reform goes depth, teacher's education and professionalization get more and more attentions and strengthening. The teacher's professional ability growingly becomes the most important one in the field of teacher's professional development. As a consequence, it is imperative to study teacher's professional ability and its development. Due to that analyzing students' errors in learning is an every-day work and basic activity, the ability of error analysis is an essential and indispensable professional ability for a teacher to conduct teaching. However, the most of existed researches didn't systematically and deeply study this ability represented in the special activity of error analysis from the point of view of teacher's professional ability while focused only on the error analysis itself. For the lack of the core conception of the ability of error analysis, the existed relevant researches are scattered and their application value are also limited.Based on the teaching theory of mathematical activity and the cognitive constructive theory, the subject conception of mathematics teacher's ability of error analysis is presented. In this dissertation, the mathematics teacher's ability of error analysis is defined as the mathematics teacher's ability to identify, to explain, to evaluate and to correct students' mathematical errors in mathemtics learning, in which the mathematics teacher take students' mathematical errors as his or her thought object in order to ensure students' high efficiency and success in mathematics learning. Based on this definition, the mathematics teacher's ability of error analysis is studied. Speaking concretely, three main questions are studied in this dissertation: what is the current status of the ability of error analysis of mathematics teachers of junior high school, what are the factors influencing the ability of error analysis of mathematics teachers of junior high school and what are the leading avenues and strategies for developing the ability of error analysis of mathematics teachers of junior high school.Due to its exploration and initiation, the methodology of this dissertation is based on the phenomenological theory, and the data are collected and analyzed through the qualitative method which has widespread use in social science. The concrete approaches are questionnaires and interviews. The questionnaire consists of three questionnaires which have the same efficiency. The core components of each questionnaire are four contexts and problems relevant to the mathematical errors of students of junior high school. 107 mathematics teachers of junior high school were involved in the questionnaire investigating. The interviews include two types: based on the tasks and based on the semi-structure. The tasks-based interviews are based on the questionnaire investigating results. Its object is to understand the teachers' thinking processes more detailedly and clearly, in which the special attentions are particularly put on the underlying reasons for the mathematics teachers' decision-making during error analysis. 36 teachers of the 107 mathematics teachers involved in the questionnaire investigating were interviewed, among them 18 teachers were interviewed at second time consisting of 9 ordinary teachers and 9 expert teachers. The semi-structure-based interview is to directly or indirectly find out the avenues and strategies for developing teachers' ability of error analysis, in which 9 expert teachers were involved.Through studying, we got many findings and conclusions as follows. Firstly, the conclusion with respect to the current status of the ability of error analysis of mathematics teachers of junior high school is that there are four different levels in the ability of error analysis of mathematics teachers of junior high school.The four different levels are 'goose egg' analysis level, indistinct analysis level, partly exact analysis level and totally exact analysis level respectively, which reflect certain internal law's characteristics of the ability of error analysis of mathematics teachers of junior high school. From the point of view of current reality status, as a whole, the ability of error analysis of the mathematics teachers of junior high school is low; most of them are in the position of indistinct analysis level.There are many problems in the ability of error analysis of the mathematics teachers of junior high school, namely, (1) the identifying of the students' logic errors in mathematics learning is difficult for mathematics teachers of junior high school, (2) there widely exists 'knowing that without knowing why' phenomenon to students' mathematical errors in mathematics teachers of junior high school, (3) a majority of mathematics teachers of junior high school attribute students' errors to students themselves.The ability of error analysis of the mathematics teachers of junior high school shows three different characteristics: the 'consciousness' and the 'sub-consciousness', the 'pertaining to student' and the 'pertaining to teacher', and the 'openness' and the 'closeness'.Secondly, the conclusion about the factors influencing the ability of error analysis of the mathematics teachers of junior high school is that teacher's knowledge and ideas are the main factors influencing the ability of error analysis of mathematics teachers of junior high school.As far as the knowledge about the subject matter, the teaching, the curriculum and students is concerned, the difference between ordinary teachers and expert teachers mainly lies in the enrichment or shortage of relevant knowledge. Meanwhile, in mathematics belief, teaching belief, learning belief, error belief and self-confidence, the difference between ordinary teachers and expert teachers mainly lies in that whether their ideas are firm and definite and whether they have their own 'theories'.The different behaviors on knowledge and belief between ordinary teachers and expert teachers lead to different decision-makings in the identification, explanation, evaluation and correction of students' mathematical errors, and then lead to different levels of ability of error analysis. Thus, in order to develop the ability of error analysis of the mathematics teachers of junior high school, the efforts to be made on the improvement of their knowledge and belief.Thirdly, as for the avenues and strategies for developing the ability of error analysis of mathematics teachers of junior high school, the study conclusion is that the development of the ability of error analysis of mathematics teachers of junior high school mainly comes from teacher's reflection in teaching practice, which includes the reflection from experiences, the reflection from communication and the reflection from study. The formal pre-service education and the in-service professional activities don't fall into the main avenues and strategies for developing the ability of error analysis of mathematics teachers of junior high school.Two strategies are planned for the development of the ability of error analysis of mathematics teachers of junior high school. The first one is that starting from the teachers themselves, to prompt the mathematics teachers of junior high school to learn to reflect skeptically. The second one is starting from the external of teachers, to improve the development of the ability of error analysis of mathematics teachers of junior high school, i.e., based on imparting certain theoretical knowledge about the error analysis to mathematics teachers of junior high school, taking cases analysis of students' typical mathematical errors as the emphasis, to impart contents of other mathematical tasks to them.Based on the above findings and conclusions, some suggestions about the cultivating of the ability of error analysis of mathematics teachers both for the mathematics teacher educators and the mathematics teachers are presented, furthermore, some issues to be further studied are also explored.The innovation points of this dissertation are as follows: (1) the ability of error analysis of mathematics teachers of junior high school is firstly studied relatively systematically and deeply in home, (2) the structural model of the ability of error analysis of mathematics teachers is presented, which makes a primary attempt to scientifically explain the ability of mathematics teachers presented in the special activity of error analysis and (3) this research is conducted through a complete procedure of qualitative methodology rather than the traditional quantitative methodology. The thinking processes of teachers in error analysis are extrapolated by analyzing teachers' essential characteristics showed in the activity of error analysis.
Keywords/Search Tags:Mathematics Teacher of junior High School, Ability of Error Analysis, Mathematical error, Professional Development
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