TEACHER KNOWLEDGE OF STUDENTS' MATHEMATICAL ERRORS

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Instruments Data were collected with an author-constructed Mathematical Error Analysis Questionnaire and in-depth interviews followed the questionnaire. The questionnaire consisted of four tasks that were designed to examine how mathematics teachers analyse student’s mathematical errors in typical algebraic and geometric topics of polynomial, equation and triangle. Each of the four tasks focused on mathematics teacher knowledge of identifying, addressing, diagnosing, and correcting student’s mathematical errors, preferably, every task mainly focused on one aspect of logic, mathematical knowledge, psychology and strategy. These tasks were examined from middle school students in a pilot study. After reviewing and analysing the responses to the questionnaire, every teacher was invited to an in-depth interview to further explore how teachers understand and handle student’s mathematical errors. Every interview occurred within 1 hr. The interviewer posed the initial question and then followed the teacher’s lead, asking follow-up questions based on the teacher’s responses. The interviewer cycled back to topics to elicit more detail. Each interview was audio taped and transcribed. Data analysis Qualitative analysis method was used in the analysis of the questionnaire and the transcriptions of the interviews. Firstly, 4 different categories consisted of identifying, addressing, diagnosing, and correcting students’ mathematical errors was identified which included the responses to every task. Next, different perspectives from logic, mathematical knowledge, strategy and psychology were identified. The responses were categorized into groups and assigned a descriptive code. Two researchers used the resulting codes to analyse the responses independently. Both sets of codes were compared, and then, through discussion with the third researcher, the disparities were reconciled to reach valuable agreements on the responses. The coding of the four tasks of questionnaire was used by T1, T2, T3, and T4. And the investigated teacher was used by six codes ABCDEF, which represented age, gender, degree, teaching years, school district and confidence about analysing students’ mathematical errors respectively. RESULTS According to teachers’ responses to questionnaire and interview, their knowledge of students’ mathematical errors manifested differently in every dimensions of phrases of error analysis and perspectives for sources of errors. But when they were mixed in one picture through focusing on every specific task, the distinctive different levels of knowledgeable of students’ mathematical errors were shown. The results were presented including the clarification of the levels (see table 2) and exemplification of the typical features of the levels supported by some interview excerpts (see table 3). 1- 4 Level 1 ● Couldn’t identify the students’ mathematical errors.
Peng ●Couldn’t find the reasonable causes of students’ mathematical errors; couldn’t find the reasons for students’ mathematical errors or simply attribute to students’ mathematical errors to such as ‘non-seriousness of learning’ and ‘poor basic knowledge and basic skills’. ● Couldn’t evaluate the influence of students’ mathematical errors on their latter learning, couldn’t evaluate students’ levels of performance according to their mathematical errors. ● Couldn’t present teaching strategies for correcting students’ mathematical errors. Level 2 ● Could identify the students’ mathematical errors but couldn’t find the underlying reasons. ● Couldn’t find the reasonable causes of students’ mathematical errors, could explain the reasons for students’ mathematical errors, but only consider them as they stand, couldn’t analyse them for advanced viewpoint. ● Could simply evaluate the influence of students’ mathematical errors on their latter learning, can evaluate students’ levels of performance according to their mathematical errors to a certain degree. ● Could present teaching strategies for correcting students’ mathematical errors, but not so suit for the specific cases. Level 3 ● Could identify the mathematical errors of students and find the underlying reasons. ● Could evaluate students’ mathematical errors from a reasonable point of view, could analyse students’ mathematical errors for a singly relative high level theoretical point of view. ● Could properly evaluate the influence of students’ mathematical errors on their latter learning, could evaluate students’ levels of performance according to their mathematical errors. ● Could present singly teaching strategies for preventing students’ mathematical errors. Level 4 ● Could identify the students’ mathematical errors and the underlying reasons in a right and quick way. ● Could understand the reasonability of students’ mathematical 1- 5
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Page 3: Peng Dimension Nature of mathematic

TEACHER KNOWLEDGE OF STUDENTS' MATHEMATICAL ERRORS

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