Pre-service Teachers’ General and Specific Arguments in Real Number Contexts
Keywords:
General and specific arguments, real numbers, mathematics subject-matter beliefs, pre-service teachersAbstract
A study of pre-service elementary school teachers’ subject-matter beliefs regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents’ teacher education using questionnaires and interviews on both occasions. The data were analysed in terms of subject-matter beliefs from traces of students’ concept images, focusing on general and specific arguments in different contexts. The results show that the students often used conflicting general and specific arguments to explain the same phenomena. Some concrete arguments used for explanation represented other mathematical structures than the ones intended. Several issues indicate students’ need for further work with the concepts studied to raise awareness of their capabilities. Implications for mathematics teaching on teacher education programmes are discussed concerning the results.
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