• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.57-65
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• 2011

The conceptions of definition and proof radically change in the transition from secondary to tertiary mathematics. Specifically this paper analyses the historical development of the axiomatic method from Greek to modern mathematics. To understand Greek and modern axiomatic method, it is important to know the different characteristics of the primitive terms, constant and variable. Especially this matter of primitive terms explains the change of conceptions of definition, proof and mathematics. This historical analysis is useful for introducing the meaning of formal definition and proof.

• The Mathematical Education
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• v.62 no.2
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• pp.211-236
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• 2023

The purpose of this study is to derive implications of preservice mathematics teacher education in Korea by analyzing the case of edTPA used in the preservice teacher training process in the United States. Recently, there has been a growing interest in promoting professional competencies considering not only the cognitive dimension related to knowledge development of preservice mathematics teachers but also the situational dimension considering reality in the classroom. The edTPA in the United States is a performance-based assessment based on lessons conducted by preservice teachers at school. This study analyzes the professional competencies required of preservice mathematics teachers by analyzing handbooks that described the case of edTPA in which preservice mathematics teachers in the United States participate. The edTPA includes planning, instruction, and assessment tasks, and continuous tasks are performed in connection with classes. Thus, the analysis is conducted on the points of linkage between the description of evaluation items and criteria in the planning, instruction, and assessment tasks, as well as the professional competencies required from that linkage. As a result of analyzing the edTPA handbooks, the professional competencies required of preservice mathematics teachers in the edTPA assessment were the competency to focus on and implement specific mathematics lessons, the competency to reflectively understand the implementation and assessment of specific mathematics lessons, and the competency to make a progressive determination of students' achievement related to their learning and their uses of language and representations. The results of this analysis can be used as constructs for competencies that can be assessed in the preservice in the organization of the preservice mathematics teacher curriculum and practice training semester system in Korea.