Journal ArticleDOI
Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan
TLDR
In this paper, the differences in preservice teachers' procedural knowledge in four areas of fraction operations in Taiwan and the United States, and correlation in preserve teachers' conceptual knowledge and procedural knowledge of fractions in Taiwan, were examined.Abstract:
This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowledge and procedural knowledge of fractions in Taiwan and the United States. Participants were preservice teachers (N = 49) in a teacher education program in the United States and comparable Chinese preservice teachers (N = 47). Results indicated that Chinese preservice teachers performed better in procedural knowledge on fraction operations than American preservice teachers. No significant differences were found for conceptual knowledge on fraction division. Further, the correlation in this study showed that for Chinese and American preservice teachers, the relationship between conceptual and procedural knowledge of fraction operations was weak.read more
Citations
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Journal ArticleDOI
Why is learning fraction and decimal arithmetic so difficult
TL;DR: This review identifies and discusses two types of difficulties: inherent difficulties of fraction and decimal arithmetic and culturally contingent difficulties that could be reduced by improved instruction and prior knowledge of learners.
Journal ArticleDOI
Conceptual knowledge of fraction arithmetic.
TL;DR: In this paper, the authors presented preservice teachers (Study 1), middle school students (Study 2), and math and science majors at a selective university (Study 3) with a novel direction of effects task with fractions.
Why Is Learning Fraction and Decimal Arithmetic so Difficult
TL;DR: A review of fraction and decimal arithmetic can be found in this paper, where the authors identify and discuss two types of difficulties: inherent difficulties and culturally contingent difficulties that could be reduced by improved instruction and prior knowledge of learners.
Journal Article
Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions
TL;DR: In this paper, the authors discuss the main findings from a research summary of existing studies on prospective elementary teachers' fraction knowledge to identify directions for future research, and propose a framework for mathematical knowledge for teaching based on Shulman's (1986) categories of knowledge.
Journal ArticleDOI
Hard lessons : Why rational number arithmetic is so difficult for so many people
TL;DR: This article identified two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent, and discussed interventions that can improve learning of fraction and decimal arithmetic for children and adults.
References
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CONOCIMIENTO Y ENSEÑANZA: FUNDAMENTOS DE LA NUEVA REFORMA 1 Knowledge and Teaching: Foundations of the New Reform
TL;DR: Lee S. Shulman as mentioned in this paper builds his foundation for teachi ng reform on an idea of teaching that emphasizes comprension and reasoning, transformation and reflection, and argues that this emphasis is justified by the resoluteness with which research and policy have so blatantly ignored those aspects of teaching in the past.
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Knowledge and Teaching: Foundations of the New Reform
TL;DR: Lee S. Shulman as mentioned in this paper builds his foundation for teaching reform on an idea of teaching that emphasizes comprehension and reasoning, transformation and reflection. "This emphasis is justified," he writes,...
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Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement:
TL;DR: It is found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates.
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Relational Understanding and Instrumental Understanding.
TL;DR: One gets faux amis between English as spoken in different parts of the world as discussed by the authors and English as used in mathematics and in everyday life there are such words as field, group, ring, ideal.
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Bridging Practices: Intertwining Content and Pedagogy in Teaching and Learning to Teach
TL;DR: For example, the authors argues that subject matter and pedagogy have been peculiarly and persistently divided in the conceptualization and curriculum of teacher education and learning to teach, and this fragmentation of practice leaves t...