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Rasmussen, Chris; Kwon, Oh Nam – Journal of Mathematical Behavior, 2007
To improve undergraduate mathematics learning, teachers need to recognize and value characteristics of classroom learning environments that contribute to powerful student learning. The broad goal of this special issue is to share such characteristics and the theoretical and empirical grounding for an innovative approach in differential equations…
Descriptors: Equations (Mathematics), Mathematics Instruction, Inquiry, Teaching Methods
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Marrongelle, Karen – Journal of Mathematical Behavior, 2007
The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate…
Descriptors: Mathematics Education, Graphs, Equations (Mathematics), Nonverbal Communication
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Rasmussen, Chris; Blumenfeld, Howard – Journal of Mathematical Behavior, 2007
An enduring challenge in mathematics education is to create learning environments in which students generate, refine, and extend their intuitive and informal ways of reasoning to more sophisticated and formal ways of reasoning. Pressing concerns for research, therefore, are to detail students' progressively sophisticated ways of reasoning and…
Descriptors: Instructional Design, Mathematics Education, Heuristics, Equations (Mathematics)
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Keene, Karen Allen – Journal of Mathematical Behavior, 2007
Students incorporate and use the implicit and explicit parameter time to support their mathematical reasoning and deepen their understandings as they participate in a differential equations class during instruction on solutions to systems of differential equations. Therefore, dynamic reasoning is defined as developing and using conceptualizations…
Descriptors: Figurative Language, Equations (Mathematics), Mathematics Instruction, Thinking Skills
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Ju, Mi-Kyung; Kwon, Oh Nam – Journal of Mathematical Behavior, 2007
As part of developmental research for an inquiry-oriented differential equations course, this study investigates the change in students' beliefs about mathematics. The discourse analysis has identified two different types of perspective modes--i.e., discourse of the third-person perspective and discourse of the first-person perspective--in the…
Descriptors: Discourse Analysis, Equations (Mathematics), Mathematics Instruction, Beliefs
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Wagner, Joseph F.; Speer, Natasha M.; Rossa, Bernd – Journal of Mathematical Behavior, 2007
In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as…
Descriptors: Mathematics Education, Equations (Mathematics), Teaching Methods, Mathematics Instruction