Journal ArticleDOI
Designing and scaling up an innovation in abstract algebra
TLDR
The authors describe the process of designing and scaling up the TAAFU group theory curriculum, which emerged along with local instructional theories as the result of small-scale design experiments conducted with pairs of students.About:
This article is published in The Journal of Mathematical Behavior.The article was published on 2013-12-01. It has received 52 citations till now. The article focuses on the topics: Curriculum development & Design process.read more
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I on the Prize: Inquiry Approaches in Undergraduate Mathematics
TL;DR: The authors describe the intellectual origins and development of two major strands of inquiry in US higher education, offer an explanation for apparent differences in these strands, and argue that they be united under a common vision of Inquiry-Based Mathematics Education (IBME).
Journal ArticleDOI
Inquiry-Oriented Instruction: A Conceptualization of the Instructional Principles
TL;DR: In this paper, a characterization of a particular form of IBL instruction, called inquiry-oriented instruction, is presented, which draws on K-16 research literature in order to explicate the instructional principles central to Inquiry-Oriented Instruction.
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A local instructional theory for the guided reinvention of the quotient group concept
Sean Larsen,Elise Lockwood +1 more
TL;DR: In this article, a local instructional theory for supporting the guided reinvention of the quotient group concept is described, which takes the form of a sequence of key steps in the process of reinventing the concept.
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Implementing inquiry-oriented curriculum: From the mathematicians’ perspective
TL;DR: In this article, the authors present and discuss each teacher's perspective on these three themes: coverage, goals for student learning, and the role of the teacher, by drawing on interview data, classroom data, and first person commentaries.
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Journal ArticleDOI
Concept Image and Concept Definition in Mathematics with particular reference to Limits and Continuity
TL;DR: The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept and may have aspects which are quite different from the formal concept definition as discussed by the authors.
Book
Proofs and Refutations
Margarita R. Levin,Imre Lakatos +1 more
TL;DR: In this article, the authors present a problem and a conjecture, and a proof of the problem and the conjecture, as well as a proof against the conjecture by lemma-incorp oration.
Journal ArticleDOI
What Is an “Expert Student?”
TL;DR: The authors suggests that conventional methods of teaching may, at best, create pseudo-experts, students whose expertise, to the extent they have it, does not mirror the expertise needed for real-world thinking inside or outside of the academic disciplines schools normally teach.