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Teaching calculus with infinitesimals and differentials
Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits....
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First-Year Engineering Students’ Interpretations of Differentials and Definite Integrals
In this paper we focus on Norwegian first-year engineering students’ interpretations of differentials and definite integrals. Through interviews with...
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Learning Integrals Based on Adding Up Pieces Across a Unit on Integration
Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of...
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Mathematics Is Indefinite: An Ethical Challenge
Mathematics is indefinite with respect to concepts and proofs. Mathematical concepts are constructed and deconstructed, and conceptions of what is...
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Long-Term Principles for Meaningful Teaching and Learning of Mathematics
As mathematicians reflect on their teaching of students, they have their own personal experience of mathematics that they seek to teach. This chapter...
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Approaches to Integration Based on Quantitative Reasoning: Adding Up Pieces and Accumulation from Rate
Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for...
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Critique of Mathematics
Several obstructions are in the way of us conducting a critique of mathematics. One is the general glorification of mathematics, which, for instance,...
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Mathematics in Nature
This chapter gives the Renaissance and rationalist philosophers of the 16th and 17th century have the word. The Renaissance is generally...
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Asé O’u Toryba ‘Ara Îabi’õnduara!
In this chapter, we aim to problematize the alleged uniqueness and universality of Western logical-formal mathematics and the philosophies that...
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The Winning Ways of John Conway
John Horton Conway combined his passion for mathematics with an unquenchable enthusiasm for games. In addition to inventing a bewildering variety of...
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Language of Science
Science develops only through proper communication. As language is a medium of communication, it is important to ponder a little on the language of...
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A Framework to Design Creativity-Fostering Mathematical Tasks
Fostering students’ mathematical creativity is important for their understanding and success in mathematics courses as well as their persistence in...
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The Fundamental Theorem of Calculus and Conceptual Explanation
This chapter employs ideas about rates of change and Cavalieri’s (2D) principle for conceptualizing area to offer an intuitive justification for the...
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Transition from high school to university calculus: a study of connection
In Tunisia, calculus is a fundamental component of mathematics curriculum in high school and a major requirement at the advanced level in the...
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Mathematics, the Common Base for Science
Does one require mathematics to understand the world around us? Yes, Mathematics as a common base for science has been and is playing a fundamental...
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The theory of calculus for calculus teachers
The aim of this paper is to narrate a significant part of the experience of a professor over several semesters teaching fundamental ideas of the Theory...
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Queer identity and theory intersections in mathematics education: a theoretical literature review
Researchers have become aware of a need to focus on the continued development of gender and sexuality research in mathematics education, as...
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Emergent Quantitative Models for Definite Integrals
Prior research on students’ productive understandings of definite integrals has reasonably focused on students’ meanings associated to components and...
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The Limit Notion at Three Educational Levels in Three Countries
This paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this...
