scholarly journals Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function

2020 ◽  
Vol 57 ◽  
pp. 100752 ◽  
Author(s):  
Keith Weber ◽  
Juan Pablo Mejía-Ramos ◽  
Timothy Fukawa-Connelly ◽  
Nicholas Wasserman
Keyword(s):  
Secondary Mathematics ◽  
Advanced Mathematics ◽  
Domain Restrictions ◽  
Inverse Functions

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Inverse Functions of y = x 1/x

2001 ◽  
Vol 108 (10) ◽  
pp. 963 ◽  
Author(s):  
Yunhi Cho ◽  
Kyunghwan Park
Keyword(s):  
Inverse Functions
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