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Human and Machine Understanding of Mathematics  (Make Corrections)  
Edmund Furse



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Abstract: Mathematics provides a rich domain for discussion of deep questions about cognition in both humans and machines. Roger Penrose claims that it is impossible for a machine to understand mathematics, and therefore that a machine cannot be a mind. Research over several years into how university students learn and understand mathematics has led to a computational model of the task known as the Mathematics Understander (MU). MU can to some limited degree understand university level pure mathematics... (Update)

Active bibliography (related documents):   More   All
0.4:   Learning University Mathematics - Furse (1994)   (Correct)
0.4:   The Contextual Memory System: An architecture for declarative .. - Furse, Nicolson (1995)   (Correct)
0.2:   Perception and Experience in Problem Solving - Furse, Nicolson (1993)   (Correct)

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0.3:   An Adaptive Parser for Mathematics - Furse (1993)   (Correct)
0.3:   Learning Problem Solving Heuristics From Worked Examples - Morgan, Nicolson, Furse (1995)   (Correct)
0.3:   Tackling Engineering Retention: A Firsthand Experience - Hammoudeh, Barrett (2002)   (Correct)

BibTeX entry:   (Update)

@misc{ furse-human,
  author = "Edmund Furse",
  title = "Human and Machine Understanding of Mathematics",
  url = "citeseer.ist.psu.edu/106920.html" }
Citations (may not include all citations):
303   Unified Theories of Cognition (context) - Newell - 1990
128   Understanding Computers and Cognition (context) - Winograd, Flores - 1987
49   The Computer Modelling of Mathematical Reasoning (context) - Bundy - 1983
40   Dynamic Memory: A theory of reminding and learning in comput.. (context) - Schank - 1982
30   Mind over Machine (context) - Dreyfus, Dreyfus - 1986
26   Shadows of the Mind - Penrose - 1995
24   Darwin's Dangerous Idea (context) - Dennett - 1995
10   The Mathematics Understander (context) - Furse - 1994
6   You can't play 20 questions with nature and win: Projective .. (context) - Newell - 1973
6   Escaping from the Box - Furse - 1993
4   Perception and Experience in Problem Solving - Furse, Nicolson - 1993
1   The Emperor's New Mind (context) - Press, Massachusetts et al. - 1989
1   Reprinted in the AISB Quarterly Spring/Summer (context) - Sloman, Hogg et al. - 1993
1   The Contextual Memory System: An architecture for Declarativ.. - Furse, Nicolson - 1995
1   Learning Mathematics by Experience: a Model of Declarative L.. (context) - Furse - 1996

Documents on the same site (http://www.comp.glam.ac.uk/pages/staff/efurse/list-of-papers.html):   More
Learning Problem Solving Heuristics From Worked Examples - Morgan, Nicolson, Furse (1995)   (Correct)
Learning University Mathematics - Furse (1995)   (Correct)
The Mathematics Understander Edmund Furse - Furse (1994)   (Correct)

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