V. Giraldo, L. Carvalho, and D. Tall. Proceedings of the 27 thAnnual Conference of the International Group for the Psychology of Mathematics Education, (2003)
L. Radford. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, page 143-145. Melbourne, Australia, University of Melbourne, (2005)
J. DeLoache. Child Psychology in Retrospect and Prospect: In Celebration of the 75th Anniversary of the Institute of Child Development, Lawrence Erlbaum Associates, Mahwah, NJ, (2002)
L. Lee. Approaches to algebra: perspectives for research and teaching, Kluwer Academic Publishers, p 102
… it is much of a challenge to demonstrate that functions, modelling, and problem solving are all types of generalizing activities, that algebra and indeed all of mathematics is about generalizing patterns.
p 103
The history of the science of algebra is the story of the growth of a technique for representing of finite patterns.
The notion of the importance of pattern is as old as civilization. Every art is founded on the study of patterns.
Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of patterns.(1996)
M. Cerulli, A. Chioccariello, and E. Lemut. 5th CERME conference - congress of European Society for Research in Mathematics Education, Larnaca, Cyprus, (2007)
D. Carraher, A. Schliemann, and B. Brizuela. Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education, (2001)
A. Newell, and H. Simon. Communications of the ACM, 19 (3):
113-126(March 1976)p. 116:
"The Physical Symbol System Hypothesis. A physical
symbol system has the necessary and sufficient
means for general intelligent action."
p. 120:
"Heuristic Search Hypothesis. The solutions to
problems are represented as symbol structures.
A physical symbol system exercises its intelligence
in problem solving by search--that is, by
generating and progressively modifying symbol
structures until it produces a solution structure."
p. 121:
"To state a problem is to designate (1) a test
for a class of symbol structures (solutions of the
problem), and (2) a generator of symbol structures
(potential solutions). To solve a problem is
to generate a structure, using (2), that satisfies
the test of (1).".
S. Fincher, M. Petre, and M. Clark. Springer-Verlag, London, UK, (2001)page 2: patterns as -
ä form, a "packaging", for transfer materials which does not prescribe or patronise and equally does not överwhelm with information".".