Pupils' needs for conviction and explanation within the context of dynamic geometry.
Citations
218 citations
Cites background from "Pupils' needs for conviction and ex..."
...…Balacheff, 1988a and b; Bell, 1976a and b; Harel and Sowder, 1996; Sowder and Harel, 1998), and descriptions of students’ beliefs when deciding whether they are convinced by an argument about the truth of a statement, or not (De Villiers, 1991; Harel and Sowder, 1996; Sowder and Harel, 1998)....
[...]
98 citations
51 citations
51 citations
46 citations
References
1,157 citations
318 citations
"Pupils' needs for conviction and ex..." refers background or result in this paper
...It also takes cognisance of the levels expounded by the Van Hieles and also previous research conducted by other authors and researchers, including that of De Villiers (1990;1991) and Zack (1997 : 291-297)....
[...]
...For example, Hanna (as quoted in De Villiers, 1990 : 21) claims that "mathematical concepts and propositions are .. . conceived and formulated before proofs are put in place"....
[...]
...Although it is quite possible to achieve a high level of conviction that a conjecture holds true by experimentation, this does not provide a deeper understanding as to why the conjecture may be true (De Villiers,1990 : 19)....
[...]
270 citations
"Pupils' needs for conviction and ex..." refers background in this paper
...Besides, we do not fully understand the physical processes by which the computer works (Hersh, 1993 : 393)....
[...]
...This view of proof functions "as the last judgement, the final word before a problem is put to bed" (Hersh,1993 : 390)....
[...]
...100 years from now the map theorem will be, I think, an exercise in a first - year graduate course, provable in a couple of pages by means of the appropriate concepts, which will be completely familiar by then" (Hersh, 1993:393)....
[...]
261 citations
"Pupils' needs for conviction and ex..." refers background in this paper
...(Bell, 1976 : 26) This function of proof is concerned with the logical organisation of propositions into a deductive system....
[...]
203 citations