2001
DOI: 10.1080/14926150109556452
|View full text |Cite
|
Sign up to set email alerts
|

Symbols and the bifurcation between procedural and conceptual thinking

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

2
35
0
2

Year Published

2002
2002
2023
2023

Publication Types

Select...
5
4

Relationship

3
6

Authors

Journals

citations
Cited by 59 publications
(39 citation statements)
references
References 7 publications
2
35
0
2
Order By: Relevance
“…On the other hand, rectangles were translated semantically into "long squares" in Chinese language, so the mental image of rectangles in S2's mind was that one side needed to be longer than adjacent sides, but S1 was not influenced by "long squares" and identified squares as a kind of rectangles according to the attribute of determining rectangles, right angles. The result exhibited that subjects could extract the structure of a mathematical concept from mental images by informal reasoning in practical activities, which offer another strategy for understanding definition except giving meaning to a definition and extracting meaning from the definition (Tall et al, 2001). Furthermore, we would predict a procedure of recurring the development from mental images to mathematical definitions.…”
Section: Conclusion and Implications 61 The Characterization Of Menmentioning
confidence: 99%
See 1 more Smart Citation
“…On the other hand, rectangles were translated semantically into "long squares" in Chinese language, so the mental image of rectangles in S2's mind was that one side needed to be longer than adjacent sides, but S1 was not influenced by "long squares" and identified squares as a kind of rectangles according to the attribute of determining rectangles, right angles. The result exhibited that subjects could extract the structure of a mathematical concept from mental images by informal reasoning in practical activities, which offer another strategy for understanding definition except giving meaning to a definition and extracting meaning from the definition (Tall et al, 2001). Furthermore, we would predict a procedure of recurring the development from mental images to mathematical definitions.…”
Section: Conclusion and Implications 61 The Characterization Of Menmentioning
confidence: 99%
“…What causes mathematical proof to be one threshold of mathematics education, especially in geometry? Some researches (Vinner, 1991;Fishbein, 1993;Moore, 1994;Duval, 1998;Tall et al, 2001) have suggested major sources of the students' difficulties in doing (geometrical) proof, and definition is one of them. Definitions not only help form the concept image but every often have a crucial role in cognitive tasks (Vinner, 1991).…”
Section: Introductionmentioning
confidence: 99%
“…Our data (summarized in Tall, Gray, et al, 2001) reveals both general themes and specific information on cases (1)- (5) above. The general themes illustrate diverging approaches from procedural to proceptual in a spectrum of students from elementary arithmetic (Gray & Tall, 1994), through algebra (DeMarois, 1998;McGowen, 1998;Crowley, 1999), symbolic calculus (Ali, 1996), and on to formal mathematical theory (Pinto, 1998).…”
Section: E How Has the Theory Been Validated?mentioning
confidence: 99%
“…Reflecting on many aspects of learning over many years with the help of colleagues and students has led me to extend childhood experiences of perception and action to ideas of advanced mathematical thinking as used at a more formal level (Tall, et al, 2001;Tall, 2006). This builds on human perceptions and actions and their consequences in terms of symbolism and proof.…”
Section: Extending the Kaputian Programmentioning
confidence: 99%