Structure-genetic Coding 
Stage I 
IA 
IB 
Stage II 
II A 
IIB 
Stage III 
III A 
III B 
Stage II-III was assigned to subjects 
under stage III unambiguously. 
product. 
Example: '4 buttons = 6 paper clips, 2 buttons = 
3 paper clips, 6 buttons = 9 paper clips. 2 buttons = 
3 paper clips, so Ihave to calculate 3 * 3 clips, 
because 3 * 2 buttons = 6 buttons. 
Preoperational 
Arbitrary answers, guessing, lacking explanations 
illogical conclusions 
Random use of numbers, arbitrary additions 
Concrete Operations 
Main criterion: Reference to differences 
Conservation of differences, simple scaling, 
differentiated additive method 
Method of differences 
Formal Operations 
Differences and estimations, empirical proportions: 
Concrete proportions' 
Reasoning is based entirely on proportions, 
division and multiplication to find the value in 
question 
who could neither be subsumed under stage II nor 
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