Balacheff (1987) described four levels of justification, which are those as follows: (1) Native empiricism;

2) Crucial experiment;

3) Generic example; and 4) Thought experiment. (Taflin, nd)

Naive empiricism is stated to be "an assertion based on a small number of cases." (Taflin, nd) Crucial experiment is stated to be "an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) the generic example is stated to be "...an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) Thought experiment is "an assertion detached from particular examples and begins to move toward conceptual proofs." (Taflin, nd)

The work entitled: "Adding it Up: Helping Children Learn Mathematics" states that proficiency in instruction of mathematics is "related to effectiveness: consistently helping students learn worthwhile mathematical content. It also entails...

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