Mathematics Education the Objective of Term Paper

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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.

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It also entails versability: being able to work with a wide variety of students in different backgrounds and across a range of mathematical content." (2001) in fact, discussions "build on student' thinking. They attend to relationships between problems and solutions and to the nature of justification and mathematical argument. All strands of proficiency can grow in a coordinated interactive fashion." (2001) Four specific prompts for extending the thinking of students: (1) Tell me what you were thinking; (2) Did you solve this in a different way? (3) How do you know this is true? (4) Does this always work? (2001).....

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