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Several major concepts are incorporated into this single problem.
Choosing (C), which is the correct choice, the student demonstrates that he understands:
Subtracting Mixed numbers
The Commutative Principle
Finding and Converting to a Common Denominator
Borrowing within Mixed Numbers
Reducing a Fraction
Choosing (B) would imply that the student does not understand subtracting fractions with different denominators. He does not know that he must first convert fractions to a common denominator before he can subtract.
Choosing (A) would imply that the student does not understand Borrowing. He Borrows as he would in decimal arithmetic and not as he should relative to the common Denominator.
Choosing (D) would imply that the student does not understand how to reduce a fraction
Choosing (E) "I don't know" would indicate confusion with the complexity of the problem
If the student chooses any thing other then the correct answer, EduCAD would deduce the students misconceptions or lack of understanding and relax those conditions on the next problem presented. If the previous choice represented his single issue then logically he would choose the correct answer on the reduced problem.
At this point, EduCAD would have established a boundary between what the student knows and does not know.
EduCAD WOULD NOW ENTER PRACTICE MODE.
Assuming that the Student, in the previous problem, choose "I don't know'" we would now enter practice mode with a set of problems of reduced complexity.
In this case the student has requested to be shown the first two steps in the process necessary to solve the problem.
He has been given enough hints to be able to correctly answer the question. He should now select a new problem - which will be of the same type. He can, at any time, exit and return latter. this iterative process will continue until the student has successfully solved the problem without any hints from EduCAD.
On January 15, 2008 EduCAD-ST will be available in a FREE Public BETA and we are overjoyed to be able to offer pre-registration for access to the product.
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