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*Monday, November 07, 2005*

Outline of Work to be done on

Learning Theory and the Core Liberal Arts Curriculum

Part Three

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**The
starting question ”What is 1/2 + 1/3
equal to?”**

Part one is given at { hyperlink }.

Let us start with the question

What is 1/2 + 1/3 equal to ?

If the question is “in base 10”, then we have a problem that many developmental mathematics students are not comfortable with. So the learning strategy is to change the question into one that has never been posed to these students. The idea, grounded in behavioral science, is that novelty often has an orienting response, and that this response overrides a learned discomfort with basic arithmetic.

The new question is:

What is 1/2 + 1/3 equal to in base 5 ?

This problem is difficult, at first, even for students who have majored in mathematics, since a “system of reasoning” and a “set of conventions” is required if the correct answer is to be determined. One has to appeal to foundational notions about counting and to understanding the formal properties of the “operations” of addition and multiplication.

More important than the correct answer is a motivation for attempting to determine the answer.

The use of a “participatory” and “self discovery” learning pedagogy requires that the student or students discover a path to personal understanding.

Many different learning strategies can be seen. The group can work together or individuals can work alone. The key is that the group be allowed to examine the nature of the social philosophy and self-image.

There is a bottom line. Something is simple and yet something inhibits the student’s learning. The positive outcome is a student whose awareness is open to his or her involvement in higher learning.