Monday, November 07, 2005

Outline of Work to be done on

Learning Theory and the Core Liberal Arts Curriculum

Part Four

The Hints and Pedagogy

Part one is given at { hyperlink }.

How might one go about, as a class or as an individual, discovering the correct answer to the following question:

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

Hints:

Develop the system of mathematics that describes addition, multiplication and division of positive integers in bases other than 10.

What is counting?

What is the addition table for base 5?

What is the multiplication table for base 5?

What is positional notation and how does one convert a number in one base to a number in another base and yet preserve the “meaning” of the converted numbers?

What is division in base 5?

Questions:

In base 5

4+3+4 = ?

3*2 = ?

What is 3421 (in base 5) when converted to base10?

What is 3421 (in base 5) when converted to base 7?

Suppose that r is a prime number expressed in base n, and q is the quantity r expressed in base m.  Is q also prime?

Pedagogy

The pedagogy is based on ancient discovery pedagogy.  The most famous of these is the “Socratic Method” where the teacher poses questions to the student, rather and giving the student facts to memorize.