Abstract / Synopsis

As mathematicians, we often fail to appreciate the opportunities open to us when we teach developmental mathematics. One such opportunity is that we may deepen our understanding of mathematics that we have taken for granted. This paper contains a brief case study concerning what we have learned about operations, inverses, and exponents in the process of teaching beginning algebra. Our inquiry takes us from student questions about signed numbers, through the category of rings, to the world of Lie groups and Lie algebras.



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