Coherence and Connections

[lhwalker]

Every time I read “coherence” and “connections,” I feel a twinge of guilt knowing that after ten years of teaching high school math, I still don’t have all those down.  I know I’m not alone because every year my Algebra 3 students are surprised by many of the connections I do make.  For example, when I explain adding complex numbers is consistent with adding “like terms” beginning with adding tens to tens and ones to ones, followed by adding fractions with common denominators, radical expressions, etc., it becomes apparent it is the first time anyone has made those connections for them.  Can you recommend some reading on “coherence” and “connections?”

[Bill McCallum]

Well, there are the progressions documents! When I was growing up (in the previous century) I remember reading books by W.W. Sawyer which really brought out a lot of connections for me. His “Vision in Elementary Mathematics” deals with middle and high school topics, and is available on Amazon. Another nice book at a higher level is Gelfand and Shen’s Algebra. Maybe others could add their suggestions.

[lhwalker]

Both books are on their way.  And, yes, you know I’ve read the progressions!

[Author]

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