Friday, October 4, 2013

Math problems of the week: 1960's vs. 21st century introductory geometry problems

I. From Weeks Adkins A Course in Geometry (1961), pp. 3-4 [click to enlarge]:

II. From Discovering Geometry: An Investigative Approach (2003), pp. 4-6 [click to enlarge]:

III. Extra Credit:
Discuss the relative importance of logical reasoning vs. recognizing symmetry in the 20th vs. the 21st centuries.


Auntie Ann said...

The wording of the 1961 problems is strange. If I were a smart-aleck student, I would answer them: 1) yes 2) no 3) yes 4) yes 5) yes, etc.

Can you deduce? is a different question from: Can you deduce, and if so, what is your deduction?

kcab said...

To be honest, I think both logical reasoning and recognition of symmetry have a place in the geometry curriculum. Where to place what content is a choice. DS's class is working from Jurgenson, Brown, Jurgenson (McDougall Littel, 1997) and his text devotes chapters to each. In fact, page 4 of his book has a series of questions about optical illusions - which could look pretty light. I've found it a good geometry textbook though, and was surprised to see 2 column proofs crop up in the 2nd or 3rd week.

But...since my older child's class used the Discovering Geometry book I know that text doesn't get any more demanding as the course goes on.