Thursday, October 6, 2011

Math problems of the week: 1900's algebra vs. Chicago Math algebra

Final problem sets on graphing

I. From the end of Wentworth's New School Algebra (1898), p. 423 [click to enlarge]:


II. From the end of The University of Chicago School Mathematics Project Algebra: Integrated Mathematics (2002), p. 815:

III. Extra Credit:

How do you think 21st century Chicago Math students, equipped with graphing calculators, would do on the 1900's graphing problems?

6 comments:

Anonymous said...

It seems to me the 1898 example leads to understanding, whereas the 2004 example leads students to becoming calculator technicians, but most likely without understanding of what they are doing.
--Lynne Diligent
expattutor.wordpress.com

Anonymous said...

That seems to always be the case with the use of calculators. But it is possible that they want to push students through math not to really learn math but to use it at a simplistic level. For example, most people don't know assembler language, and then there is a step up from that, and then from that, and so on until you get to object oriented programming, and now overlays where all you practically have to do is write sentences to program. And still with that people can make a simple programs. Most people do only want to be at a simple level in math, use it, not understand it, as with most anything now, which is why something like common core state standards is so low in expectations. If you keep the population dumb enough, you can tell them anything and control them to your ends and they won't bother to find the facts. Or believe the facts.

Anonymous said...

One question I have about Wentworth's book is what grade or age level he intended to be writing for. Of course, I realize that algebra, like any other subject, can be taught when the student is ready for it. That said, I wonder, in practice, for which grades his book was used in 1898. Can anyone provide this information? I would find that useful. Also, were all children expected to learn this material, or was the expectation that only college-bound students, for example, expected to? Thanks.

Barry Garelick said...

Good question about grade level. I can say though that the questions and problems in Wentworth weren't too terribly different from the algebra book I had in 1964, and I took algebra in 9th grade. The material is within the grasp of most students who have had sufficient math in the preceeding grades.

Anonymous said...

However, in 1898 most children finished school at the 8th grade level (if that). High School was for the more academically-inclined of the middle class and on up.

Barry Garelick said...

Most people do only want to be at a simple level in math, use it, not understand it, as with most anything now, which is why something like common core state standards is so low in expectations. If you keep the population dumb enough, you can tell them anything and control them to your ends and they won't bother to find the facts. Or believe the facts.

Common Core standards are laden with "students shall understand" this or that, for the lower grades, to the extent that "understanding" may overshadow the procedural. The expectations for the lower grades is unrealistic for both teachers and students. For high school grades, I agree, the expectations are quite low.

As to