Friday, November 22, 2013

Math problems of the week: traditional vs. Integrated Math algebra

Highest Common Factors in 1900's algebra vs. Integrated Mathematics

I. The first problem set involving highest common factors in Wentworth's New School Algebra (published in 1898) [click to enlarge]:

(Repeated from last week's post).


II. The only discussion of and problem set involving highest common factors in Integrated Mathematics 2: Algebra * Statistics * Trigonometry(published in 2002) [click to enlarge]:


III. Extra Credit:

Just as you did in last week's extra credit assignment, write a formula relating the depth and difficulty of these problem sets to their respective page numbers.

2 comments:

Anonymous said...

It seems to me some of the difficulty of the problems depends on what has already been taught. It may be that factoring special quadratic equations has not yet been taught in the second example, while it must have been in the first. You cannot have problems relating to something not yet taught so it is hard to compare the two. Except that it is likely taught in many more stages in the second text.

Katharine Beals said...

"It seems to me some of the difficulty of the problems depends on what has already been taught."

Right. Assuming you're talking about difficulty in terms of how hard students find the problems, as opposed to difficulty in terms of mathematical complexity.

"It may be that factoring special quadratic equations has not yet been taught in the second example, while it must have been in the first."

Right. That's one of the points that this comparison implicitly makes.

"You cannot have problems relating to something not yet taught so it is hard to compare the two."

Unless what you're comparing is how advanced the math is in the two curricula, and the quantity and relative mathematical difficulty the highest common factor problems (which we find 110 pages into the first curriculum, as compared with 517 pages into the the second curriculum).

"Except that it is likely taught in many more stages in the second text."

In the second text, as we see here, there is only this one set of hcf problems. So there's only one stage taught. On the other hand, there are a number of stages that students of the first text go through, in the course of those 110 pages, that get them to where they are here.