Friday, March 9, 2012

Math problems of the week: 1900's algebra vs. Core-Plus Math

Introducing simultaneous equations.

I. From Wentworth's New School Algebra (published in 1898), "Simultaneous Simple Equations" chapter, pp. 174-175, p. 177, p. 178 [click to enlarge]:





II. From Core-Plus Mathematics Project, Course 1, "Linear Equations and Inequalities" chapter, pp. 227-228 [click to enlarge]:




III. Extra Credit:

Core Plus Course 1 (9th grade) contains about a dozen simultaneous equations problems, none involving more than two variables, and all with one of the variables isolated on the left side of the two equations as above. Thus, one variable is already "solved for," and the other one, appearing in two expressions that are equal to one another, can be solved for in a few easy steps.

Wentworth's New School Algebra contains many hundreds of simultaneous equations, many involving three variables, some with the variables in the denominators. Solving them involves multiple algebraic manipulations.

Relate this contrast to the amount of explanation given by the Core-Plus textbook (the entirety of which you see here) to the amount of explanation given by Wentworth above for just one of several algebraic methods.

3 comments:

Unknown said...

Funny, i have most of my g-grandfathers school books from the mid 1870s, among them a copy of Frenchs Common Arithmetic. Our district uses TERC Investiigations (trying to get rid of). Not only is the currciulum in the book published in 1869 clearer--my ggrandfather had a habit of working problems in the margins and end pages.

Finally took it into a Board of Ed meeting one night and actually showed them how an 11 year old kid who went ot a one room school house on the Illinois prairie actually had better math fluency at the same age as his gg grandaughter, who attends a supposedly first class Westchester County NY public school. Were the problem sets not geared to a farmers offspring--lots in rods, furlongs, bushels etc--I'd just teach her from the old book.

bky said...

The newer problems are an example of what I see in my kids public middle school algebra: they take as much of the algebra out as they can. There is almost no manipulation of expressions except for the simplest equation solving. They introduce 2x2 systems like this, with both lines already in point-slope form and lots of questions about what you would do with a table? a graph? etc? It gets really depressing when they get to exponentials. Instead of algebra (manipulating expressions) they make tables and graphs, tables and graphs. They eliminate the handicraft aspect of algebra.

Catherine Johnson said...

Unknown - do you mind telling us which town you live in? (I'm in Westchester, too.)

I'm thinking Ardsley may still have Terc. (And perhaps Ossining as well?)