Friday, February 8, 2013

Math problems of the week: introducing algebra in 1900s vs. Singapore Math

I. From the end of the 5th chapter (out of 27 chapters) of Wentworth's New School Algebra (published in 1898), pp. 70-71 [click to enlarge]:


II. From the end of the 5th chapter (out of approx. 16 chapters) of the Singapore Math Discovering Mathematics 7A (Common Core), p. 29) [click to enlarge]:


III. Commentary:

My daughter finished up the Singapore Math Challenging Word Problems for 6th grade back in October and, after checking out the two Singapore Math sequels, New Elementary Mathematics and Discovering Mathematics, I opted instead to start her on Wentworth's New School Algebra. She's no math genius, but, after all that solid 1st-6th grade Singapore Math, complete with the Challenging World Problems series, I felt she was ready to move beyond arithmetic straight into algebra--something that neither the Singapore Math sequels do. There is some algebra in New Elementary Mathematics and Discovering Mathematics, but there's still a lot of arithmetic mixed in.

Wentworth's 1898 New School Algebra, on the other hand, moves straight into algebra, in the most straight forward, systematic way I've seen in any algebra book. Chapter I: Definitions and Notation; Chapter 2: Simple Equations; Chapter Three: Positive and Negative Numbers [in algebraic expressions]; Chapter Four: Addition and Subtraction [of polynomials]; Chapter Five: Multiplication and Division [of polynomials]. So straight forward and systematic is Wentworth's curriculum that my 6th grade daughter, after doing every single problem leading up to this, is now working on the above problem set with minimal assistance from her mother.

It makes me wonder how many other 6th graders could get this far with algebra, if only they were given a Singaporean foundation in arithmetic followed by a Wentworthian systematicity in introductory algebra.

11 comments:

FedUpMom said...

Katharine, you've got your titles ("Singapore" vs, "Wentworth") reversed.

I'm happy to report I've gotten my Younger Daughter started on Singapore Math. So far it's review, but I see it will start getting harder soon. I'm looking forward to showing her the old-fashioned stacking method, which is no longer taught in our district ...

Katharine Beals said...

Thanks for catching that, FedUpMom! Good to hear about your daughter. Make sure she doesn't get in trouble for stacking at school--it happens...

C T said...

They no longer even teach the stacking method? I thought understanding place value was one of those all-important standards they try to meet. Stacking correctly requires implicit understanding of place value! Not to mention it's straightforward, efficient, and easy to remember. Why must they make something so straightforward into multiple mysterious processes? Sigh. SO glad I'm not forced to submit my children to them for their version of math instruction...I mean, discovery.

TerriW said...

Excellent -- I was wondering which direction you went after Singapore.

Auntie Ann said...

Our boy is finishing Singapore 5. He'll take the ISEE next December, we're wondering what to do next?

I'm thinking of using the PurpleMath website to get him the little prealgebra things needs like absolute value, working hard on double negatives, etc.

Any recommendations?

Anonymous said...

My boy and I enjoy the Art of Problem Solving Pre-Algebra book.

Auntie Ann said...

I have that one (APS), but the sheer size of it is daunting! I'll take a look through it. We're not homeschoolers, so this is a supplement to his other homework.

Auntie Ann said...

And, the school uses EM, so his homework is worse than useless.

Anonymous said...

Auntie Ann, I think APS is a good book for doing it yourself. Call me weird, but it seems like great fun to me and is very much the book I wish I'd had when I was that age. My boy is enjoying it as well.

I hear you on useless school math. TERC Investigations and bullying are the reasons we stopped using school. It doesn't get any better, does it?

Cassandra Turner said...

My boys went from 5 years of Singapore to Foerster's Algebra with no issues. Foerster's is also a straight forward, no-nonsense Algebra book.

Crimson Wife said...

I like Discovering Math 7, but I skipped my DD directly to it after finishing Primary Math 5A. There is a lot of overlap between 5B-6B and DM 7. So I decided to accelerate to the book that would quickly review pre-algebra before getting into the easier aspects of algebra 1. She will do DM 8 in 6th grade and that is mostly algebra with some geometry thrown in.

I am also incorporating some of the word problems from Larson's Elementary Algebra. I like those because they show how algebra is used in real life situations.