Posts
...starting with volume 4A, which is used in the first half of 4th grade, algebra story problems begin to appear. Consider the following problems:
1. 300 children are divided into two groups. There are 50 more children in the first group than in the second group. How many children are there in the second group? (Primary Mathematics volume 4A, page 40, problem 8)
2. The difference between two numbers is 2184. If the bigger number is 3 times the smaller number, find the sum of the two numbers. (Primary Mathematics volume 4A, page 40, problem 9)
3. 3000 exercise books are arranged into 3 piles.
The fist pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile? (Primary Mathematics volume 4A, page 41, problem 10)
source:
Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore (pdf file)
Sybilla Beckmann
Used copies of the first edition of Beckmann's textbook are here. Dipping in and out of the book, I've found it somewhat difficult to understand. Not sure whether it would be easier if I sat down and worked straight through.
This isn't exactly a 'no' vote....I think the book is probably valuable.
But its look to me as if it may not serve well as a self-teaching text.
The Parker and Baldridge text may be better for that purpose, but I'm not sure. At the time I was working with Parker and Baldridge I was in desperate need of basic understanding of arithmetic, so I was highly committed to getting through that book. And, in fact, I didn't get through it; I made it through only 50 pages....which may tell me that Parker & Baldridge is no more accessible to the self-teacher than Beckmann's work appears to be.
I ended up doing best just teaching myself math out of math textbooks.
I'm going to give Parker & Baldridge another go.
3 comments:
Haha, at that time though, I didn't know we were using algebraic principles.
In fact my teacher explicitly discouraged using algebraic variables on the exam (especially since they were more like unknowns, not variables). We thought that algebra meant substituting numbers with letters, and we didn't know that writing lines like "(3000-10) books = 2*second pile + 1/2 second pile = 5/2 second pile" and therefore "second pile = 2/5 * 2990 = 1196" was algebra.
The effect is that I think we avoided the whole issue with using abstract letters for concrete concepts. IIRC, they don't "officially" introduce algebra until primary six or something, when people get "5p slippers" and we're supposed to find q in terms of p, or something. But by then the principles are so well-grounded that this change is of no consequence.
We thought that algebra meant substituting numbers with letters, and we didn't know that writing lines like "(3000-10) books = 2*second pile + 1/2 second pile = 5/2 second pile" and therefore "second pile = 2/5 * 2990 = 1196" was algebra.
That is so cool.
I have to put this comment "up front."
Chris once asked me, "Are there any numbers in algebra, or is it all letters?"
I thought it was funny at the time, until Tracy explained to me that his question was basically correct.
(assuming I'm not putting words in her mouth...)
That is unbelievable.
How is it that they can do this at such a young age?
Still, this is basic algebra, so it's not necessarily HARD, specifically speaking. If one gets that each group has such more than the other, a simple method can be used to solve the problem.
For problem number three, an algebra system can easily be created, but I think Singapore-wise, it's basically what is part of what and so forth.
Post a Comment