Friday, May 1, 2009

Math problems of the week: 4th grade Trailblazers vs. Singapore Math

1. From the "Patterns in Multiplication" unit, Unit 7 of the Math Trailblazers grade 4 Discovery Assignment Book, p. 80:

For the following problems, make a prediction of what you think the answer will be. Then, do the problem on your calculator to check.

A. 6 × 70 = ____
B. 8 × 400 = ____
C. 800 ×6 = ____
D. 7000 ×4 = ____
E. 800 × 8 = ____
F. 60 × 4 = ____

2. From "The Four Operations of Whole Numbers" unit, unit 2 of the 4th grade Singapore Math Primary Mathematics 4A, p. 60:

Estimate and then multiply.

218 × 37 =
⇓ ⇓
200 × 40 =

218
× 37


483 × 59 =
⇓ ⇓
___ × ___ =

483
× 59


372 × 64 =
⇓ ⇓
___ × ___ =

372
× 64


648 × 78 =
⇓ ⇓
___ × ___ =

648
× 78


3. Extra Credit Question:

Need I say more?

1 comment:

Anonymous said...

Although comparing problems is good, the more interesting, difficult, and unanswered question is how the problems were written and then tested in classrooms. A comparison between US and Singapore institutions would be helpful.

Imagine the effort that went into writing, testing, and then evaluating some 50 odd textbooks (those textbooks that were eventually submitted for state adoption. By comparison, the Singapore MOE not only funded, but wrote, piloted, and evaluated just one curriculum.

Not only that but Singapore developers reverse-engineered the content of their books. They started with the goal of what high school graduates should know to be prepared for college level mathematics, not that all students should be prepared for college, as in the US (which we know from practice is false). They used standard algorithms and no others, to avoid confusing students. They actually thought about their target audience - students who's second language was English.

In the US, curriculum developers are constrained by what is age appropriate. And they compound the problem by ignoring the majority of their target audience. Every evaluation funded by the NSF is constrained only to the students who remained in the program for the entire year. The reader does not get to learn about who left the program and why. Secondly, the students needed to be able to read and understand the textbooks to become a part of the evaluation. We do not know what extra math instruction they received. The list is endless.

The question should be how can our goverment serve the people best. What is being done presently to students on a daily basis cannot be the answer.