subtraction, multiplication and division,
and fractions, decimals, percents, and
ratios. If not linked to the concepts
embedded in the lessons, the bar model
would not necessarily be meaningful.
The bar model and the basic skills
embedded in the mathematical problems
bootstrap each other.
The end result of the Singapore Math
program is that 6th graders can solve
complex, multistep problems that most
U.S. students, even those in algebra
classes, would find challenging.
According to a 2005 study by the American
Institutes for Research (AIR), Singapore
Math 6th grade problems are
"more challenging than the released
items on the U.S. grade 8 National
Assessment of Education Progress"
(p. xiii). AIR also found that