Originally Posted by ElizabethN
I just find that these studies that start with "there's a correlation between not understanding fractions and not being able to learn algebra" and go directly to "we need to teach fractions better" may be skipping an important logical step.

That's a fair point. The authors make this argument:

Originally Posted by Siegler et al Early Predictors of High School Mathematics Achievement
If students do not understand fractions, they cannot estimate answers even to simple algebraic equations. For example, students who do not understand fractions will not know that in the equation 1/3X = 2/3Y, X must be twice as large as Y, or that for the equation 3/4X = 6, the value of X must be somewhat, but not greatly, larger than 6. Students who do not understand fraction magnitudes also would not be able to reject flawed equations by reasoning that the answers they yield are impossible. Consistent with this analysis, studies have shown that accurate estimation of fraction magnitudes is closely related to correct use of fractions arithmetic procedures (Hecht & Vagi, 2010; Siegler et al., 2011). Thus, we hypothesized that 10-year-olds’ knowledge of fractions would predict their algebra knowledge and overall mathematics achievement at age 16, even after we statistically controlled for other mathematical knowledge, information-processing skills, general intellectual ability, and family income and education.

This argument makes sense to me. US elementary schools and math books generally teach kids how to do algorithms and don't go into depth about what's really happening when you do the algorithm, why it works, and how things in mathematics are inter-related. Fractions is a really good example of what I've said. Kids aren't taught about relationships between fractions and division, yet understanding these relationships is critical for doing algebra.