Mathematics teachers and mathematics educational researchers were asked to rank order arithmetic and algebra problems for their predicted problem-solving difficulty for students. It was discovered that these predictions matched closely the view presented implicitly by common mathematics textbooks, but they deviated systematically from actual algebra students' performances in important ways. The Textbook view of early algebra development was contrasted with the Verbal Precedence (VP) model of development. The latter was found to provide a better fit of students' performance data. Implications for student and teacher cognition are discussed in light of these findings.
