This study sought to compare the effectiveness of teaching with manipulatives versus algorithms and procedures. Assessment data were collected before instruction, after instruction with algorithms and procedures, and after instruction with modeling and manipulatives. Data were collected from 113 students from the 5th, 6th, and 7th grades within…

Accurate placement into an initial college mathematics course is a key step toward the successful completion of college mathematics and, eventually, a college degree. Conversely, misplacement in mathematics may lead to a reduced likelihood of course completion and degree attainment. This study investigated the ability of two placement models to…