The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…

In this study, we analyzed student participation and success in a college-level Calculus I course that utilized standards-based grading. By measuring the level to which students participate in this class structure, we were able to use a clustering algorithm that revealed multiple groupings of students that were distinct based on activity…

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)