Adaptive tutoring systems often model student knowledge in ways that break away from a "one size fits all" approach to learning. Nonetheless, the strengths of these systems can often be limited, as knowledge representations are not easily interpreted by teachers, which make these systems difficult to integrate into pedagogical practices.…

An approach to solving equations is presented. (SD)

The author describes a technique for teaching various aspects of the subtraction algorithm (e.g., regrouping, borrowing) by relating them to the use of money. (SD)

Algorithms for the four basic operations on whole numbers are described; these algorithms provide for sequential recording of all steps in the operations. (SD)

The author proposes that computer programs which are designed to make algorithmic structures accessible and comprehensible be employed as advance organizers in mathematics instruction. These programs would bring clarity and structural integration to mathematical, instructional, and cognitive structures important to the mastery of mathematical…

This study investigated the effects of the nature of the algorithm, reinforcement, and level of problem difficulty on the ability of fourth graders to solve addition problems as measured by the number of problems correctly solved and the number of columns attempted. Subjects were selected for high scores on a test of basic addition facts; only…

The four sections of this monograph review current research related to mathematics education from the points of view of studies concerning (1) the curriculum, (2) the child, (3) the learning environment, and (4) teaching methods. Topics addressed in part one include the sources of mathematics curricula, the curricular validity of "new…