Place value underpins much of what people do in number. In this article, the author describes some simple tasks that may be used to assess students' understanding of place value. This set of tasks, the Six Tasks of Place Value (SToPV), takes five minutes to administer and can give direct insight into a student's understanding of the number system…

Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…