Twelve students at each of Grades 3, 5, 7, and 9 were individually given tasks that presented problems with solutions from hypothetical students, accompanied by questions requiring students to contrast and compare the solutions. These tasks were followed by open-response estimation problems. The older children understood better than the younger children what was asked but were uncomfortable with estimation processes and outcomes. Acceptance of multiple estimates and rounding-then-computing rather than computing-then-rounding were both slow to develop. Recognition of the need to compensate for rounding errors increased with grade level. Schooling factors such as emphasis on unique answers and instruction on rounding and computional procedures seemed to influence results. Careful development of foundational concepts is recommended to prevent learning computational estimation as a set of algorithmic rules