ABSTRACT
There are many situations in which the people make comparisons without consciously assigning a measure. The Davydovian school of thought proposes that young children can be introduced to measure comparisons long before they need to know anything about number as quantity. To focus students' attention on a unit of measure, Barret et al. introduced a "broken ruler" task, in which students were asked to use a ruler where the beginning was intentionally broken and 2 was the first shown number. In several tasks, the authors emphasized the idea that all the "standard" units of measurement used today are, in a way, arbitrary; they have been agreed upon at some point and eventually became common usage. Compare two ideas using different bases to present numerals symbolically and different units of measure.
