These common errors, so often, are born out of the idea that students are handed numbers
and asked to reason with them. They draw from what they know the best. And in this case, students have spent the vast majority of their primary years working with whole numbers. When third grade rolls around and students are asked to compare these fractions it is entirely understandable that they draw on their knowledge of whole number comparisons. Who could blame them?
It is then imperative that we consider methods of building understanding of fractions and comparison for students before they overgeneralize and draw their own “connections” that are doing little more than building confusion. Using the concrete, representative, abstract model for instruction you can build understanding in the concrete and representative stages and slowly fold in opportunities for abstract thinking. Students will then have anchors in their concrete and representative work to pull from rather than drawing on whole number generalizations.
The concrete, representative abstract (C-R-A) model calls for instruction to be built from concrete hands-on experiences, linked to visual representations and ultimately these experience allow students to generalize their understanding through purely numeric or mental work.