Making errors and experimenting with new strategies are a natural part of learning. However, if inappropriate thinking about fractions becomes established as a misconception, a barrier to progress in conceptual understanding is formed.
Usually misconceptions will not be corrected unless explicitly addressed by instruction. Teachers need to be aware of common misconceptions and look for evidence of them in their students' thinking. Identifying misconceptions requires careful observation or purposeful diagnostic assessment.
Further details about common misconceptions can be found in the article Developing an Understanding of the Size of Fractions on the AAMT website.
