Teaching equivalent fractions – five cognitive difficulties to address

This post is less about e-learning than about maths programme design in a wider sense, but it was inspired by reading a study on e-learning resources. I came across this statement when reading a PhD thesis from Arla Westenskow at Utah State University (you can find the original doc here). The thesis was about using physical and virtual manipulatives (applets etc) to help struggling maths students to learn equivalent fractions.

Five cognitive difficulties many students have in developing equivalent fraction understanding have been identified in the literature: (a) conceptualizing fractions as a quantity, (b) partitioning into equal subparts, (c) identifying the unit or whole, (d) building sets of equivalent fractions, and (e) representation model distractions.

How could this influence our teaching of fractions? I haven’t been teaching long and am just starting to move beyond the basic knowledge-delivery with teaching this topic. If we were to focus on each of these five cognitive difficulties and nail them, what would that look like? What resources can you share or suggest that could be useful for this? For those of you who are already doing this or partially doing this, can you share your insight or experience? Keen to pick your brains.

The thesis goes on to explore and discuss using manipulatives for remediating these five difficulties but the focus is more on the effectiveness of the types of manipulatives (which is why I’m reading it for my e-learning assignment), rather than focusing on the best way to remediate the difficulties from a more holistic programme-design perspective. Thoughts?

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