Ladder of Abstraction

Today in PL, K-2 had an awesome talk about Bruner’s CPA theory and the impact on our Mathematics teaching. While we were unpacking the Singapore Bar Model method as a way for our K-2 students to visualise number problems, we stopped to acknowledge the sequence of learning experiences that scaffold the documents we program with.

We noticed that the documents encourage tangible and concrete experiences, but the more familiar we become with the content we begin to remove the concrete and rush children to the abstract (such as symbolic representations).

Here lies the stumbling block. In our eagerness, we hustle the learning to quickly and don’t allow for enough time where students are sitting in a representational or pictorial zone. Students require opportunities to record their thinking in many ways, including in picture format. Strong connections between concrete and pictorial encourage smoother transition between pictorial and abstract representations of the same concept.

The ladder of abstraction analogy was a way that we could meet our children’s needs by moving flexibly up/down the ladder. We don’t want to rush our children too fast up the ladder until they have been challenged enough at the concrete and pictorial level and been able to play with, test, conjecture, prove and disprove their understanding of concepts.

It was a real flow moment for myself and the K-2 team.