Analogical scaffolding and the learning of abstract ideas in physics: An example from electromagnetic waves

This paper describes a model of analogy, analogical scaffolding, which explains present and prior results of student learning with analogies. We build on prior models of representation, blending, and layering of ideas. Extending this model’s explanatory power, we propose ways in which the model can be applied to design a curriculum directed at teaching abstract ideas in physics using multiple, layered analogies. We report on a recent empirical study that motivates this model. Students taught about electromagnetic waves in a curriculum that builds on the model of analogical scaffolding posted substantially greater gains pre- to postinstruction than students taught using a more traditional (non-analogy-based) tutorial (21% vs 7%).

Figure 1

Relationship between sign, referent, and schema.

Figure 2

(Color) Sign-referent-schema for (a) the solar system and (b) the atom.

Figure 3

Conceptual blending diagram. Adapted from Ref. 12.

Figure 4

(Color) Blending the solar system and a rudimentary model of the atom.

Figure 5

Adding quantization produces the Bohr atom blend. The additional node between sign and schema represents a blend which incorporates quantization into the schema linked to this sign.

Figure 6

Scaffolding analogies of increasing abstraction.

Figure 7

Layering blends from string (top) to sound (middle) to EM waves (bottom). Each triplet of circles represents two input spaces and a blend space. The string and sound wave blends combine to become an input space for EM waves. Here we show a subset of possible blends. The association of pressure with air density could potentially come from a previous blend.

Figure 8

EM wave concept question. Correct answer is (D) $1=2=3=4$.

Figure 9

Results from study 2. Shifts on partially correct answer (Partial) which includes the 3D feature of EM plane waves. The correct answer includes both 3D and traveling wave features.

Figure 10

Two possible diagrams representing layering of mental spaces.