“The rivalry between the two philosophies is suggested by the anecdote that Antisthenes said to Plato: ‘I see a horse, but I don’t see horseness,’ to which
Plato replied: ‘No, for you have the eye with which a horse is seen, but you have not yet acquired the eye to see horseness.’” Guthrie, W.K.C. (1969). A History of Greek Philosophy (Vol. 3, p. 543). Cambridge: Cambridge University Press. p. 214.

For the past three Faculty Fridays we have highlighted “Back to Basics” instructional strategies – borne out by the research – to help your students in the
fight against forgetting. Our source is Organizing Instruction and Study to Improve Student Learning, a
2007 practice guide from the Institute of Education Sciences (IES).

Click below to read

• The Overview
  and Recommendation 1
• Recommendation 2
• Recommendation 3

Below is Recommendation 4 directly from the guide.

Recommendation 4: Connect and integrate abstract and concrete representations of concepts.

“Connect and integrate abstract representations of a concept with concrete representations of the same concept.

Evidence Level: Moderate

We recommend that teachers connect and integrate abstract representations of a concept with concrete representations of the same concept. Connecting
different forms of representations helps students master the concept being taught and improves the likelihood that students will use it appropriately
across a range of different contexts. (p. 15).”

In Practice

This week’s practice guideline evokes Plato’s doctrine of universals, in which every tangible object – or particular – shares in the essence of an ideal
“Form.” A chair – which can take myriad physical shapes – is a chair because it has “chairness.” Each horse participates in the ideal of horseness. What
happens, though, if you can’t recognize “chairness” or “horseness”? Although Plato hoped to lift people’s perspective up the world of Forms, as teachers
today we know that connecting abstract concepts to concrete representations is critical to equip students with understanding that is transferable to new
contexts.

For example, as the guideline suggests, if you are teaching gravity, you might consider how many ways you can instantiate gravity in real contexts: gravity
on Earth, on other planets of different sizes, gravity between small objects versus large objects, gravity in different kinds of substances or atmospheres,
or gravity at astronomical scale. Having students see gravitational force played out in different concrete representations will help build a stronger, more
flexible understanding of the concept of gravity. As a corollary, if you use a single concrete example as a prelude to your initial explanation, creating
comparisons to other concrete examples will help you ensure that their understanding of the concrete example is not at the expense of building an abstract
(and more transferable) understanding of that concept.

Two additional methods from the Guide that can help you lead your learners’ minds to build the appropriate conceptual understanding: 1) scaffolding, or
fading, the concrete representation; and 2) asking your students questions about the differences and similarities between the particular, concrete
representations, which will bring them to reflect and generate meaning around the essence of the abstract concept. To return to our epigraph, these methods
are the ones that can help your learners acquire the eye for “horseness,” and not just to see the horse itself.

Next week, we will discuss the fifth recommendation – Use quizzing to promote learning and see what the research suggests is best practice. Join us on
September 17.

Note: The Organizing Instruction and Study to Improve Student Learning guide was intended primarily for educators in grades 3-12, but the authors believe their findings are generally extensible to higher education.