he Virtual Playground: an Educational Virtual Reality Environment for Evaluating Interactivity and Conceptual Learning

connecting them to real-world situations []. In other words, fractions lend
themselves to designing learning tasks that are, at the same time, conceptually
difficult, abstract enough to justify representation via a VR simulation of a
real-world situation, and can allow for a kind of varied and incremental
interactive treatment.

4.1. The conceptual learning problem: representing fractions

Research has shown that students begin to construct a deeper understanding
of fractions when these are represented in a variety of ways and when there
are explicit linkages to everyday life and familiar situations involving their
use. Elementary-school children’s difficulties in learning fractions and
understanding their representations have been well documented [] while a
number of educational technology research projects and products have been
developed on this topic [] []. Traditionally, fractions have been represented
with a formal symbolic system (for example “1/3”), which essentially is an
“artificial” construct used for performing arithmetical operations and learning
fractions in school. To facilitate understanding of fractions, educators have
been using various means and methods to teach them, such as 2D pictorial
representations (the “pie” metaphor), manipulative models (rods, arithmetic
blocks, bars, number lines, paper folding exercises, and others), and “real
world” story scenarios.

Figure 2. Lesh’s translational model (left) illustrates the five distinct types of representing
mathematical ideas (fractions) for instructional purposes. We propose enhancing Lesh’s
translational model with an immersive and interactive VR representational component (right).

The problem, however, of connecting the symbols to real-world situations
remains; it is often difficult for students to integrate formal instruction with
their informal knowledge. Mack [] suggests that comparison of fractions is

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