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

sometimes difficult for students who regard fractions as discrete whole
numbers rather than as proportions. For example, when comparing fractions
such as 1/3 and 1/4, it is common for students to conclude that the fourth is
larger than the third because four is a bigger number than three in the
counting series. Students committing this type of error are probably applying
knowledge of whole numbers to fractions. By relating the formal symbols to
realistic situations and manipulative representations of fractional amounts,
students may be less likely to consider the fourth as larger than the third.
Similarly, Lesh and his colleagues, from their interviews with children, noted
that children constructed what they refer to as informal strategies for ordering
fractions []. These strategies reflect students’ use of mental images of
fractions to judge the fractions relative size and not taught procedures, such as
least common denominators and cross-products.

Based on the above, we believe that a simulation-based environment, such as
the kind provided by a VR environment, could provide an additional method
of representation of such deep concepts that might aid in conceptual learning.
This form of representation can combine the pictorial representation of
fractions with a simulation of real-world situations and, in the case of
interactive VR, the power of manipulative aids. Thus, we have enhanced
Lesh’s model with an immersive VR representational component (Figure 2)
and have designed appropriate learning problems in an interactive virtual
environment that involves tasks with fractions.

4.2. The virtual environment: redesigning the layout of a
playground

We decided to incorporate learning problems based on fractions into an
engaging VR application with a game-like scenario. Consequently, the idea of
designing a playground emerged. We created both a Virtual Playground for a
CAVE-like environment and a physical model using LEGO™ bricks. The
tasks designed for the virtual playground application involve modifying the
areas that the six main elements of the playground (swings, monkey bars, a
slide, a roundabout, a crawl tunnel, and a sandpit) cover. Each element covers
an area which is colour-coded and represented by blocks. The area
representing each playground element is initially incorrect (either too big or

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