A simple game built on E-slate, where the user must try to juggle two balls using two rackets. The educational idea of the game is to build a simplified model that embodies specific notions of mathematics and science and to apply mathematical concepts in a virtual realistic phenomenon. Our intention is to make students feel free to control the environment and play with variables making meaningful conjectures while playing the game.
- Games as attractors to motivate and engage puplis
- Games as meaningful contexts for pupils to develop mathematical contents
- Mathematical learning as a side effect of playing games
- Games and concepts, strategies and rules
- characteristics of toy and rules (mathematical concepts embodied in virtual realisticphenomena, logo programming)
- educational objective (enquiry through gaming, learning through re-constructing a game)
As genres: simulations, programming games
As media: computer game
boundary components (formal-informal rules, specific goal that can be changed, e.g. juggle the balls, change the logo program)
temporal components (no time limits, no end conditions (the player can continue playing even if he/she has achieved the goal of the game), no evaluation by the game)
structural components (2D interface (scene, logo code, representation of vectors))
inputs (dynamically (click and drag) change of representations, code editing), one player or more as team mates, computer facilitated, no structurally enforced rules)
intended use (edutainment)
As social activity: computer mediated, single player
Platform: pc, requires java
Development environment: E-slate - authoring system, toolkit of generic pieces of software which the user can connect in a variety of ways with the use of the Logo programming language
Design and development of software: academic, authoring system, research prototype
Context of play: local (collaborative groups), systemic/organizational (outside classroom, outside curriculum)
Intervention: research group aiming to perturb
The "Juggler" game
Functionalities of the game
Juggler is a simple game built on E-slate, where the user must try to juggle two balls
using two rackets (see figure 1), by manipulating the rackets with the mouse, in order
to "save" the balls from faling down. The balls move according to functions whose variables
can be dynamically changed by students through the manipulation of vector representations.
figure 1. The "Juggler" microworld
The educational idea of the game is to build a simplified model that embodies specific
notions of mathematics and science and to apply mathematical concepts in a virtual
realistic phenomenon. Our intention is to make students feel free to control the environment
and play with variables making meaningful conjectures while playing the game.
Thus we created a microworld that simulates velocity, gravity and motion of an object
in the Newtonian plane, in a playful way. The game is constructed by means of a logo
program about a page long, connecting the various E-slate components (vectors,
logo editors and scene) and defining the rules of motion and collision through several fuctions.
The logo program can be understood by a high school student (in Greek curriculum
this program is fully tangible by students of age above 15).
The simulation incorporates mathematical representations of vectors that students
must dynamically manipulate in order to achieve the game goal. Additionally, students
are able to interfere with the logo program and change the variables of he functions,
that is to modify and predict the response or trajectory of the balls.
The initial parameters are set by means of vector representations of the initial velocity
and the force of gravity. Once the game has started, the vector representations change
dynamically as the balls move, while the gravity remains constant of course. The difficulty
of the game increases when the gravity vector becomes larger or when the initial velocities
are placed in corresponding magnitudes and orientations.
Our design agenda was to investigate what students can make of the game and what
mathematical meaning could derive from the interaction of students with the environment.
We introduced the game into two groups consisted of two students each and gave them
the following tasks retrospectively:
1. The first group had to juggle the balls using the rackets or changing and
editing the logo program.
2. The second group had to play with the game in ordr to change the rules
or representations, and by this action to recostruct the game.
Students of the first group tried to juggle the balls by using three different strategies.
i) They moved the rackets and set the parameters of velocity and force through dynamic
manipulation of vector representations.
ii) They tried to predict balls' trajectory in order to juggle the balls by moving the rackets.
For acheiving this, they alternated the functions regarding the trajectory of the balls, in
the logo program.
iii) They placed the rackets in different places and tried to juggle the balls between them
(see figures 2, 3, 4).
figure 2. Students changed the orientation of force and velocity in order to
juggle the balls reversely.
figure 3. Replacement of rackets in order to juggle the balls top-down.
figure 4. Students juggled each ball top-down associating the velocity
and the force in a way that balls moved in a springy way.
Students trough the process of playing this game constructed several
- The trajectory of the ball is related to the combination of the two vectors
(velocity and force). Thus they made several different conjectures about
how to set the initial vectors in order to define the orientation of the ball's trajectory.
- The trajectory of the balls is related to functions and "looks like the graphic
of a hyperbola or parabola".
- Physical phenomena can be described and explained using mathematical
models which give us the power to predict the objects reaction.
Students of the second group wanted to "create their own game", so they
used the juggler idea and developed an 'arcanoid' bricks game.
figure 5. The "Bricks" microworld.
Their design idea was based on functionalities they created and were not
easily found in commercial versions of the game. For example, they wanted
the user to be able to place the bricks wherever he or she liked and to choose
the number of bricks placed in the court. They also wanted to be able to move
the racket freely on the court and not have the usual racket movement restricted
to a horizontal line at the base of the court. The students thus re-constructed
the Logo code by taking away the rules of Newtonian motion and gravity, inserting
different rules for ball collision, one for the racket and another for the bricks
(they disappear on collision) and a constant velocity rule for the ball.