Initially, the teacher offers guidance to the workgroups so as to access the MoPiX environment by visiting the ReMath website (http://remath.cti.gr) and load from the MathDiLS library the saved model “One red ball”.

During the previous phase the students have already explored some of the basic functionalities of the microworld and have already been introduced to some of the main features of the MoPiX environment. Thus, they are expected to start the animation without requiring any specific instructions from the teacher.

After giving the students some time so as to interact with the microworld and observe the animation generated, the teacher will ask the students what they would change in the behaviour or the properties of the object on the “Stage” if they had the chance to do so. Students are expected to discuss such an option while working in pairs and come up with some ideas about making the object behave in a different way and therefore produce a different animation of its motion. Since there is a high possibility that some of the students' suggestions could be infeasible or extremely time - consuming the teacher asks the students to discuss not only about making the object behave differently but also about how this will be achieved after taking into consideration certain limitations. The WorkSheet C will be distributed.

While discussing in pairs about the new desired behaviour assigned to the object and how it will be attained, students could use some of the features of the MoPiX to which they have already been introduced during the previous phase, such as the “Flipping Objects” feature. This feature's main purpose is to render visible the equations attributed to the object. Making visible the equations defining the objects initial behaviour and trying to deconstruct them has a twofold effect on students understanding.

Firstly, they develop their understanding about what makes the object behave the way it does e.g the x (ME,t) defines the objects position on X axis and secondly, they develop their understanding on the structure of the equation e.g in the x (ME,t) equation ME represents a variable and it has to be included in the function on the left part of the equation.

In order to attribute a new behaviour to the object, it is likely for the students to think at first place to modify the existing equations assigned to the object and particularly those equations that include numerical values. For example they could think of editing the equation Vx (ME,0) = 3 and changed it into Vx (ME,0) = 4. However, after acquiring some familiarity with the Editor and having developed
an understanding regarding the structure of the one-object equations
and MoPiX algebraic formalism, students are expected to start editing other elements of the originals equations, such as the variables.

**Picture 1:**Using the "Flipping Objects" feature and editing an equation using the "Equations Editor"

The students are expected to assign the newly constructed equations
to the object and observe its behaviour. The animation generated by the
tool will help them test their original hypotheses concerning the
object's behaviour after assigning it the equation they constructed and
evaluate the strategies they implemented so as to construct the
equation.

In case the behaviour of the object is not the desired
one, students are urged by the teacher to deconstruct their equations,
examine its content and its structure. A trial-and-error procedure, the
animation offered by the tool and the intra workgroup discussions will
help students to refine their models.

The students are expected to assign the newly constructed equations to the object and observe the new behaviours. The animation generated by the tool will help them test their original hypotheses concerning the object's behaviour after assigning it the equation they created, and evaluate the strategies they implemented so as to produce the equation. In case the behaviour of the object is not the desired one, students are urged by the teacher to deconstruct their equations, examine its content and its structure. A trial-and-error procedure, the animation offered by the tool and the intra workgroup discussions will help students to refine their models.

Near the end of this phase, we expect the students to use the “New Equation” button so as to create from scratch new
one-object equations. The User's Manual and Translations on the Editor's Buttons' names could be proved to be helpful for the students' new explorations.

*Picture 2: **Using the "New Equation" and the "Function" button to construct an equation*

Finally, in order to save the one-object equations model the students created themselves and render it shareable through the MathDiLS library, with the assistance of the teacher, they will follow the procedure mentioned below:

press the “Save” button which is situated on the upper part of the MoPiX environment

provide the necessary “username” and “password” on the corresponding fields an click “OK”

type the model' s desired name on the “Enter the tag” field

click “OK” to save the new model