MoPiX is conceived as a constructionist toolkit. The constructionist approach to learning (Papert, 1980; Harel & Papert, 1991; Kafai & Resnick, 1996) promotes investigation through the design of microworld environments, i.e. technology-enhanced educational tools and activities, and the observation of learners’ actions, developments and communication within these environments. As developed by Strohecker and Slaughter (2000) constructionist toolkits are very much based on these principles. They are dynamic visual environments that support building activities in social contexts. Learners build constructs with fundamental elements and then activate these constructions as a means of investigating their hypothesis. The fundamental elements of MoPiX are equations and objects whose properties and behaviours are defined by the equations assigned to them. Working with MoPiX thus provides students with opportunities to explore and develop their understanding of equations and relationships within a Cartesian plane as well as to investigate the behaviours of the objects they construct.

MoPiX is a multi-semiotic environment involving formal notation of equations and visual animated models. Specialised animations may also be constructed to leave a trace in the form of a cartesian graph. These three semiotic systems, with their various elements and grammars, have different meaning potentials (O'Halloran, 2005; Kress, 2001). In addition, students may use pencil and paper-based representations involving conventional or informal notations or diagrams. They can also communicate with each other using 'natural' language in face-to-face speech and by sharing MoPiX objects, equations and models electronically. Again, these modes of communication have distinctive elements, grammars and meaning potentials. The multi-semiotic nature of the environment thus provides rich possibilities for students to interpret mathematical ideas and for them to express their own mathematics through constructing new animations.

Duval (2006) argues that conversion between semiotic systems (which he names representational systems or 'registers') is of fundamental importance to mathematical learning. Conversion demands that the student distinguishes what is mathematically relevant in each system and separates the mathematical object from its representation. The MoPiX environment not only demands that students engage in conversion (using different forms of representation for the 'same' mathematical object) but also that they actively use the representations available in the system of equations to effect changes in the visual forms of representation. In the opposite direction, the process of 'debugging' faulty animations again demands conversion: identifying those equations which are responsible for the 'buggy' behaviour. We hypothesise that activities in this environment will enable students to develop their understandings of algebraic notation and of definition of motion.

The tasks proposed in this pedagogical plan are designed to allow students to engage in constructive activity, while providing them with support structures to assist in this process. We draw on the idea of learner-centred design (Soloway, Guzdial and Hay, 1994), based on socio-cultural and constructivist theories of learning and the user-centred approach to interaction design. Learner-centred design is based on the premises that a user of technology constantly changes through learning, and that their needs from the technology change in the process. In particular, the user learns through using the technology, and the design of the technology needs to account for that learning. This leads to the question of how can environments support learners and learning? LCD suggests that students learn through an active, social process of meaning construction (Vygostky, 1962). Critically, understanding is built up through the acts of conversing with others, constructing artefacts, and reflecting on those conversations and artefacts. Soloway, Guzdial and Hay (1994) see scaffolding as the main role of teachers in constructivist learning, and propose that this should be the role of the interface in technology-rich environments. We see a more critical role of the teacher in mediating the communication among a group of learners (see below).

Quintana et al (2005) propose a framework for designing scaffolding structures. Position this framework in the context of inquiry-based learning. Consequently, organize the framework around three processes: ‘sense making’, which involves the basic operations of testing hypotheses and interpreting data; 'process management', which involves the strategic decisions involved in controlling the inquiry process; and articulation and 'reflection', which is the process of constructing, evaluating, and articulating what has been learned. From these principles, they derive a framework that includes several elements:

- The task model, the constituents of activity derived from the inquiry based learning literature.

- Obstacles encountered by learners.

- Scaffolding guidelines provide principles for designing scaffolds to help learners overcome the obstacles.

- Scaffolding strategies, more specific implementation approaches

While each student will have their personal tablet pc with which to build and investigate scenes, communication between the devices will allow them not only to share what they have built but also to investigate, modify and play each other’s constructions in a game-like manner. The multi-semiotic environment, including equations, animation, graphical representation, oral communication within the group and pencil and paper representations, allows opportunities for participants to contribute in different ways to the construction of a problem solution. For example, while one student might focus their attention and arguments on the behaviour of an animation proposed as a solution to a problem, another could corroborate or criticise the solution by reference to the properties of a graph showing relationships between chosen variables or by constructing a conventional paper and pencil forces diagram. Alternative modifications to the construction could be carried out by different students and the results compared immediately either by sending them to each other’s personal devices or by laying several devices together to be viewed simultaneously by the group. This environment aims to encourage collaboration and ‘exploratory talk’, enabling students to exchange ideas and to engage critically with each other’s contributions - a form of talk that, it is argued, supports learning through group interaction (Barnes, 1976; Barnes & Todd, 1995; Edwards, 2005; Mercer, 1995).