Technology as Object: Instrumental Approach [Activity Theory]

Purpose: To analyse the potential impact of the adoption of technology as a tool for automating & reinforcing routines; supporting transformative and manipulative actions; and/or making tools and procedures visible and comprehensible.

References: 47, 50, 62, 73

The “instrumental” approach of IC Technologies distinguishes a technological artefact and the instrument that a human being is able to build from this artefact. While the artefact refers to the objective tool, the instrument refers to a mental construction of the tool by the user. The instrument is not given with the artefact, it is built in a complex instrumental genesis and it shapes the mathematical activity and thinking.

1. Instrumental approach:
1. Is there recognition of the fact that an instrument is a psychological construct that a human being is able to build from an artefact or objective tool?
2. How much time is allowed for the learner to appropriate and integrate the technological artefact into their activity?
3. What consideration is given to linking the artefact’s possibilities and constraints with the learner’s former method of working?
4. In what ways does the instructional material address the learner’s implicit knowledge with respect to:
1. pragmatic function (it allows the agent to do something)?
2. heuristic function (it allows the agent to anticipate and plan actions)?
3. epistemic function (it allows the agent to understand what s/he is doing)?
5. To what degree does the instructional material focus on managing the technological artefact?
6. To what degree is the instructional material oriented by the activity itself?
7. How are the following constraints addressed:
1. Internal constraints intrinsically linked to the hardware
2. Command constraints linked to the existence and to the form (i.e., the syntax) of the various commands;
3. Organization constraints, linked to the organization of the keyboard and, more generally, of the interface between the artefact and the user.
8. How can the technological artefact be organised, structured, integrated into the learner’s mathematical practice, enabling them to analyse its uses, define new specifications, etc.?
9. What is the didactic configuration (i.e., the layout of artefacts available in the environment, with one layout for each stage of the mathematical treatment)?
10. What are the main objectives of the activity and the secondary objectives of the exploitation of the artefacts?

The configurations and their exploitation modes produce accounts of activity. The socialization of these accounts (research reports, calculators screens, etc.) is essential:

1. In what ways are the production, interpretation and negotiation of accounts of the technologically mediated activity supported, cognitively (personally) and culturally?
2. At the operations level, where the focus is on the ordinary utilisation of the artefact, how are learners helped learn the mechanics of computing and to understand the limits of functions on instruments [e.g., symbolic calculators]?
3. At the action level, where artefacts as instruments correspond to both representations and action modes, how are debates encouraged and how are procedures made explicit?
4. At the activity level, how are the artefacts utilised to offer reflective methods of self analysis of the activity, both individually and collectively?
5. Which artefacts should we propose to learners and how can we guide them through instrumental genesis and along the evolution and balancing of their instrument systems?
6. For which learning activities and which components of mathematical knowledge?
7. How might breakdowns and failures of technological performance be taken as a possibility for creating new ways to redesign the product — and the whole setting — together with the users?

2. Which developmental stage is presently the case:
1. the initial phase, when performance is the same with and without a tool because the tool is not mastered well enough to provide any benefits?
2. the intermediate stage, when aided performance is superior to unaided performance?
3. a final stage, when performance is the same with and without the tool but now because the tool-mediated activity is internalized and the external tool (such as a checklist or a visualization of complex data) is no longer needed?
4. Is the focus on the technological artefact in question a reflection on the object itself and/or as a tool mediating interactions with the world?

3. When faced with interpretation of multiple representations of the same material:
1. How are the tensions between subject (the person interpreting) and object (graph to be interpreted) and the contradictions within and between the three levels [collective activity, individual action, and unconscious operation] addressed? [These constitute the generative forces that drive the interpretation, which stops once the contradictions have been removed.]
2. How do learners reconcile an apparent a lack of coherence or incompleteness among symbolic, graphic, and/or tabular representations?
3. At the unmediated operation level how do the contradictions caused by a lack of coherence between visual (symbolic, graphic, tabular) and verbal modalities play out?