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Table of Contents:

The Final Framework:

  

Technology as Object: Tool, Instrument [technologies, resources, processes] Dimension

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.

Reference: 50

Eight Dimensions for Analysis by Researchers and/or Developers

  1. The Integration Dimension
    1. Does technology enhance learner’s achievement, conceptions, views of mathematics, etc.?
    2. What are the effects on learners of the introduction of technology, taking into account ecological conditions?

 

  1. The Epistemological and Semiotic Dimension
    1. What is the relationship between the content knowledge at stake and the new means provided by technology — in particular, what changes might technology bring to mathematical practices, with what possible obstacles, and with what semiotic aspects?
    2. What difficulties do representations of knowledge in new technological environments, even when epistemologically relevant, cause for the learners or for teachers to integrate into teaching?
    3. What is the role played in conceptualisation processes by the interplay between the different semiotic registers of representation through which mathematics objects are accessed and worked with, and more globally by cognitive flexibility [i.e., connecting representations]?

 

  1. The Cognitive Dimension [i.e., the framework used to analyse the learner’s functioning and learning processes]
    1. What is the role played by perception in cognitive processes?
    2. What is the cognitive power of visualisation tools in the underlying cognitive processes?
    3. What support can new technologies bring as new cognitive tools for learners’ activity?
    4. What are the characteristics of problems and situations which can foster the dialectic interplay between these perceptive and cognitive conceptual competencies of different nature?
    5. What are the potentialities of ICTs for connecting knowledge from varied experiences, drawing upon situated cognition theories?

     

  2. The Institutional Dimension
    1. To what extent are the content to be taught as well as tasks and procedures (or techniques) affected by the institution in which they are taught?
    2. What kind of the tasks are being offered to learners (tasks especially designed to be solved with technology or “ordinary” tasks)?
    3. What is the relationship between new instrumental techniques and mathematical productivity?
    4. What is the relationship between new instrumental techniques and the teacher’s organisation of classroom activities?

 

  1. The Instrumental Dimension

“The subject develops procedures and rules of action when using the artefact and so constructs instrumentation schemes and simultaneously a representation of the properties of the tool … But the knowledge acquired by the subject about the tool and the ways to use it may differ from what the tool was intended to do and the ways it was intended to be used. This approach postulates that a tool or an artefact is not transparent.”

    1. How available to learners is the technology and what are its features?
    2. How is the work organised?
    3. What are the social dimensions of the activity?

 

Even with technology, instant mathematical conceptualisation cannot happen and thus time is necessary for learners to understand the mathematical implications of the use of the instrument.

    1. How much time is necessary for learners to understand the mathematical implications of the use of the instrument?
    2. Does technology provide a wealth of opportunities for a “more conceptual” use of time?
    3. Whereas an initial hypothesis may be that technology is able to save time in conceptualisation, do some learners feel the increased burden of a problem-solving and multiple approach with technology?

[More complex problems bring a heavier load and technology, by itself, does not solve this difficulty.]

 

  1. The Situational Dimension
    1. What changes does the introduction of technology bring into didactical situations?

 

  1. The Human-Machine Interaction Dimension
    1. What is known about learners’ activity and interaction with the technological tools?

 

  1. The Teacher Dimension
    1. What is known about teachers’ beliefs about new learning technologies and the way they [re-]organise the classroom activity?