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Tools & Instruments, June 2019, p. 1

Tools & Instruments, June 2019, p. 1. Tools and instruments A tribute to Luc Trouche John Monaghan Universities of Agder, Norway Leeds, Yorkshire. Tools & Instruments, June 2019, p. 2. 3 parts Luc (& me) Tools and instruments Beyond Luc schemes.

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Tools & Instruments, June 2019, p. 1

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  1. Tools & Instruments, June 2019, p.1 Tools and instruments A tribute to Luc Trouche John Monaghan Universities of Agder, Norway Leeds, Yorkshire

  2. Tools & Instruments, June 2019, p.2 3 parts Luc (& me) Tools and instruments Beyond Luc schemes

  3. Tools & Instruments, June 2019, p.3

  4. Tools & Instruments, June 2019, p.4 Mathematicseducationresearchpapers • important MER papers Guin & Trouche(1998). The complexprocessofconvertingtoolsintomathematical instruments: The case ofcalculators. IJCML Trouche (2004). Managingthecomplexityof human/machineinteractions in computerizedlearningenvironments. IJCML Gueudet & Trouche(2009). Towardsnewdocumentation systems for mathematicsteachers? ESM

  5. Tools & Instruments, June 2019, p.5 Kortenkamp, U., Monaghan, J., & Trouche, L. (2016). Jonathan M Borwein (1951–2016): exploring, experiencing and experimenting in mathematics–an inspiring journey in mathematics.  Educational Studies in Mathematics,93(2), 131-136. Instruments & tools

  6. Tools & Instruments, June 2019, p.6 This book originates in discussions between John and Luc. We had similar backgrounds: …school teaching and then university work. In both sites we’d done a lot of experimenting (both practical and research) using digital technology. We shared prejudices for the types of tools/systems we liked to use with our students: graph plotters, Logo, computer algebra systems and similar tools/systems which our students could use to express mathematical relationships rather than tools/systems that might go under the name of ‘computer aided instruction’. …Our theoretical frameworks were not identical (John was influenced by activity theory and Luc by instrumentation theory) but they was plenty of room for productive dialogue …

  7. Tools & Instruments, June 2019, p.7 What is a tool? John’s attempt … Rather than a definition I make 4 distinctions related to tools   • between an artefact and a tool • between an artefact/tool and ways of using the artefact/tool • between ‘mental representations’ of and material actions in artefact/tool use • between signs and tools

  8. Tools & Instruments, June 2019, p.8 Luc’s attempt ... one epistemological position, specified by four dualities ... • Acting (performing a task) is a process of using and creating artefacts ... The historical act of creation reappears in use • A double shaping process ...the artefact shapes the way the user acts …the user shapes, along the course of her/his situated action, the artefact

  9. Tools & Instruments, June 2019, p.9 • The process of using an artefact is both a process of producing something and a process of constructing knowledge • An essential distinction between an artefact and an instrument. …When an artefact has been appropriated by a user, I will name instrument the mixed entity composed of the artefact and the associated knowledge

  10. Tools & Instruments, June 2019, p.10 That was from Chapter 1. Chapter 2 was Doing mathematics with tools: one task, four tools And was written by me

  11. Tools & Instruments, June 2019, p.11

  12. Tools & Instruments, June 2019, p.12 But the last word came from Luc

  13. Tools & Instruments, June 2019, p.13 ...construct the bisector without an obvious tool, by folding the sheet on which the angle is drawn. The tool in this case is the sheet of paper coupled with knowledge of an axis of symmetry

  14. Tools & Instruments, June 2019, p.14 Thank you Luc (and Jon) for conceiving, creating and constructing ‘the tool book’ with me But we both move on ... to retirement! My last words are for after Luc ... His academic legacy and his academic children

  15. Tools & Instruments, June 2019, p.15 Brousseau came from the community of mathematicians, Vergnaud came from the community of developmental psychologists. … Vergnaud shared with Piaget the idea that even highly structured concepts develop from the most elementary actions of a subject …Studying the processes of mathematics learning leads Vergnaud to specify this notion of scheme Luc, Tool book

  16. Tools & Instruments, June 2019, p.16 Scheme ... hmm ... important but ... What is certainly crucial for mathematical learning, is the conceptual component of schemes, namely the operational invariants: concepts-in-action and theorems-in-action Luc again Again, important but ...... very French ... I value French didactics highly but ... Can other researchers contribute to DAD?

  17. Tools & Instruments, June 2019, p.17 Well, yes, but look at what is happening to the didactic contract in the literature! Maybe, in the future French didacticians Close to French didacticians Other didacticians should approach DAD with a more open view to basic constructs

  18. Tools & Instruments, June 2019, p.18 Bonne retraite Luc Amicalement, John

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