Tools and Cognition

Tools influence what we can do, and also how we think.  The quipu was a useful tool for storage of information, but apparently not for manipulation. So if we have quipus but not a calculating board, we will be disinclined to do calculations. On the other hand, the calculating board does not allow storage of information.

Unfamiliarity with the tools (quipus, contour maps, swell maps, etc.) was a important experience to have as educators. The tools we are use to seem intuitive, but this may be substantially due to familiarity. Learning new things helps us remember that learning is effortful, and to feel like a learner in unfamiliar territory.

Ultimately, I do not want students to merely know the tools of the trade; these will change. More important is to be able to learn to adopt and create new tools as necessary. This brings us to recurring themes: we should be helping students to learn how to learn, the habits of mind of learners, more that the subject details themselves. Tools can change the focus of our learning, from Babylonian square roots (algorithms) to explicitly graphical/approximate techniques on the slide rule.

Reflections on Marshall Islanders contour map

Reflections on the importing the Marshall Islanders ‘contour’ map into our working group experience.

The activity challenged us to visually record the characteristics of an outdoor space using the stick maps of the Marshall Islanders to record wave movements. This tool was striking in three significant ways: 1) We attend to what we value; 2) As much as the user adapts the function of the tool, the tools also changes the user; 3) As a tool constructed for one purpose by a culture is appropriated into a different culture it revels new insight on the new culture through the lens of the old. 

1) We attend to what we know.

A small group of five participants moved into the small outdoor space and were charged with the job of producing a “Marshall Islander” map of the space using sticks and found natural objects. The space selected by the group was defined by a pathway that meandered through it. We map what is important to us as an exploration and a recording of what is useful. We selected the gravel pathway which has function.

2) A tool imparts its meaning into the experience of using it.

As we struggled to make meaning of the space through the map it became apparent that there was a tension between the Marshall Islanders mapping techniques and how we viewed our space. During the second day of the working group I was struck when Richard Barwell noticed that a child using fraction tiles as a mathematical tool was not using them as a way to build the concept; rather she was overlaying the tiles on the algorithms she already had practiced for addition of fractions. Here we were overlaying our fixed pathway on top of the Marshall Islanders map. This tension between our cultural choice of the use of a map versus the use of the map for the Marshall Islanders is important to consider.

3) As a tool constructed in one culture is appropriated into a different culture it reveals new insights. The tool becomes the lens through which the user attention is filtered.

As we reflected on the pathway versus the Marshall Island map Susan Gerofsky noted the Marshall islanders used the map to track the movement of waves. This prompted members of our group to move around the space and shift what we were attending to. Once we shifted our attention to the natural rhythms of the space we began to build the map. 

The activity shifted our focus from the visible modern pathway to the movement of nature below the pathway (trees, tree roots, slopes,…). It suggested to us how the movement of nature contributed to the formation of the path. The map, seemingly an object without language, communicated an alternate perspective to our group.

reflections on tools - alayne

What really struck me was how versatile the idea of tool is in terms of its relationships to other concepts:

  • When does a tool become media (and vice versa)
  • When does a tool become art (and vice versa)
  • The tool as an extension of the body which can then extend the tool, and so on (which I think touches on the recursivity that Joyce mentioned during our group discussions); yet, as Susan pointed out, the tool can also distance the body from itself, and from the natural world.
  • Tools as vehicles/conduits for story telling (the activities with the stick maps, wooden relief map, knotting) – related to this, what Florence noted about how educators usually remove the (his)tory of the tool when they teach with it in mathematics classes (how *did* the protractor come to be?)

As well, it was interesting to consider the tool as a means of thinking, how the design of the tool affords and constrains that thinking, and can reveal/shape concepts but not perhaps as the user/teacher anticipates. As Jean-Francois noted, the tools carry things that we might not want or anticipate.

De Marie-Line

Je rédigerai cette réflexion au « je ». Et je tâcherai d’à la fois ne pas trop réfléchir et laisser émerger les pensées à moi. Voici tout ce qui émerge.

D’une certaine manière, ma relation avec l’outil a changé. D’une vision statique de l’objet outil, je suis arrivé à une vision plurielle. L’outil peut -être à la fois culturelle (ex : une fourchette), matérielle (une fourchette) et/ou même mental (langage, mathématique).

À cet instant précis, alors que j’écris ces lignes à l’aide de mon ordinateur, mon ordinateur me change, il modifie mes pensées, alors que je pose mes pensées en mots par l’ordinateur. D’une certaine manière, je modifie ainsi l’ordinateur qui devient porteur de mes mots. En se sens, l’ordinateur est à la fois porteur et l’extension de ma pensée. Prendre conscience de cette dernière phrase vient de modifier mon rapport à l’ordinateur ; il a maintenant un côté plus poétique, plus humain et moins qu’utilitaire.

Au cours des trois derniers jours, nous avons eu une conversation sur « le fait que l’humain « were smarter now than before » L’humain en lui-même n’est pas « smarter » il est simplement transformé par la technologie, par exemple : il peut maintenant avoir une extension (ou une instance) de ses dires, de sa pensée, de ses rêves à l’intérieur même d’une machine portable que l’on nomme ordinateur. Cet ordinateur peut être vu comme portable du à l’invention du sac-à-dos. « (La technologie) est dans (le dos) de l’humain » Wills

What if math is a tool ?

Nous avons beaucoup parlé des outils mathématiques, mais les mathématiques en eux-mêmes comme outils… Nous en avons moins parlé.

Les objets, les outils, viennent en eux-mêmes porteur d’une culture. Ces outils me semblent à la fois limités à une culture et porteur de nouvelles possibilités dans une culture. Les sortir de leur culture est acte de créativité et permet-ouvre de nouvelles possibilités.

Sortir un objet de « sa culture » s’est aussi se sortir soi-même de sa culture.

J’ai été grandement étonné de voir que les grecques et les indiens sont arrivé avec des manières différents de trouver, calculer le même enjeux (la racine carré). Deux outils de différentes cultures pour répondre au même besoin… Est-ce que la racine carrée en elle-même est un besoin humain ?

Un élément final qui m’a sidéré fut le commentaire de Tanya Noble à propos du fait que c’était « beautiful » de voir la dimension approximative des mathématiques dans la règle à calculer. Ce commentaire m’a fait réfléchir, car, il me semble en effet qu’on ne la voit jamais (ou très peu) cette approximation en mathématique… Pourtant, elle est toujours là… Nous avons inventé des outils qui font en sorte que nous ne voyons plus la dimension approximative des math. Certains outils changent donc la nature même des choses…, ou du moins change nos perceptions humaines.

Par : Marie-Line L.Lamarche

Some images from our working group (when I wasn't too busy to take photos!)

Marta's notes

Dionysia's notes