Paper and Pencils: Difference between revisions
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(Starting the page.) |
(included Papert's opinions against pen and paper technologies) |
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This page is started in the hope that a sponsor can be found for paper and pencil packs to be provided to the children. |
This page is started in the hope that a sponsor can be found for paper and pencil packs to be provided to the children. |
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However, we might want to use the laptops as a disruptive element in the traditional mindset of teaching and learning that glorifies the use of pen and paper. Papert says: |
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In Mindstorms (Papert, 1980), I asked (choosing one out of a vast |
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number of possible examples) why the quadratic equation of the |
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parabola is included in the mathematical knowledge every educated |
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citizen is expected to know. Saying that it is "good math" is not |
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enough reason: The curriculum includes only a minute sliver of the |
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total body of good mathematics. The real reason is that it matches the |
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technology of pencil and paper: It is easy for a student to draw the |
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curve on squared paper and for a teacher to verify that the assignment |
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has been done correctly. |
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I have noted elsewhere (Papert, 1996b), that School's math can be |
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characterized by the fact that its typical act is making marks on |
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paper. Explorations in the Space of Mathematics Education develops |
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this idea by imagining an alternative mathematical education in which |
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the typical activity begins with and consists of creating, modifying, |
|||
or controlling dynamic computational objects. In this context the |
|||
parabola may be first encountered by a child creating a videogame |
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as the trajectory of an animal's leap or a missile's flight; here, |
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the natural first formalism for the parabola is an expression in a |
|||
child-appropriate computational language of something like "the path |
|||
followed when horizontal speed and vertical acceleration are both |
|||
constant." |
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Many readers will say that is too abstract for children. This is |
|||
because they have in mind children who grew up using the static |
|||
medium of pencil and paper as the primary medium for representing |
|||
mathematical ideas. Attempts to inject this treatment of the parabola |
|||
as an isolated innovation into an otherwise unchanged School will |
|||
confirm their negative view. For children who have acquired true |
|||
computational fluency by growing up with the dynamic medium as a |
|||
primary representation for mathematical thinking, I argue that it |
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would plausibly be more concrete, more intuitive, and far more |
|||
motivating than quadratic equations. My experiments support this |
|||
expectation by showing that the dynamic definition is indeed |
|||
accessible even to elementary school children who are given the |
|||
opportunity to acquire a degree of computational fluency that is still |
|||
very limited though considerably more than a few students develop in |
|||
what are misleadingly called computer labs in contemporary schools. |
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http://www.papert.org/articles/school_reform.html |
Revision as of 17:22, 6 June 2006
In the External Developers page is the following comment.
Expect that the kids have no paper, pens, pencils, books or trained teachers. Many OLPCs will be deployed into just such an environment.
This page is started in the hope that a sponsor can be found for paper and pencil packs to be provided to the children.
However, we might want to use the laptops as a disruptive element in the traditional mindset of teaching and learning that glorifies the use of pen and paper. Papert says:
In Mindstorms (Papert, 1980), I asked (choosing one out of a vast number of possible examples) why the quadratic equation of the parabola is included in the mathematical knowledge every educated citizen is expected to know. Saying that it is "good math" is not enough reason: The curriculum includes only a minute sliver of the total body of good mathematics. The real reason is that it matches the technology of pencil and paper: It is easy for a student to draw the curve on squared paper and for a teacher to verify that the assignment has been done correctly. I have noted elsewhere (Papert, 1996b), that School's math can be characterized by the fact that its typical act is making marks on paper. Explorations in the Space of Mathematics Education develops this idea by imagining an alternative mathematical education in which the typical activity begins with and consists of creating, modifying, or controlling dynamic computational objects. In this context the parabola may be first encountered by a child creating a videogame as the trajectory of an animal's leap or a missile's flight; here, the natural first formalism for the parabola is an expression in a child-appropriate computational language of something like "the path followed when horizontal speed and vertical acceleration are both constant." Many readers will say that is too abstract for children. This is because they have in mind children who grew up using the static medium of pencil and paper as the primary medium for representing mathematical ideas. Attempts to inject this treatment of the parabola as an isolated innovation into an otherwise unchanged School will confirm their negative view. For children who have acquired true computational fluency by growing up with the dynamic medium as a primary representation for mathematical thinking, I argue that it would plausibly be more concrete, more intuitive, and far more motivating than quadratic equations. My experiments support this expectation by showing that the dynamic definition is indeed accessible even to elementary school children who are given the opportunity to acquire a degree of computational fluency that is still very limited though considerably more than a few students develop in what are misleadingly called computer labs in contemporary schools.