EDU236X Beyond Bits and Atoms
Reflection Paper 02 : Edwards & Eisenberg
Edwards, L. (1998). Embodying mathematics and science: Microworlds as representations. The Journal of Mathematical Behavior, 17 (1), pp. 53-78
“In Logo microworlds, it is often assumed that the student will be engaged in at least a simple level of programming, and in many other microworlds a symbolic language of some kind is an essential component. An important design issue is whether an explicit symbolic language is necessary for learning with microworlds. Certain exploratory tools, for example, the Geometer's Sketchpad and Cabri, link the graphical representations of mathematical objects not to a set of commands that the user can enter and combine into more complex sequences, but rather to items selected from pull-down menus.”
I was particularly attracted to this section of the Edwards paper. Yes – I fully appreciated his explanations about the potential educational value of microworlds, and of the “debugging” process. BUT as I reflected upon my own brief encounter with Logo microworlds, the recurring question that went through my mind is what has been articulated in the paragraph below :
“What is gained and what is lost when commands are selected from a menu rather than composed from primitives? Do symbolic commands enhance expressiveness and highlight the linkage among multiple representations? Or are they simply an obstacle to efficient and intuitive interaction with the environment?”
As someone who was totally new to programming, the Assignment last week was a traumatizing experience. The learning curve was so steep that, in Vygotsky’s terms, it was way beyond my Zone of Proximal Development. It was such a far reach that I almost fell into the depths of frustration. I found myself entertaining thoughts of dropping the class, and when that was not an option for me, I found myself harboring bad thoughts about everything to do with the class. Imagine my joy and delight when I realized that I could do all that was expected in Assignment 2, with just logically entering commands into the Turtle’s backpack, and clicking menu items with the mouse. I could then take a step back and ask myself what I was learning, and what I was meant to learn.
The point of it all lies in the word “purpose”. If the purpose of the exercise was to learn a programming language, then, by all means, expect students to be engaged in programming. But if the purpose of a microworlds exercise is to learn Math, or a scientific concept, and the purpose of the microworld is representational, then I would prefer being allowed to focus on that, rather than on the tedium of understanding the syntax of the programming language. Like I did, with my turtle and backpack! It helped me see the forest, rather than be caught up with planting the trees.
Eisenberg, M. (2007). Pervasive Fabrication: Making Construction Ubiquitous in Education. Fifth Annual IEEE International Conference on Pervasive Computing and Communications Workshops.
“There is a productive tension in the language that surrounds transitional objects (and their mathematical-manipulative cousins). On the one hand, there is an intended universality—or at least broad applicability—of transitional objects in their role as a cognitive bridge. Presumably, many children have common experiences with physical objects that make number rods and turtles such powerful carriers of mathematical ideas. On the other hand, a rich theory of transitional objects would probably highlight their variety and personal resonance for individual children—the more affective or aesthetic side of the objects’ roles. Not all children respond with intensity to the particular affordances of the turtle (just as not all children respond to gears, or any other particular example of a transitional object).
It is along this dimension—of the personal, the emotional, the socially connected, the aesthetic—that the (screen) turtle is most potentially limited, in large part because of its disconnection from the material life of the child.”
I feel that with this Eisenberg paper, “the turtle has come full circle”. The quintessential turtle went from an actual physical object, to a virtual turtle, and now, the suggestion of tangible, physical artifacts. Since Papert first came up with his ideas about gears and transitional objects, the whole movement around “Mindstorms” was focused on teaching kids to program. Even Papert acknowledged in his paper on “The Big Idea” that people seemed to have taken off on a tangent, and began to focus on technology, and the Logo programming language.
What this paper does is to shift the focus back to the idea (the Big Idea) of transitional objects, and their role as a cognitive bridge. These objects may take the form of a physical turtle, they may take the form of a virtual turtle, or they may take the form of tangible physical artifacts. The point is to be cognizant of the fact that transitional objects perform a very powerful role as carriers of ideas. And our challenge as educators is not just to be fixated on one manifestation of transitional objects that we want kids to learn with, but to explore a myriad of forms of objects, in the hope that kids will respond to one, or some of these objects, and own them as their “gears” to think with.
“In Logo microworlds, it is often assumed that the student will be engaged in at least a simple level of programming, and in many other microworlds a symbolic language of some kind is an essential component. An important design issue is whether an explicit symbolic language is necessary for learning with microworlds. Certain exploratory tools, for example, the Geometer's Sketchpad and Cabri, link the graphical representations of mathematical objects not to a set of commands that the user can enter and combine into more complex sequences, but rather to items selected from pull-down menus.”
I was particularly attracted to this section of the Edwards paper. Yes – I fully appreciated his explanations about the potential educational value of microworlds, and of the “debugging” process. BUT as I reflected upon my own brief encounter with Logo microworlds, the recurring question that went through my mind is what has been articulated in the paragraph below :
“What is gained and what is lost when commands are selected from a menu rather than composed from primitives? Do symbolic commands enhance expressiveness and highlight the linkage among multiple representations? Or are they simply an obstacle to efficient and intuitive interaction with the environment?”
As someone who was totally new to programming, the Assignment last week was a traumatizing experience. The learning curve was so steep that, in Vygotsky’s terms, it was way beyond my Zone of Proximal Development. It was such a far reach that I almost fell into the depths of frustration. I found myself entertaining thoughts of dropping the class, and when that was not an option for me, I found myself harboring bad thoughts about everything to do with the class. Imagine my joy and delight when I realized that I could do all that was expected in Assignment 2, with just logically entering commands into the Turtle’s backpack, and clicking menu items with the mouse. I could then take a step back and ask myself what I was learning, and what I was meant to learn.
The point of it all lies in the word “purpose”. If the purpose of the exercise was to learn a programming language, then, by all means, expect students to be engaged in programming. But if the purpose of a microworlds exercise is to learn Math, or a scientific concept, and the purpose of the microworld is representational, then I would prefer being allowed to focus on that, rather than on the tedium of understanding the syntax of the programming language. Like I did, with my turtle and backpack! It helped me see the forest, rather than be caught up with planting the trees.
Eisenberg, M. (2007). Pervasive Fabrication: Making Construction Ubiquitous in Education. Fifth Annual IEEE International Conference on Pervasive Computing and Communications Workshops.
“There is a productive tension in the language that surrounds transitional objects (and their mathematical-manipulative cousins). On the one hand, there is an intended universality—or at least broad applicability—of transitional objects in their role as a cognitive bridge. Presumably, many children have common experiences with physical objects that make number rods and turtles such powerful carriers of mathematical ideas. On the other hand, a rich theory of transitional objects would probably highlight their variety and personal resonance for individual children—the more affective or aesthetic side of the objects’ roles. Not all children respond with intensity to the particular affordances of the turtle (just as not all children respond to gears, or any other particular example of a transitional object).
It is along this dimension—of the personal, the emotional, the socially connected, the aesthetic—that the (screen) turtle is most potentially limited, in large part because of its disconnection from the material life of the child.”
I feel that with this Eisenberg paper, “the turtle has come full circle”. The quintessential turtle went from an actual physical object, to a virtual turtle, and now, the suggestion of tangible, physical artifacts. Since Papert first came up with his ideas about gears and transitional objects, the whole movement around “Mindstorms” was focused on teaching kids to program. Even Papert acknowledged in his paper on “The Big Idea” that people seemed to have taken off on a tangent, and began to focus on technology, and the Logo programming language.
What this paper does is to shift the focus back to the idea (the Big Idea) of transitional objects, and their role as a cognitive bridge. These objects may take the form of a physical turtle, they may take the form of a virtual turtle, or they may take the form of tangible physical artifacts. The point is to be cognizant of the fact that transitional objects perform a very powerful role as carriers of ideas. And our challenge as educators is not just to be fixated on one manifestation of transitional objects that we want kids to learn with, but to explore a myriad of forms of objects, in the hope that kids will respond to one, or some of these objects, and own them as their “gears” to think with.