An Exploration in the Space of Mathematics Educations Export

@article{citeulike:620347, author = {Papert, Seymour}, citeulike-article-id = {620347}, citeulike-linkout-0 = {http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html}, comment = {"The obvious simple way to make a jump is to give it a rectangular path. In traditional Logo one might do SETY YCOR + 1 and later SETY YCOR -10. But most of the students with whom I have worked are not satisfied with this jump. To obtain a more realistic, or at least a more interesting, trajectory, several powerful ideas are helpful. The first of these is naming (which really means thingifying) the mathematical object we call a trajectory. This is not something one can see, and in my experience children do not think of the path as a thing with its own identity. The next powerful idea is combining velocities to make new velocities. When this is available the character in the game might be represented as having not one but two velocities, a horizontal velocity and a vertical velocity. Suppose at the beginning that both are set to zero speed. One can make the character run by making the horizontal speed, say, 20. Now initiating a jump could start by making the vertical speed 10. This is a step in the right direction but results in the character going off into the sky. "}, journal = {International Journal of Computers for Mathematical Learning}, keywords = {algebra, constructionism, learning, logo, naming}, number = {1}, pages = {95--123}, posted-at = {2006-05-09 11:40:15}, priority = {2}, title = {An Exploration in the Space of Mathematics Educations}, url = {http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html}, volume = {1} }

TY - JOUR ID - citeulike:620347 L3 - citeulike-article-id:620347 IS - 1 JF - International Journal of Computers for Mathematical Learning EP - 123 TI - An Exploration in the Space of Mathematics Educations VL - 1 SP - 95 KW - algebra KW - constructionism KW - learning KW - logo KW - naming N1 - "The obvious simple way to make a jump is to give it a rectangular path. In traditional Logo one might do SETY YCOR + 1 and later SETY YCOR -10. But most of the students with whom I have worked are not satisfied with this jump. To obtain a more realistic, or at least a more interesting, trajectory, several powerful ideas are helpful. The first of these is naming (which really means thingifying) the mathematical object we call a trajectory. This is not something one can see, and in my experience children do not think of the path as a thing with its own identity. The next powerful idea is combining velocities to make new velocities. When this is available the character in the game might be represented as having not one but two velocities, a horizontal velocity and a vertical velocity. Suppose at the beginning that both are set to zero speed. One can make the character run by making the horizontal speed, say, 20. Now initiating a jump could start by making the vertical speed 10. This is a step in the right direction but results in the character going off into the sky. " AU - Papert, Seymour UR - http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html ER -