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Drawing a line

Technology out of the past, learning in our future.
by

Robert Klein

on 20 April 2010

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Transcript of Drawing a line

Drawing a Line Connecting the past to future learning http://demonstrations.wolfram.com/LinkageInvertingFigureEightCurves/ http://kmoddl.library.cornell.edu/linkages/ Technology NCTM(2000) Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Calculators and computers are reshaping the mathematical landscape, and school mathematics should reflect those changes. Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction. In the mathematics classrooms envisioned in Principles and Standards, every student has access to technology to facilitate his or her mathematics learning... The teacher must make prudent decisions about when and how to use technology and should ensure that the technology is enhancing students' mathematical thinking. Support Enhance Technology can motivate deep thinking Source rather than support "Thing to think with" Build it... and learning will come. In the concrete or the abstract http://www.artknowledgenews.com/files2009nov/Leonardo_da_Vinci_Notebooks.jpg our biggest our best our most complex ideas begin with one approach beautifully imperfect but not perfectly straight How do we draw a straight line? not very well. create an ideal Linkage series of hinged "rods" or "bars" Math Segments with common endpoints Mechanically Called "linkages
wiper blades
robotic arm movements How can a machine trace
a mathematical curve? Circle? http://www.freeclipartnow.com/d/11455-1/compass-drawing-circle.jpg http://www.edward-weston.com/kimweston_12.htm Ellipse? http://kmoddl.library.cornell.edu/linkages/ Line daVinci Durer van Schooten Watt Steam Engine Chebyshev Charles Nicolas Peaucellier (1832- 1913) 1864 1871 Lipmann I. Lipkin (1851-1875) But how do we know it works? proof OBJECT MOVIE http://www.howround.com How can SOMETHING create a perfect certainty http://www.howround.com
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