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http://web.hku.hk/~amslee/gsp.pdf 

Geometer's Sketchpad

prepared by Arthur Lee

amslee@hku.hk Jun 2008

please download the Sketchpad file for workshop:http://web.hku.hk/~amslee/jun08.gsp

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Locus Exploration

Find B so that BC to AB is 2.

Construct & Explore

Make a table to record positions of such points.

Plot the points stored in the table.

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http://screencast.com/t/DlZ4cyql

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Explore the locus with parametric coloring.

Locus Exploration

http://screencast.com/t/7FSrs6WQn

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Two parabolic chords, difference of slopes

Mark 3 points on a quadraticgraph.

Construct & Explore

Measure the slopes of 2chords.

Calculate the difference of 

the slopes.What happens if the pointsare changed?

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http://screencast.com/t/Zf7pPcBORM

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http://screencast.com/t/Mo9SLI7q

Construct a quadratic graphs with 3 given points

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http://screencast.com/t/w4MHDevQ

Antiderivative of a quadratic function

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Quadrilateral, Sum of Squares of Opposite Sides

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Construct tangents with custom tools

http://screencast.com/t/IdpCDc9AQH

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Another construction of tangents

http://screencast.com/t/dGuewyDqf 

equation of tangent is created from the derivative calculated and coordinates of the given point on the graph

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Exponential Function

http://screencast.com/t/W7RHdPxmf 

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Perimeter and Area of a Regular Polygon

http://screencast.com/t/h1gfQNgvNJg

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Line Pattern

http://screencast.com/t/SeD51wyB4

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Some readings about use of images and videos withdynamic tools 

Oldknow, A. (2005)

ICT - bringing maths to life and vice versaMicromath; Summer 2005; 21, 2; Academic Research Library. pg. 16

Oldknow, A. (2003)Geometric and Algebraic Modelling with Dynamic Geometry SoftwareMicromath (Summer, 2003, pp.16-19)

http://cripe03.ugent.be/Vidshell/Vidshell.htm

Vidshell 

http://www.atm.org.uk/mt/micromath/mm192oldknowa.pdf 

Oldknow, A. (2003)Mathematics from still and video imagesMicromath (Summer, 2003, pp.30-34)

Sharp, B.D. (2007)Making the Most of Digital ImageryMathematics Teacher 100-9, May 2007, pp.590-593free preview at

http://nctm.org/publications/mt.aspx?id=8594

a free program for video analysis is mentioned inOldknow (2003) 

http://www.atm.org.uk/mt/micromath.htmlFrom

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Students do not make the Cartesian connection

van Dyke, F. & White, A. (2004) Making Graphs Count. Mathematics Teaching (188) pp. 42-45 

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Students simply do not see the connection and so do not take advantage of graphs to solve an equation.

Only 35% of the students tested saw that (12,1) provided them with a solution to the equation. Overall, students onaverage correctly answered only one out of four questions concerning the Cartesian connection. Many students, wheninterviewed, said that when they saw the word solutionthey immediately felt they had to do some algebraic process in order to discover some unknown quantity. Weneed to be aware that students often associate terms inmathematics with set procedures and in general feel that doing mathematics always entails algebraic manipulation.

Students do not make the Cartesian connection

van Dyke, F. & White, A. (2004) Making Graphs Count. Mathematics Teaching (188) pp. 42-45 

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Students have difficulty using functional notation with graphs

van Dyke, F. & White, A. (2004) Making Graphs Count. Mathematics Teaching (188) pp. 42-45 

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Knuth, E. (2000). Student Understanding of the Cartesian Connection: An Exploratory Study. Journal for Research inMathematics Education. 31(4), 500-508.

http://www.jstor.org/view/00218251/ap020152/02a00060/0

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http://math.buffalostate.edu/~mcmillen/Kunth.pdf 

Knuth, E. (2000). Understanding connections between equations and graphs. The Mathematics Teacher. 93(1), 48-53.

Only 1/5 of the 35 students responded that finding a solution without the

missing coefficient was possible,although the most obvious responsewas that the coordinates of any point on the graph would yield a solution.

... the majority of students did not perceive that the graph had any 

relevant information that would directly contribute to finding a solution.

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http://math.buffalostate.edu/~mcmillen/Kunth.pdf 

Knuth, E. (2000). Understanding connections between equations and graphs. The Mathematics Teacher. 93(1), 48-53.

Students solved part (b) primarily intwo ways: (1) rewriting the equation in

slope-intercept form and using theslope found from the graph to find themissing coefficient; or (2) substituting an x-value and its corresponding y- value, both found from the graph, into the equation and solving for themissing coefficient.

75% of the students selected the former method, ... only 3 students used thelatter method.

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http://math.buffalostate.edu/~mcmillen/Kunth.pdf 

Knuth, E. (2000). Understanding connections between equations and graphs. The Mathematics Teacher. 93(1), 48-53.

Ironically, a number of students responded to part (a) by stating that 

finding a solution was impossiblewithout the missing coefficient;however, these same students responded to part (b) by stating that using the graph would allow them to find the missing coefficient.

... these students did not recognize that the procedures that they used relied onthe fact that any point on a line is a solution to the equation of the line.