Comments on: Goodie of the Month – Tangents to Quadratics
http://www.mathcasts.org/janita/?p=169
Second Life & Real Life MathematicsThu, 01 Apr 2010 00:12:02 +0000hourly1http://wordpress.org/?v=3.2.1By: Jonathan
http://www.mathcasts.org/janita/?p=169&cpage=1#comment-50
JonathanSun, 12 Apr 2009 23:35:56 +0000http://www.mathcasts.org/janita/?p=169#comment-50There is a definite sense of limit that gets played with here - I am uneasy with it as an Algebra I topic.
If they cannot derive 2a + b, then they have to accept it, which is problematic.There is a definite sense of limit that gets played with here – I am uneasy with it as an Algebra I topic.

If they cannot derive 2a + b, then they have to accept it, which is problematic.

]]>By: admin
http://www.mathcasts.org/janita/?p=169&cpage=1#comment-43
adminSat, 28 Mar 2009 06:37:28 +0000http://www.mathcasts.org/janita/?p=169#comment-43Absolutely cool idea about using the slope of the secant to get to s(x)! Just stating the formula for s(x) was indeed a weak point. (I actually use this topic in a very abbreviated calculus course and they take the derivative.) I will think about how to add this to the applet. Many thanks for the comment!Absolutely cool idea about using the slope of the secant to get to s(x)! Just stating the formula for s(x) was indeed a weak point. (I actually use this topic in a very abbreviated calculus course and they take the derivative.) I will think about how to add this to the applet. Many thanks for the comment!
]]>By: The Math Maker
http://www.mathcasts.org/janita/?p=169&cpage=1#comment-42
The Math MakerSat, 28 Mar 2009 03:05:16 +0000http://www.mathcasts.org/janita/?p=169#comment-42I really like this GeoGebra applet and I agree that the visual nature of the whole thing makes it much more compelling. It's interesting and satisfying to see so many concepts all tied together from a single application. My initial concern was that the student may query the significance of s(x) and hence some of the impact dissipated, but I thought that this can be overcome by using the general high school expression for slope (i.e. change in y over change in x). Then by discussing what is happening to the change in x as the secant approaches the tangent, the student should be able to come to some conclusion (maybe even with a slight addition to the applet) and actually show the expression for s(x) is correct ... and a nice little introduction to limits without them even knowing.I really like this GeoGebra applet and I agree that the visual nature of the whole thing makes it much more compelling. It’s interesting and satisfying to see so many concepts all tied together from a single application. My initial concern was that the student may query the significance of s(x) and hence some of the impact dissipated, but I thought that this can be overcome by using the general high school expression for slope (i.e. change in y over change in x). Then by discussing what is happening to the change in x as the secant approaches the tangent, the student should be able to come to some conclusion (maybe even with a slight addition to the applet) and actually show the expression for s(x) is correct … and a nice little introduction to limits without them even knowing.
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