This applet allows students to sketch the anti-derivative of a function with almost immediate feedback and develop their understanding of the anti-derivative in relationship to the original function. It enables students to see the role that inflection points play in the process.
Type of Material:
Classroom demonstration; student exploration
Java-enabled browser; JAVA 2 plug-in
Identify Major Learning Goals:
Develop a geometrical understanding of the anti-derivative of a function through repeated creation of real-time visual examples.
Target Student Population:
Beginning Calculus students
Prerequisite Knowledge or Skills:
Graphing skills, familiarity with the concept of derivative
The applet requires students to connect the concept of slope of the tangent line to the actual graph of a function. Students can develop their geometrical understanding of the anti-derivative by practicing with the applet. The role of inflection points becomes clear in the process as do the zero slope values at relative minima and maxima.
More explanations would be useful. The visual examples alone may not be enough for students to grasp the connections between the two graphs.
Potential Effectiveness as a Teaching Tool
This applet provides excellent visual practice in drawing anti-derivatives based on a given function. It takes a bit of practice and concentration to catch onto the process, but the almost immediate feedback is most helpful.
The title of the applet indicates that it involves graphing an anti-derivative of a function. The author might facilitate student understanding by pointing out that there is an infinite family of anti-derivatives for a given function, each anti-derivative differing from the others only by vertical position. The users graph of an anti-derivative will be correct as long as is it has the same shape and relative position as the graph sketched by the Java applet.
Alternatively, if the author desires a unique anti-derivative for each function, he might modify the applet by specifying a particular point through which the anti-derivative must pass. For example, this could be achieved by plotting a very prominent point at the left-most boundary of the graph. The student user would be instructed to begin drawing his/her graph through that point.
The ability to start with simple linear examples and move to more complicated ones would be useful for beginners. At present, the graph selection is random. It would be helpful to comment that reversing the roles of the two curves matches the relationships demonstrated in the related applet entitled Graphing a Derivative of a Function by the same author.
Ease of Use for Both Students and Faculty
No technical difficulties were encountered in the use of this site.
In cases where the original graph did not appear to begin at the left edge of the applet window (i.e., where the graph was asymptotic with the x-axis), it wasnt evident that the user had to begin dragging the mouse from the left edge of the window. The natural tendency in these cases is to begin dragging the mouse at the point where the graph appears to begin; however, this doesnt activate the anti-derivate plot. This could be addressed by modifying Instruction #1 to indicate the need to begin dragging the mouse at the left edge of the applet window.
The instruction drag the mouse could be misinterpreted as rollover. In fact, it means click and hold as you drag. It is not clear what information is given by the graph of the mouse trace no matter the y value of the mouse, the derivative graph is the same because it illustrates the provided sample graph not the graph of the mouse
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