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Peer Review

Rational Functions - Spikes and Spears

by Alan Cooper


Overall Numeric Rating:

4.4 stars
Content Quality: 5 stars
Effectiveness: 4 stars
Ease of Use: 4.2 starsstar
Reviewed: Oct 07, 2005 by Mathematics
Overview: This learning activity allows the student to explore the vertical and horizontal
asymptotes of a rational function. It also gives a graphical introduction to
partial fractions.
Type of Material: Simulation
Recommended Uses: Classroom demo; student exploration
Technical Requirements: Requires a "Java-enabled" browser.
Identify Major Learning Goals: The successful student will learn how to identify the asymptotes of a rational
function and will understand the idea of partial fractions

Target Student Population: Pre-Calculus Students
Prerequisite Knowledge or Skills: The activities assume no prior knowledge other than the Cartesian coordinate
system, although critical thinking abilities at the Pre-Calculus level or above
is needed.

Evaluation and Observation

Content Quality

Rating: 5 stars
Strengths: This learning object consists of a graphing tool accompanied by five activities.
On the left is a frame containing well written instructions that guide the
student through the activities. The frame’s width can easily be resized. On
the right is the graphing tool. In the activities, the student is asked to
enter the equations of rational function and then explore the graphs. The
equations are entered with parameters and the student is instructed to change
the parameters to see how the graph is affected. The parameters can be inputted,
incremented manually, or automatically so that the student can explore the
effect of the graph when the parameters change. Instead of telling the student
what to do, the activities ask to students to explore on their own. The
concepts of vertical, horizontal, and slant asymptotes as well as partial
fractions are explored.
Concerns: Reformatting the left activity frame to use bulleting, numbering, or some other
organizational technique would make the instructions easier to follow.

Potential Effectiveness as a Teaching Tool

Rating: 4 stars
Strengths: The object is can be used by students learning on their own without the
assistance of an instructor. The student using this activity will have the
opportunity to explore the graphs of rational functions without getting
frustrated. They will develop an understanding of asymptotes visually. This is
especially effective for the student who learns well visually and
kinesthetically. For the user who may be unsure of the expected results,
summaries are provided at various intervals to keep the user on track.
Concerns: The animation can be extremely quick, depending on the user’s computer. An
additional comment that using a value of E that is negative will produce a
slower graph would be helpful to the student who does not realize this in
advance. In activities 2 and 5, the there are so many graphs shown, it is
difficult to see what is going on.

The variable h has multiple uses in the applet, which can be confusing to the
user. The h is used as a view dimension, and in the activity directions to Plot

The graph window is relatively small, making it difficult to see the detail
required to reach conclusions regarding the concepts under review.

Ease of Use for Both Students and Faculty

Rating: 4.2 stars
Strengths: The instructions for each of the activities are easy to follow. If the student
follows the directions then there should be no difficulties in using this
learning object. A help link that gives explanations on how to use the graphing
tool is provided.
Concerns: The parameter controls could be enlarged and separated so that they do not
overlap. It would be helpful to have the Stop button present whenever the
animation feature is used.

The requirement of using * to indicate multiplication is cumbersome since most
graphing utilities now use syntax with implied multiplication.

Other Issues and Comments: