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MERLOT II


    

Peer Review


Linear Functions

by Philippe Laval
 

Ratings

Overall Rating:

4 stars
Content Quality: 4 stars
Effectiveness: 4 stars
Ease of Use: 4 stars
Reviewed: Nov 29, 2004 by Mathematics
Overview: This site is a sub collection of a larger set by Philippe Laval containing a
variety of explorations. It is a self-contained collection of Java Applets that
can be used in the teaching and learning of mathematics.
Learning Goals: The Linear Functions applet investigates the concepts of slope and y-intercept
and the corresponding equations for the line.
Target Student Population: Students in a beginning, intermediate or college algebra course.
Prerequisite Knowledge or Skills: The applets are self-explanatory and could easily be used by any mathematics
student without assistance, however may be most effective if preceded by an
instructor demonstration and explanation of terms.
Type of Material: Computation, graphics and simulation.
Recommended Uses: classroom demonstrations, student explorations.
Technical Requirements: It requires a Java-enabled browser.

Evaluation and Observation

Content Quality

Rating: 4 stars
Strengths: The Linear Functions page contains two applets: ?Slope? and ?Role of m and b?.
Its features are best used initially as a demonstration by the instructor,
followed by student experimentation.

The ?Role of m and b? allows the user to enter values for x and y using a scroll
bar. Accuracy to the tenth place is provided. As the scroll bar is moved, the
corresponding graph is simultaneously updated.

The ?Slope? applet allows the user to plot points on a graph by double clicking
on the location of the desired point. The corresponding coordinates, the slope
and the graph are then provided, as well as a triangle demonstrating the slope
between the points. The user is then instructed to drag one of the points along
the line. In doing so, the coordinates of that point are restated, the slope
is recalculated with the new numerator and denominator shown, and the graph is
redrawn with a new triangle between the new coordinates. The value for the
slope clearly remains constant.

In the ?Slope? applet, the slope of a horizontal line is reported as zero.
Concerns: The meanings of ?m? and ?b? are not defined in the applet. In the ?Slope?
applet, the slope of a vertical line is reported as ?infinity? rather than
?undefined?, and the denominator of the slope formula is shown as zero,
indicating division by zero is permissible. In the meanings of ?m? and ?b? the
screen flickers as the graph is dragged.

Potential Effectiveness as a Teaching Tool

Rating: 4 stars
Strengths: The ?Role of m and b? applet demonstrates effectively that changing the value of
the y-intercept creates a line parallel to the previous one that passes through
the new y-intercept. Changing the value of the slope using the scroll bar is
effective in demonstrating that the line is actually pivoting around the fixed
y-intercept.

The ?Slope? applet is effective in demonstrating that the slope of the line will
not change if different points are selected to make the calculation. It also
effectively demonstrates visually the constant ratio of the ?rise? and ?run? by
resizing the triangle as a new point is selected for the slope calculation.
Concerns: The applet does not provide background information on the mathematical concepts
or ask the students questions that would lead to specific conclusions. As a
result, the user must be given background information on the concepts to
effectively understand the purpose of the demonstration. In the slope applet,
the line occasionally disappears while the dragging process is going on. When
this occurs, the user must hit the ?Clear? button and start over.

Ease of Use for Both Students and Faculty

Rating: 4 stars
Strengths: Students will need no explanation to use these applets, although there is an
itemized explanation available just below the applet.

In the ?Role of m and b? applet, the scroll bar allows easy entry of values for
?m? and ?b?. Right and left arrows on the scroll bar assist the user in
selecting specific values and consecutive values accurate to the tenths place.
The simultaneous appearance of the corresponding graph allows the user to
visualize the change in the graph that occurs as the values of ?m? and ?b? are
increased or decreased.
Concerns: The ?Slope? applet requires the user to double click to select each point and
provides the coordinates with two place decimal accuracy. This can make it
difficult to obtain specific values such as integers. Once a point is selected,
the screen must be cleared if the user is not satisfied with the result.
Obtaining two points with predetermined coordinates is not feasible.

The values shown for ?m? and ?b? are in textboxes that are not editable. Either
presenting these as labels or allowing the student to enter values and having
the graph adjust according to the entered values would make the applet easier to
use.

Other Issues and Comments: