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.
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.
classroom demonstrations, student explorations.
It requires a Java-enabled browser.
Evaluation and Observation
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.
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
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.
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
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.
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.