The authors describe their goal as promoting new ways of learning and understanding mathematics ? particularly in regard to abstract structures. Interaction rather than explanation is the primary objective.
Target Student Population:
Almost all the materials here range from basic mathematics through calculus. There are a couple of more advanced items such as Fourier series.
Prerequisite Knowledge or Skills:
No specific prerequisites are needed other than standard background for the level of mathematics selected. Almost all topics are lower division college mathematics.
Type of Material:
Mainly interactive java applets plus some other graphics modules.
These materials would be appropriate for use in student discovery activities.
Java enabled browser. As usual there are some compatibility difficulties with different operating systems and browsers of different ages. The site includes a page that mentions some of the known side effects of different configurations. There are several mirror sites for this material.
Evaluation and Observation
Standard topics included in the gallery include sets, variables, equations, vectors, functions, trigonometry, analytic geometry, limits, differentiation, integration, probability and statistics, power series. More advanced material includes structures and spaces, Fourier series and model building.
Most of the applets allow exploration, input of answer and check for correctness and include a pop-up help window. Some are rather simple and hence a bit uninteresting; however, others offer excellent feedback and enhance conceptualization of math operations such as finding derivatives of a function, the effect of polynomial coefficients in graphing, etc.
For examples, the "Sets" applet allows an exploration of set builder notation; "Polar Coordinates" allows a point to be moved and displays coordinates; "Function Plotter" includes a fairly standard graph plotting utility; ?First and Second Derivatives? allows the coefficients of a function to be altered via a set of scroll bars while the derivatives are displayed graphically; ?Power Series 1? allows similar scroll bar input for coefficients. The "Math by Playing? applet is a fractal game that allows repeated image distortion.
"Computation of Sequences and Series" gives a good visual/numeric display of convergence and allows user control of formula and step size.
There is limited explanation of the underlying mathematics ? more complete explanations are available in German. The pop-up background explanation comments more on the teaching concept behind the module than on the background mathematics.
Potential Effectiveness as a Teaching Tool
This gallery is a good resource for those wishing a variety of easily accessible interactive visual experiments.
Users desiring explanation of the underlying mathematics will need to explore other resources ? but given the goal of encouraging interaction this is acceptable.
Ease of Use for Both Students and Faculty
Site navigation is excellent; java applets pop up in separate browser windows.
Each gallery item is labeled as either an applet, a set of graphics, or computational program.
Most of the applets work effectively in a variety of MAC and Windows environments and the controls are relatively simple.
Some combinations of operating system and browser produced system crashes although many were resolved by allocating additional memory.