About Exercise Maker
The information on this page is related to Exercise Maker version 1 and the collection of exercises on Matrix Algebra that are now available for Macintosh. If you are interested in trying out the package download it from here.
EM provides interactive environment for doing exercises in Matrix Algebra, checking their answers, giving advises and instructions.
It uses Mathematica through MathLink protocol both
The algorithms used for that purpose are coded in an ordinary Mathematica Notebook which has the same file name as the main exercise file with additional extension ".m". EM extracts the first two input cells from this notebook and uses the code which they contain as generating and verifying program, respectively. Anything else in this notebook is ignored by EM.
- to generate random matrices on-line
- and to check the answer.
All exercises provided in "Interactive Exercises" folder use a Mathematica package "Utils.m". EM is set to load it if you choose to "Link to Local Kernel" or to "Link to Remote Kernel" in the start up dialog box.
You MUST make the package visible to Mathematica by following the instructions given in "EM Packages:ReadMe" file.
The generating Mathematica program is executed when an exercise is opened. In addition under the file menu there is a command called "New Values" which will execute the generating program once again and new matrices will replace the older ones.
The verifying Mathematica program is executed whenever CHECK button is pressed. The purpose of this program is to determine whether the answer is correct and, if possible, what is exactly wrong. It must return a string which EM will display in a dialog box.
Because Mathematica is not always available to link to, there is possibility to open the exercises even when it is not. For that purpose EM uses a collection of values stored in advance into the main file (the resource fork of that file). In this case EM will check the answer in a very simplified way. There must be exact matching between the "proposed answer" and the "correct answer". The later is stored in advance.
The exercises may have up to three levels of hints which can be seen, if provided, by pressing corresponding buttons.
Our goal in the near future is to extend the user interface of EM, so that not only matrices are supported but also generic mathematical formulas. The next version of Exercise Maker is under development already and it is not so matrix algebra oriented. Mathematica would be again extremely useful tool in the final interpreting of different mathematically equivalent expressions and implementing sophisticated generating and checking algorithms. The interaction between EM and Matematica kernel will basically remain the same. Again we are not going to force students to use Mathematica's syntax in order to give their answers, instead we are looking for a solution similar to graphical equation editors. If interested to see a prototype of an answer editor for Macintosh in a very early stage of its development download it from here.
The authors would be very grateful to obtain any information about similar expression editors available that could be easily integrated with the rest of our software. Email:
The Hypermedia Laboratory