Profile of Programs of Calculator Based Algebra
Most of the programs consist of a set of four basic problem types. The problem set is repeated four times resulting in a total of 16 problems. Sixteen was chosen because it allows for missing one problem and still having a score of 94% (an A in most schools). The problems are presented in an order of increasing difficulty in the first set of four. Thereafter, the order is randomized to eliminate pure memorization of a sequence of procedures. The rote memorization of a procedure without any understanding of the underlying principles is perhaps the most common failing of algebra students.
The numbers used in any given problem are generated randomly so that copying someone else's answer will not work.
Two of the programs deal with the derivation of the Pythagorean Theorem and the quadratic formula from simple concepts. They are provided for their heuristic value, and are not intended to be graded.
The programs congratulate correct answers with a phrase chosen randomly from 80 possibilities. Similarly, wrong answers are indicated by a randomly selected phrase. The latter phrases begin and end with negative signs (-) to insure that the student interprets the phrase correctly. The congratulatory phrases end with "!".
The program keeps track of the number of correct answers, and of the total number of problems attempted. At the conclusion of 16 problems, the Performance Summary Screen reports the name and number of the program, the student number, the beginning problem number, the number attempted, the number correct, and the percentage correct. Most of this information is also stored in a revolving history in matrix [E] (described under Recording Scores).
All of the programs make extensive use of subroutines that are common to all. These subroutines reside in a file called SBR which must be present in RAM. Otherwise an ERR:UNDEFINED error message will result. If SBR is present but archived, then the message will be ERR:ARCHIVED.