The problem under investigation in this research is the development of a general approach that will establish a students knowledge level so that the student's learning can be optimized by beginning it at the most effective point. In preparation for this study, an active test with an acceptable CT3 homogeneity index was found. Two computer programs, RightOrder and MathTest, were written in Visual Basic. The latter administers the test, producing a file or responses that serves as input for the former, which performs the calculations and matrix manipulation necessary to determine the CT3 of a set of test items and construct a difficulty strata scale. The test was administered twice to the same population, the first time in the original item order. In the second administration, one item from each successive level of difficulty, beginning with the easiest, was given until the respondent answered incorrectly. Then all the remaining items were presented in order of difficulty, beginning with the easiest. The three hypothesis of this study are (a) the difficulty strata scale generated from the computerized retest, using a z-score to be determined as critical value, is congruent with that derived from the analysis done on the data of the first application of the computerized test, (b) the time spent to establish the knowledge level is shorter than the time spent taking the full test, and (c) the test, reordered according to ordering theory principles, is an accurate method of establishing a student's knowledge level.
