MATHCAT: A Flexible Testing System in Mathematics Education for Adults

Abstract

One of the mathematics courses in adult basic education in the Netherlands is offered at three different levels. The majority of the students are foreign and, due to a large variation in background, most of their educational histories are unknown or can be determined only unreliably. In the program's intake procedure, a place-ment test is used to assign students to a course level. As the students' abilities vary widely, the paper-and-pencil placement test currently used has the two-stage format described in Lord (1971). In the first stage, all examinees take a routing test of 15 items with an average difficulty matching the average proficiency in the population of students. Depending on their scores on the routing test, the examinees then take one of the three follow-up tests. Each follow-up test consists of 10 items. There are several drawbacks to this current testing procedure: 1. Test administration is laborious because of the scoring that has to take place after the routing test. 2. Preventing disclosure of the test items is difficult due to the flexible intake pro-cedure inherent in adult basic education. Disclosed items can easily lead to misclassifications (assignment of prospective students to a course level for which they lack proficiency). 3. Because only one branching decision is made, possible misroutings cannot be corrected (Weiss, 1974) and measurement precision may be low. A computerized adaptive placement test has offered a solution to these problems. First, such tests have as many branching decisions as items in the test. Erroneously branching on the items, because of incorrect responses to items that are too easy or correct responses to items too difficult, is corrected later in the test. Second, computerized test administration offers the advantage of immediate test scoring and