A TEST OF ALGEBRA READINESS: THE CONSTRUCTION OF A TEST OF THOSE COGNITIVE SKILLS THAT ARE PREREQUISITE TO THE LEARNING OF ALGEBRA

This study defines algebra readiness by listing fifty-seven cognitive skills which are beyond numerical computations but are prerequisite to learning algebra. The skills are grouped into eight categories: identifying equivalent expressions or statements, making numerical comparisons, making comparisons on a number line or scale, recognizing the nature of mathematical operations, understanding number relationships, understanding the concept of infinity, interpreting information, and working with unfamiliar symbols. Test items were written based on these skills.;The second round of testing was administered to 195 students who were starting algebra in three New York City independent schools. The test was organized into three subtests, distributed at random within each class. In addition to the types of analyses done for the first round, the predictive power for each subtest and for each of the original eight categories was measured. A comparison was made to the predictive power of several mathematics subtests of the Educational Records Bureau (ERB) test, including mathematics aptitude, mathematics concepts, mathematics computation, and the mathematics test as a whole.;Results showed that the algebra grades were predicted more strongly than the scores on the algebra achievement test. All three subtests predicted algebra success more strongly than the ERB mathematics test or any of its parts, in general. Two categories--recognizing the nature of mathematical operations and identifying equivalent expressions or statements--had predictive power of.585 and.574 respectively. One of the three subtests had a predictive power of.648, which was the highest of any other subtest, category, or ERB test.;The first round of testing was administered to 140 students beginning the study of algebra in four New York City independent schools. The test was organized into four subtests, distributed at random within each class. The test items were analyzed for difficulty and reliability. The validity of each item was measured by an algebra achievement test written for this study, as well as by the grade in algebra. Based on this analysis, items were either discarded, changed, or kept as is. The algebra achievement test was also rewritten based on an item analysis.