| Two instruments were developed in this study to measure aptitude in mathematical recursion problem solving, one with the latent trait approach and one with the achievement as aptitude approach. The latent trait approach instrument was designed to assess the cognitive traits, reasoning abilities, and mathematical skills essential to solve problems in mathematical recursion and the achievement as aptitude approach instrument was designed to assess the steps necessary to solve problems in mathematical recursion. The procedures from each phase of the four-phases of test construction were performed and documented for both instruments to evaluate each individually and in comparison with one another. There were two purposes for this study: to provide evidence of the advantages and disadvantages of the latent trait approach and achievement as aptitude approach to aptitude assessment development; and to obtain at least one instrument measuring aptitude in mathematical recursion problem solving with sufficient evidence of validity and reliability to support utility of the instrument.; While content validity was established with the latent trait approach instrument, results of the descriptive statistics, item difficulty and item discrimination indices, factor analysis, and calculation of Cronbach's alpha indicated there is insufficient evidence of validity and reliability to support utility of this instrument in its current form. Similarly, results of the achievement as aptitude instrument indicate content validity was established, but evidence of validity and reliability collected from descriptive statistics, factor analysis, and calculation of Cronbach's alpha fail to support utility of this instrument in its current form.; The comparison between the results of both instruments developed in this study revealed that the latent trait approach is the stronger of the two. Observation of both sets of item-level means in a 0 to 1 scale depicted higher values for items in the latent trait approach instrument. Cronbach's alpha values were also significantly higher in the latent trait approach instrument than in the achievement as aptitude instrument. Given the higher item-level means and Cronbach's alpha values in the latent trait approach instrument, this instrument is the more effective of the two and could be salvageable with revisions of some of the items. |
