Reduction is one of the key techniques used for problem-solving in computer science. In particular, in the theory of computation and complexity (TCC), mapping and polynomial reductions are used for analysis of decidability and computational complexity of problems, including the core concept of NP-completeness. Reduction is a highly abstract…

The Organization for Economic Cooperation and Development [OECD] is a global policy organization that includes the United States and about half of the Western Europe countries. It administers international comparison tests, called Programme for International Student Assessment (PISA), for 15 year-old students in Mathematics and other subjects. I…

This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

Incorrect handling of item parameter drift during the equating process can result in equating error. If the item parameter drift is due to construct-irrelevant factors, then inclusion of these items in the estimation of the equating constants can be expected to result in equating error. On the other hand, if the item parameter drift is related to…

Numerous studies have compared the Angoff standard-setting procedure to other standard-setting methods, but relatively few studies have evaluated the procedure based on internal criteria. This study uses a generalizability theory framework to evaluate the stability of the estimated cut score. To provide a measure of internal consistency, this…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

BRT Math Screening Measures focus on students' mathematics performance in grade-level standards for students in grades 1-8. A total of 24 test forms are available with three test forms per grade corresponding to fall, winter, and spring testing periods. Each form contains computation problems and application problems. BRT Math Screening Measures…

This study examined the effects of task difficulty on on-task behavior for four students exhibiting low levels of math performance and on-task behavior. Curriculum-based assessments were conducted with each student to define the difficulty level of math tasks for each student based on the individual's rate of accurate performance on computational…

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…

The purpose of this study was to document the instrument development of maze measures for grades 3-8. Each maze passage contained twelve omitted words that students filled in by choosing the best-fit word from among the provided options. In this technical report, we describe the process of creating, reviewing, and pilot testing the maze measures.…

The analytically derived asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be approximated by a mathematical function without examinees' responses to test items, and the empirically determined SEs of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates can be obtained when the same set of items is…