A 40-item free response test on signed-number subtraction was administered to 172 eighth graders. Their responses are viewed as consisting of two different components, the sign and absolute value. Each component is scored zero for wrong or one for correct, yielding a score of one only when both components have scores of one. By taking the values…

Several extended caution indices (ECIs) have been introduced earlier as a link between two distinctly different approaches: one based on standard statistics and the other, a model-based approach, utilizing item response theory (IRT). Expected values and variance of some ECIs are derived and their statistical properties are compared and discussed.…

Research recurrently indicates that children who have difficulty with arithmetic often use systematic routines that yield wrong answers. Recent research has focused less on identifying the most common errors among groups of children and more on analyzing individual children's errors. This paper considers the source of systematic errors in…

This study attempts to determine whether the syntactic errors children make while learning a second language are due to native language interference or to developmental cognitive strategies, as has been found in first language acquisition. (Author)

Nine subjects, 5 of whom claimed absolute pitch (AP) ability were instructed to rapidly strike notes on the piano to match randomized tape-recorded piano notes. Stimulus set sizes were 64, 16, or 4 consecutive semitones, or 7 diatonic notes of a designated octave. A control task involved motor movements to notes announced in advance. Accuracy,…

Using conventional mental test theory, item parameters of an aptitude or achievement test vary with each group of examinees, and as such are somewhat limited in their use and interpretation. Within the last 25 years, measurement models have emerged in which item parameters are considered to be invariant. Generically referred to as latent trait…

Results indicate that for the task of generating counterexamples to invalid syllogisms, a primary source of difficulty is the first step of forming the negation of the conclusion, especially if the conclusion is a "Some are not" statement. When this step is done for the subject, most of the errors disappear. (Author/BJG)

This report describes the test performances of 26 students who displayed a variety of erroneous rules in completing a 48-item test of fraction addition problems, constructed to diagnose at least 88 projected erroneous rules. Cases were selected for their potential usefulness in designing and implementing an error-diagnostic testing system and in…

Tutorial dialogues can be analyzed as an interaction in which a tutor "debugs" a student's knowledge representation by diagnosing and correcting conceptual misunderstandings. Some tentative steps toward a theory which describes tutorial interactions are outlined. The goal structure of a tutor, types of conceptual bugs that students have…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

One aspect of multiple regression--the shrinkage of the multiple correlation coefficient on cross-validation is reviewed. The paper consists of four sections. In section one, the distinction between a fixed and a random multiple regression model is made explicit. In section two, the cross-validation paradigm and an explanation for the occurrence…

An investigation to compare systematic behavioral observations made live with those made on television was conducted. The study was designed to answer three questions: (1) Is there a difference in the agreement between observers (Os) when both view an event Live and when both view the same event on Television? (2) Is there a difference in…