Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

Five experiments demonstrated that 6.5-month-olds perseverated in a violation-of-expectation task to examine reasoning about width information in containment events. After watching a familiarization event in which a ball was lowered into a wide container, infants failed to detect the violation when the same ball was lowered into a container half…

Students were administered either conditional syllogism, biconditional syllogism, or conditional and biconditional syllogism tests. Analyses confirmed a tendency towards biconditionality. With conditional syllogisms, results indicated variations across forms of both major and second premises and a reversed developmental trend on problems which…

The concepts of cognitive development and objectivity are explored preparatory to a discussion of a suitable theory of development to be used as the foundation for developmentally-based standardized tests. It is hypothesized that Piagetian theory is the most appropriate basis for such tests and two possible approaches for constructing…

The rule space model permits measurement of cognitive skill acquisition, diagnosis of cognitive errors, and detection of the strengths and weaknesses of knowledge possessed by individuals. Two ways to classify an individual into his or her most plausible latent state of knowledge include: (1) hypothesis testing--Bayes' decision rules for minimum…

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…