The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

In interdisciplinary studies, multiple definitions and practices proliferate. Interdisciplinarians such as William H. Newell claim that complex systems theory provides the rationale that we need to guide reform. However, complex systems theory alone cannot rationalize interdisciplinarity and inform what Ernest Boyer calls the scholarship of…

Einstein held that intuition is more important than rational inquiry as a source of discovery. Further, he explicitly and implicitly linked the heart, the sacred, devotion and intuitive knowledge. The raison d'être of universities is the advance of knowledge; however, they have primarily focused on developing student's skills in working with…

There is a gap between the facts learned in a science course and the higher-cognitive skills of analysis and evaluation necessary for students to secure scientific knowledge and scientific habits of mind. Teaching science is not just about how we do science (i.e., focusing on just "accumulating undigested facts and scientific definitions and…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Some studies conducted on ADHD have found a statistically significant relationship between those diagnosed with the disorder and a higher susceptibility to abuse alcohol. However, other studies have found no such correlation, or have found this to be true of only a nonstatistically significant subset of the population of individuals with ADHD.…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…

According to the Theory of Multiple Intelligences of Howard Gardner, there are eight intelligences. In the present study with two FLES classes, 35 students were asked to present Spanish vocabulary to their class to link their preferences of techniques used to introduce the vocabulary to their classmates with a spectrum of their multiple…

The purpose of the study is to investigate the effects of mind mapping with cooperative learning (MMCL) and cooperative learning (CL) on: (a) programming performance; (b) problem solving skill; and (c) metacognitive knowledge among computer science students in Malaysia. The moderating variable is the students' logical thinking level with two…

The science curriculum in Malaysia emphasizes the acquisition of scientific skills, thinking skills, and the inculcation of scientific attitudes and noble values. Besides that, the acquisition of scientific and technological knowledge and its application to the natural phenomena and students' daily experiences are also equally emphasized. The…

When a test is adapted from a source language (SL) into a target language (TL), the two forms are usually not psychometrically equivalent. If linking between test forms is necessary, those items that have had their psychometric characteristics altered by the translation (differential item functioning [DIF] items) should be eliminated from the…

Within the context of a mathematics reform effort to implement algebra in elementary schools, there is a pressure to provide results in the form of student achievement scores. However, widely-used measures of student achievement may be unrelated to the ideas and instructional practices encouraged by the reform effort. The inappropriate use of…

In Study 1, 10-, 13-, and 16-year-olds were assigned to conditions in which they were instructed to think logically and provided alternative antecedents to the consequents of conditional statements. Providing alternatives improved reasoning on two uncertain logical forms, but decreased logical responding on two certain forms; logic instructions…

In the context of item response theory, it is not uncommon that person-by-item data are correlated beyond the correlation that is captured by the model--in other words, there is extra binomial variation. Heterogeneity of the parameters can explain this variation. There is a need for proper statistical methods to indicate possible extra…