How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly (...) stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

_ Source: _Page Count 30 GER Lloyd discerns two conflicting hypotheses concerning human cognition: cross-cultural universality and cultural relativity. The history of science is one discipline among many actively contributing to our understanding of human cognition at present. Not surprisingly, then, the dichotomy is also present in the history of science. In contrast to current approaches to the history of science, which highlight cultural relativity, genetic epistemology, which is conceived by Jean Piaget as a science of the acquisition of knowledge, (...) emphasises cross-cultural universality. Using the multidimensionality of phenomena and different styles of inquiry, I will argue that there is no inherent contradiction in the different approaches to the history of science. However, the amicable co-existence of both approaches has been undermined by Peter Damerow, who criticised the applicability of genetic epistemology to the historical development of knowledge on historical and theoretical grounds. In this paper, I will review Damerow’s theoretical critique, and, in formulating a response, I will argue that genetic epistemology cannot be dismissed as one of many legitimate styles of inquiry into the history of science on the basis of this critique. (shrink)

Recent research shows that research programmes (quantitative, qualitative and mixed) in education are not displaced (as suggested by Kuhn) but rather lead to integration. The objective of this study is to present a rationale for mixed methods (integrative) research programs based on contemporary philosophy of science (Lakatos, Giere, Cartwright, Holton, Laudan). This historical reconstruction of episodes from physical science (spanning a period of almost 300 years, 17 th to 20 th century) does not agree with the positivist image of science. (...) Quantitative data (empirical evidence) by itself, does not facilitate progress (despite widespread belief to the contrary), neither in the physical sciences nor in the social sciences (education) A historical reconstruction shows that both Piaget and Pascual-Leone's research programs in cognitive psychology, follow the Galilean idealisation quite closely, similar to the research programs of Newton, Mendeleev, Einstein, Thomson, Rutherford, Millikan and Perl in the physical sciences. This relationship does not imply that researchers in education have to emulate research in the physical sciences. A major argument in favor of mixed methods (integrative) research programs is that it provides a rationale for hypotheses, theories, guiding assumptions and presuppositions to compete and provide alternatives. Similar to the physical sciences, this proliferation of hypotheses leads to controversies and rivalries, and thus facilitates the decision making process of the scientific community. It is concluded that mixed methods research programs (not paradigms) in education can facilitate the construction of robust strategies, provided we let the problem situation (as studied by practicing researchers) decide the methodology. (shrink)