English has a universal appeal and in India, English is associated with modernity and progress sometimes with the ideology of its cultural values. The economic value of English is very high in India as even a layman uses English words in his/her "native" communication. The second language acquisition happens for learners at various…

This study addressed one aspect of scientific reasoning, the control of variables reasoning scheme. We explored whether a short intervention aimed at accelerating this reasoning scheme by CASE lessons would improve students' ability to apply this scheme in problems related to the biology curriculum. About 120 students from grade nine were assessed…

Background: Shayer, Ginsburg, and Coe (2007) showed that children leaving primary school in Y6 entered secondary school with much lower levels of understanding of the physical conservations than in 1976. It seemed desirable to investigate cognitive development in the first three years of secondary education. Aims: By using two Piagetian tests of…

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

The author reflects on Piaget's 1972 article, "Intellectual evolution from adolescence to adulthood," addressed to questions regarding what he alleged to be the final, most advanced level of cognition in his developmental stage theory--formal operations, as described in his 1958 volume coauthored with Inhelder, "The growth of logical thinking from…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

This article explores relationships between designing and making in the work of children within the age range 5-11 when engaged in practical modelling tasks. The notion of the model is explored from the perspective of concrete representations. It is suggested that concrete models may be used as hypotheses from which to test ideas about the nature…

One of the most challenging daily experiences of teaching young adolescents is helping them transition from Piaget's concrete to the formal operational stage of cognitive development during the middle school years. Students who have reached formal operations can design and test hypotheses, engage in deductive reasoning, use flexible thinking,…