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 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…

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,…