Recent work in the area of cognitive research in mathematics education focuses on detailed examinations of the learning process of students and how this process is affected by current innovations in the classroom, including collaborative learning and the use of computers and interactive software. Much of this work is supported by the learning framework of constructivism, a school of thought which is based on the work and writings of Jean Piaget. Piaget, a French psychologist in the mid-twentieth century, observed the learning behavior of children and concluded that individuals construct their own knowledge by creating mental structures which explain their perspectives on the world. According to constructivists, learning takes place when new information is assimilated into a person's mental structures, or when new structures are formed to accommodate experience which does not 'fit' into the old structures. From this point of view, learning is primarily an individual process, motivated by the interaction between a student's beliefs and what he/she experiences. Constructivists in mathematics education encourage teachers to move from concrete to abstract representations of a concept, in order to help students build accurate mental constructions. This approach is often seen in elementary mathematics classes, where students work with manipulative objects before dealing with abstract operations such as addition and multiplication. Higher level concepts, such as those studied in calculus, are often more difficult to present in a concrete fashion. In a similar sense to the use of manipulatives in younger grades, interactive technology may provide an environment for undergraduate students to physically explore and become familiar with the concepts of calculus using the mouse and other tools on a computer screen. According to constructivist theory, students 'learn' when they refine or change their mental constructions once their experience, rather than instruction, convinces them that their existing constructions are insufficient. Interactive computer environments may provide the experiential setting for this learning to take place.
Hare, Angela, "An Investigation of the Behavior of Calculus Students Working Collaboratively in an Interactive Software Environment" (1997). ACMS Conference Proceedings 1997. 6.
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