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Traditional assessment would identify the last child as solving the problem correctly, while the children with mistakes or no answers would receive no credit. A dynamic assessment would place the children in three different categories: those who cannot solve the problem, those who can with help, and those who can independently.
Vygotsky noted that good teachers should not present material that is too difficult and "pull the students along." [5] Vygotsky argued that, rather than examining what a student knows to determine intelligence, it is better to examine their ability to solve problems independently and ability to solve problems with an adult's help. [7]
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
Piaget sees children's conception of causation as a march from "primitive" conceptions of cause to those of a more scientific, rigorous, and mechanical nature. These primitive concepts are characterized as supernatural, with a decidedly non-natural or non-mechanical tone. Piaget has as his most basic assumption that babies are phenomenists ...
Vygotsky believed that a child's development should be examined during problem-solving activities. [28] Unlike Piaget, he claimed that timely and sensitive intervention by adults when a child is on the edge of learning a new task (called the "zone of proximal development") could help children learn new tasks.
Vygotsky also believed culture is a very important part of cognitive development such as the language, writing and counting system used in that culture. Another aspect of Vygotsky's theory is private speech. Private speech is when a person talks to themselves in order to help themselves problem solve.
The Three Mountain Problem was devised by Piaget to test whether a child's thinking was egocentric, [2] which was also a helpful indicator of whether the child was in the preoperational stage or the concrete operational stage of cognitive development.
The problem, in this context, with informally formulated set theories, not derived from (and implying) any particular axiomatic theory, is that there may be several widely differing formalized versions, that have both different sets and different rules for how new sets may be formed, that all conform to the original informal definition.