750 BC – 1450
Southwest Asia The ancient civilizations of Southwest Asia used counting boards – wooden or clay trays covered in a thin layer of sand. These were used to tally inventory or whatever else they needed to count. The Salamis Tablet: the earliest counting board known to exist and was used by Babylonians. Discovered on the Greek Island of Salamis in 1899. Roman Empire The ancient Romans created the first Abacus based on a counting board. This was made of beans or stones which moved in grooves in sand or on tables of wood, stone, or metal. |
250 BC – 990
Mayan and Aztecs The Mayans and the Aztecs both had counting devices that were made of corn kernels strung on string or wires that were stretched across a wooden frame. |
221 BC - 1370
Chinese Civilization The Chinese used the abacus for counting. “Suànpán”, the Chinese abacus. |
1438 - 1533
Inca Empire The Incas also had their own counting tool, which was made out of knotted strings called Quipu. |
1800
1800 – 1900
The late 1800s saw the invention of the first true manipulative-manoeuvrable objects that appeal to several different senses and are specifically designed for teaching mathematical concepts.
The late 1800s saw the invention of the first true manipulative-manoeuvrable objects that appeal to several different senses and are specifically designed for teaching mathematical concepts.
1837Friedrich Wilhelm August Fröbel (1782 – 1852)
A German pedagogue, a student of Pestalozzi who laid the foundation for modern education based on the recognition that children have unique needs and capabilities. He is the “Father of kindergarten” and who also developed the educational toys known as Froebel Gifts or Frobelgaben, which included geometric building blocks and pattern activity blocks. |
1896Jean Piaget (1896 – 1980)
A Swiss developmental psychologist and philosopher known for his epistemological studies with children. His theory of cognitive development and epistemological view are together called "genetic epistemology". He outlined a particular cognitive development of children, stressing the importance of concrete operations in the primary stages of knowledge formation. (Resnick, 1998) Children must first construct knowledge through “concrete operations” before moving on to “formal operations”. |
1900
Maria Tecla Artemesia Montessori (1870 – 1952)
An Italian physician and educator best known for the philosophy of education that bears her name, and her writing on scientific pedagogy.
She developed the use of manipulatives. Her goal is to enable children to “learn through personal investigation and exploration”. She founded a network of schools based on the education of the senses.
Montessori’s gifts are multisensory, sequential and self-correcting materials that facilitate the learning of skills and lead to learning of abstract ideas. “Montessori Method of Learning”, which is a method of educating young children that stresses development of a child's own initiative and natural abilities, especially through practical play.
An Italian physician and educator best known for the philosophy of education that bears her name, and her writing on scientific pedagogy.
She developed the use of manipulatives. Her goal is to enable children to “learn through personal investigation and exploration”. She founded a network of schools based on the education of the senses.
Montessori’s gifts are multisensory, sequential and self-correcting materials that facilitate the learning of skills and lead to learning of abstract ideas. “Montessori Method of Learning”, which is a method of educating young children that stresses development of a child's own initiative and natural abilities, especially through practical play.
1989The National Council of Teachers of Mathematics affirmed the usefulness and effectiveness of using manipulatives in teaching Math in public classrooms. (Ivanov, 2007) And today manipulative materials are well-established in the classroom, especially in the early grades.
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1998The use of virtual manipulatives already started but because it is still a relatively new way of learning, there is limited research on its effectiveness as compared to real-life manipulatives and other alternatives. (Learning Mathematics with Virtual Manipulatives)
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