When was finger counting invented

A striking example of the importance of visual mathematics comes from a study showing that after four minute sessions of playing a game with a number line, differences in knowledge between students from low-income backgrounds and those from middle-income backgrounds were eliminated.

Visual math is powerful for all learners. A few years ago Howard Gardner proposed a theory of multiple intelligences , suggesting that people have different approaches to learning, such as those that are visual, kinesthetic, or logical.

But people who are not strong visual thinkers probably need visual thinking more than anyone. Everyone uses visual pathways when we work on math. It is hardly surprising that students so often feel that math is inaccessible and uninteresting when they are plunged into a world of abstraction and numbers in classrooms.

Students are made to memorize math facts, and plough through worksheets of numbers, with few visual or creative representations of math, often because of policy directives and faulty curriculum guides.

The Common Core standards for kindergarten through eighth grade pay more attention to visual work than many previous sets of learning benchmarks, but their high-school content commits teachers to numerical and abstract thinking. To engage students in productive visual thinking, they should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see.

They can be given activities with visual questions and they can be asked to provide visual solutions to questions. When the youcubed team a center at Stanford created a free set of visual and open mathematics lessons for grades three through nine last summer, which invited students to appreciate the beauty in mathematics, they were downloaded , times by teachers and used in every state across the U. Ninety-eight percent of teachers said they would like more of the activities, and 89 percent of students reported that the visual activities enhanced their learning of mathematics.

Work on mathematics draws from different areas of the brain and students need to be strong with visuals, numbers, symbols and words—but schools are not encouraging this broad development in mathematics now.

This is not because of a lack of research knowledge on the best ways to teach and learn mathematics, it is because that knowledge has not been communicated in accessible forms to teachers.

Research on the brain is often among the most impenetrable for a lay audience but the knowledge that is being produced by neuroscientists, if communicated well, may be the spark that finally ignites productive change in mathematics classrooms and homes across the country. The design of the schoty is based on a pair of human hands each row has ten beads, corresponding to ten fingers. The abacus is operated by sliding the beads right-to-left.

If you hold out both hands in front of you, palms facing out, you will see that your two thumbs are beside each other and two sets of 4 fingers spread out from there. Similarily, on the schoty , each row has two sets of 4 beads of the same colour on the outside, representing the two sets of 4 fingers and the two inner-most beads of the same colour representing the two thumbs.

The "home" position for the beads is on the right hand side. The bottom-most row represents 1s, the next row up represents 10s, then s, and so on.

So, counting is similar to counting on one's fingers, the beads move from right to left: 1 to 10, and then carrying upwards to the next row. Careful observers will note that the metal rods, on which the beads slide, have a slight curvature to prevent the "counted" beads from accidently sliding back to the home-position. There have been recent suggestions of a Mesoamerican the Aztec civilization that existed in present day Mexico abacus called the Nepohualtzitzin , circa C.

Since it was made from perishable materials it is impossible to know whether such a tool ever existed. There is also debate about whether the Incan Khipu was a three-dimensional binary calculator or a form of writing, or both.

According to the author, multiplication and division are easier using this modified abacus and square roots and cubic roots of numbers can be calculated. The abacus is still in use today by shopkeepers in Asia and "Chinatowns" in North America. The abacus is still taught in Asian schools, and a few schools in the West. Blind children are taught to use the abacus where their sighted counterparts would be taught to use paper and pencil to perform calculations.

One particular use for the abacus is teaching children simple mathematics and especially multiplication; the abacus is an excellent substitute for rote memorization of multiplication tables, a particularily detestable task for young children. The abacus is also an excellent tool for teaching other base numbering systems since it easily adapts itself to any base. The abacus, as a portable computing device, continued to evolve into the modern slide-rule, the last mechanical evolution of a portable calculating device before the electronic era brought about digital calculators.

In the Hewlett Packard HP scientific calculator made the slide-rule obsolete. A few decades later scientific calculators evolved into programmable calculators able to display graphs and images on bitmapped LCD screens. In the 21st century, portable counting devices rarely exist as separate entities. Instead they are simulated as Apps running on desktop computers, smartphones and tablets. Civilization, which began recording history with a stylus and a clay tablet thousands of years ago is re-using those original terms today.

The tablet is made of marble x57x5cm and was used by the Babylonians circa B. Photo from the National Museum of Epigraphy, Athens. See endnote for link to video on using a counting board. The Roman hand-abacus was the first portable counting board. It is thought that early Christians brought it to the East. The tally system revolves around scratches on sticks, rocks or bones. The number of scratches represents the number of items counted — five birds would be represented by five scratches, seven mammoths would be represented by seven scratches etc.

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