User:Phlsph7/Arithmetic - Tools and methods

By tools and methods

Calculations in mental arithmetic are done exclusively in the mind without relying on external aids.

Another distinction focuses on the tools and methods used to perform arithmetic operations. For mental arithmetic, the calculations are performed exclusively in the mind without external tools like pen and paper or electronic calculators. Instead, mental arithmetic makes use of visualization, memorization, and certain calculation techniques to solve arithmetic problems. One such technique is the compensation method. It consists in altering the numbers to make the calculation easier and then adjusting the result afterward. For example, instead of calculating $85-47$, one calculates $85-50$ which is easier because it uses a round number. In the next step, one adds $3$ to the result to compensate for the earlier adjustment. Mental arithmetic is often taught in primary education to train the numerical abilities of the students.

Finger counting uses fingers as an external tool to represent numbers. It is often introduced to young children to teach them numbers and simple calculations. In its most basic form, the number of extended fingers corresponds to the represented quantity. This system is limited small numbers and more advanced systems employ different approaches to represent larger quantities as well.

Tally marks are a closely related system that relies on strokes drawn on a board or paper or notches in a wooden stick to keep track of quantities. Some forms of tally marks arrange the strokes in groups of five to make them easier to read.

The abacus is a more advanced tool to represent numbers and perform calculations. An abacus usually consists of a series rods, each holding several beads. The beads represent quantities and a quantity is counted if the bead is moved from one side of the rod to the other, which is also how calculations are executed.

finger counting, tally marks / counting by tokens, positional counting boards / counting rods / bead abacuses, positional written arithmetic, mechanical calculators, electronic calculators (mentioning binary), mental arithmetic

• Dowker, Ann (27 March 2019). Individual Differences in Arithmetic: Implications for Psychology, Neuroscience and Education. Routledge. ISBN 978-1-317-62743-2.