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Mental Math

The ability to calculate mentally with efficiency is a very important skill for all students, but especially for visually impaired and blind students. Using the braillewriter, and the abacus can be very labor intensive and time consuming, and calculators have their own limitations (see the discussion on calculators). The more efficiently students can estimate, calculate, and check the reasonableness of answers using mental math techniques, the more facile they will be at using numbers, in both schoolwork and independent living skills. These strategies should be taught to students as soon as they begin to count and work with simple numbers.

In order to manipulate numbers and calculate mentally, students must understand the concept of “complements” or “partners” of numbers. For example, in addition and subtraction, the student needs to know that the number 5 is made up of addends of 2 and 3, or 1 and 4 (complements, partners). Likewise, the number 12 is made up of 3 and 9, or 6 and 6, or 10 and 2. In multiplication and division, the student must know that the number 24 is made up of factors of 2 and 12, or 6 and 4, or 8 and 3.

Teaching approaches

While there are many individual techniques for estimating and calculating mentally, most strategies involve one of the following four basic approaches:

  1. decomposing numbers — breaking apart numbers into meaningful and useful units or groups that can be easily recomposed
  2. making easier numbers to work with — putting numbers together that are easier to use, often by changing the order of numbers
  3. substituting numbers — replacing values with equal values that are easier to manipulate
  4. compensating — rearranging numbers so they are easier to work with, either by changing a number and then adjusting the answer, or by adjusting both numbers so there is no need to change the answers

Strategies for developing mental math skills

Following are several examples of strategies which may help students develop skills in counting and using the basic operations.

Addition

Subtraction

Multiplication

Division

Counting and general ideas

A thorough search of the literature will reveal several books which provide numerous additional ideas for developing mental math skills at different grade levels.

References

Petreshene, S. S. (1985). Mind joggers! 5 to 15 minute activities that make kids think. West Nyack, NY: The Center for Applied Research in Education, Inc.