Difficulties with Fractions

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Historical Difficulties with Fractions

Historically, fractions have been a difficult idea to mathematize. Greeks only accepted Natural numbers as genuine numbers. They never accepted fractions as numbers.

They were not accepted as numbers, by even mathematicians, until recently.

Initially they were used only in the form of &ldquo;thirds&rdquo; or &ldquo;fourths&rdquo; or &ldquo;fifths&rdquo;. They were represented by the whole number (3 for thirds, 4 for fourths etc) with a dot or a circle on top. Today we would call them as Unit fractions where the numerator is always 1.

Slowly several different ways of representing fractions were evolved. The current representation of fractions using 2 numbers (now called Numerator &amp; Denominator) evolved from an 8thcentury Hindu representation and accepted internationally in the 18thcentury. The Arabs introduced the horizontal line which separates the numerator and the denominator.

Computing with them was always difficult.

Current Difficulties With Fractions

Mathematicians took several centuries to understand, represent and compute with fractions. Today we expect children in grades 3 upwards to do this in a few periods. No wonder fractions are considered difficult all over the world.

Introducing fractions in the form of &frac12; &amp; 2/3 presents several difficulties to children. Both the notation (using a bar separating the numerator &amp; the denominator) and the interpretation are very conceptual &amp; difficult for children. The interpretation of the two numbers in a fraction as a code is conceptually like the interpretation of the two numbers with the place value idea, in a 2 digit number. We will deal with this aspect in the next chapter.

Hence children need to be introduced to the idea of fractions through a lot of real-life activities with daily use materials and visual images. Representing fractions using numbers should be done only after they have understood fractions through activities.

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