Tips for Understaning fractions

Fractions are a difficult concept for many students to grasp. Students often see fractions as an abstract concept that is nonsensical if the students do not receive proper instruction on understanding the meaning of fractions.

            Partitioning and iteration fractions are tools to aid understanding of the meaning of fractions and aids operating on fractions.  Partitioning according to the article “consists of creating smaller, equal-sized amounts from a larger amount” (Siebert, Gaskin).  This means one takes a whole or larger amount and cuts/partitions that amount into equal sized pieces from that one amount. Iterating consists of “making copies of a smaller amount and combine them to create a larger amount” (Siebert, Gaskin).  This means that one takes a smaller amount and makes exacts copies of that amount to create a larger amount. For example, one makes four copies of ¼ to make a whole. Partitioning and iterating can be used with any fraction even if the numerator of the fraction is more than one. Both partitioning and iterating is needed when working with fractions since “without partitioning, the creation of smaller, equal-sized larger pieces is difficult; without iteration, the creation of larger pieces from smaller ones is difficult” (Siebert, Gaskin).    

            Partitioning and iterating can be a useful tool for understanding operations with fractions, such as multiplication. When one multiplies fractions he or she needs to be aware that “multiplication requires finding the total amount of ones that are in a certain number of groups of a certain size” (Siebert, Gaskin). Partitioning is needed to split the fraction into equal pieces of the group that is being multiplied by and then finding the ones. Iterating can be used to justify the answer.

            For students to be able to understand fractions they need to see that the numerator and the denominator are not whole numbers.  A commonly used term when teaching fractions is “out of”.  This term is confusing and creates an image where the numerator and the denominator are just whole numbers. Also the term “out of” does not indicate the relationship of the parts to the whole, this is why educators should not use the “out of” term when teaching fractions. Terms like “cut evenly”, “separate into equal parts”, and “making copies” should be used instead to indicate partitioning and iterating.

            Fractions can be a confusing concept for many students, but with the appropriate language use and the proper images of fractions students will be able to have a greater understanding of fractions. The use of partitioning and iterating can give students the proper image of fractions and help students to multiply, add, subtract, and divide fractions since it is giving students an image that does not depend on whole numbers.