Why are Fractions So Hard? Conquering Students Lack of Comprehension of Fractions

Date of Completion


Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Nina Greenwald


Fractions have multiple roles in math: as a ratio of part to whole, as a measurement unit, and as an operator on other numbers. These roles, which have not been taught explicitly to students, have resulted in miscomprehension of fractions. Four seventh grade, from Roxbury Preparatory Charter School, were assessed by the author for their competencies in fraction understanding. This was determined through analysis of teacher created and standardized tests as well as personal interviews with each of the students. It was discovered that, while these students were able to follow the rules of fraction computation quite well, pervasive deficits were noted in their ability to apply fractions to problem solving situations. These deficits include: inability to choose a correct operation(s) to solve a problem; inappropriate comparing and ordering of fractions; and lack of understanding of the rules used in the fraction algorithms of addition, subtraction, multiplication, and division. This is ascribed to the incomplete understanding of the roles a fraction can play and how fractions interact with other numbers in various contexts. This synthesis presents a comprehensive set of standards and objectives the author has developed as a result of assessing students’ difficulties with fractions. Standards were developed to address student miscomprehension, based on student data, analysis of literature, state frameworks, and goals set forth in the prior year’s fraction unit. These standards will be taught through experiential learning, algorithmic understanding, application of fractions in word problems, and explanation of process and reasoning. Teaching colleagues of the author contributed to the creation of this plan by providing feedback on interview questions used with the four students and the standards developed through this synthesis. A result of this project is that other math teachers in the author’s school will be trained in the teaching of fractions to counteract student misconceptions. Teachers will also support fraction understanding in their own curricula, and future math curricula will integrate the basics of fraction understanding into the sixth grade math curriculum.


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