Abstract
This study investigates college students’ understanding of arithmetic fraction operations as defined by the Common Core State Standards in grades three through six Mathematics. This study is meant to extend upon an extensive body of research regarding elementary and middle grades students’ understanding of fraction operations and see if recognized erroneous thinking among younger students persist among college students. Among these misconceptions include: fraction equivalence, common denominators, the algorithm and the concept of division, whole number bias, and incorrectly applying fraction operations. The results of this study suggest that college students have the same misunderstandings and misconceptions as elementary students in regards to fraction operations.
Highlights
A plethora of research over the decades has reported that elementary school students struggle with skills and concepts regarding fractions and fraction arithmetic
Often missing is detailing the precise nature of the mathematical errors, misconceptions, and misunderstandings discoverable only through painstaking analysis of student work and communication regarding fractions and fraction operations
Under the Common Core Standards for Mathematics, elementary students begin working with fractions as early as the third grade (Common Core Standards Initiative (CCSSI, 2010))
Summary
A plethora of research over the decades has reported that elementary school students struggle with skills and concepts regarding fractions and fraction arithmetic. Often missing is detailing the precise nature of the mathematical errors, misconceptions, and misunderstandings discoverable only through painstaking analysis of student work and communication regarding fractions and fraction operations. To consider college students misunderstandings and misconceptions regarding fractions and fraction operations, a number of dimensions were researched including: the Common Core Standards for Mathematics; procedural versus conceptual understanding of fractions; why students have difficulties with fractions; areas of fraction misunderstandings; and effects of not understanding fractions. Students learn to add or subtract fractions with like denominators and solve word problems using this skill, to multiply a fraction by a whole number, and to compare decimal fractions
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