Understanding fractions is one of the most important skills that need to be developed in the mathematics curriculum. It is essential for understanding algebra and geometry and other aspects of mathematics. Yet, fractions have proven to be very difficult to understand for most students around the world. For example, on a national test, only 50% of American 8th graders correctly ordered three fractions from smallest to largest (National Council of Teachers of Mathematics, 2007). Even in countries where the majority of students do achieve reasonably good conceptual understanding, such as Japan and China, fractions are considered a difficult topic.
One reason for their difficulty is that fractions offer students their first lesson that many properties that are true of whole numbers are not true for all numbers. For example, with fractions, multiplication does not always lead to an answer larger than the multiplicands, division does not always lead to an answer smaller than the dividend, and numbers do not have unique successors. Overcoming the belief that properties that are true for whole numbers are true for all numbers is a major challenge, even in high-school many students do not understand that there are an infinite number of numbers between any two fractions (Vamvakoussi & Vosniadou, 2010). Yet, understanding fractions is essential for learning algebra, geometry and other aspects of higher mathematics.
This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on scientific research, along with the expertise and experience of successful mathematics educators, and include a variety of classroom activities and teaching strategies focused on improving students’ conceptual understanding of fractions.
