What Research Can Tell Us About the Understanding of Algebra

Abstract

Algebra is a very important component of mathematics. For students, an adequate understanding of algebra serves as a foundation for the math to come. Concurrently, algebra is also a subject where many students struggle and form mathematical misconceptions. In order to take proactive steps in being able to more effectively teach students algebra, it is first important to identify the processes involved in understanding algebra. This paper discusses the different methods of thinking used when learning algebra as well as common misunderstandings formed by teachers and students. To obtain a better understanding of students' processes when solving algebra tasks, five students were each given four math tasks to complete individually. These tasks all involved sketching the curve of a graph given the context of a situation. After analyzing the students' responses it became clear that there are specific types of thinking that the students were misusing during the completion of the tasks. From this information, one can have a better understanding of student processes and be able to better adapt instruction to meet students' needs.