The concept of variable is a center point in mathematics from elementary schools to college because understanding this concept provides a transition from arithmetic to algebra (Kuchemann, 1978; Philipp, 1992).While the goal of arithmetic which is to find numerical answers, the main focus of school algebra is to find general methods and rules and to use algebraic symbols and language in order to express these rules in a general form (Booth, 1988). In contrast to the importance of variables and their heavily usages in algebra, many of studies show that students are generally confused while passing from arithmetic to algebra in their learning processes due to the concept of variable having different meanings in different context (MacGregor & Stacey, 1997; Schoenfeld & Arcavi, 1988; Ursini &Trigueros, 2001).

In fact, there are some questions to be answered in order to overcome students’ difficulties and misconceptions concerning with the concept of variable: What is the origin of the notions of unknown and variable? How are these concepts developed? At this point, history of mathematics can provide a reasonable perspective to look at the concept in terms of teaching and learning of algebra in schools. After examining the context related to exchange of money in trading or inheritances in ancient civilization, I understood why people need to negative numbers, complex numbers, unknown, matrix or decimal fractions. As a result, it can be said mathematics is a human endeavor which has spanned over four thousand years (Katz, 2000; 2007). By blending historical and psychological perspectives, historical developments can be used as a tool in order to predict students’ behaviors because there is an analogy between historical and individual development (Sfard, 1991; 1995).

According to Sfard (1995), phylogenic and ontological approaches to mathematics reveal similarities between historical and individual construction of knowledge. In a similar way, Gallardo (2000) emphasizes the use of historical-critical analysis for learning and teaching of algebra because the corresponding notions of “epistemological obstacles” serve as central elements that link the domains of history and education. Furthermore, it provides a great opportunity to determine misconceptions of students. As a result, this methodology can be used for teacher training programs at universities. By this means, teacher will be more conscious about students’ behaviors whenever they confront a new concept which has different meaning from previous learning such as transition unknown to variable. Many of teachers are always complaining their students’ difficulties while teaching the concepts of “variable” and “unknown”. The historical analysis emphasizes that the notions of unknown and variable have a totally different origin and evolution. Even if both the concepts deal with numbers, their processes of conceptualizations seem to be entirely different (Radford, 2000). In other words, mathematics history constructs a bridge from the past to the future. From this perspective, the purpose of this article is to provide a theoretical framework about using history of mathematics in learning and teaching of the concept of variable.

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