A Study of Semiotic Registers in the Development of the Definite Integral of Functions of Two and Three Variables

An Operational Approach to Conceptual Understanding Using Semiotic Theory

“…While Duval [1] emphasizes on the need to harness various registers of representation when understanding mathematical concepts, others [2][3][4][5][6] studied the nature of how registers of representation are used. The initial introduction to a mathematical concept most often begins with an established order of representations associated with the concept known as a semiotic chain [2,6].…”

“…The initial introduction to a mathematical concept most often begins with an established order of representations associated with the concept known as a semiotic chain [2,6]. For example, when presenting a line, a presentation might begin with the formula y = 2x + 3 (symbolic register), proceed to a table of values associated with the formula (numeric register) and conclude with a graph of a line with slope two and intercept 3 (geometric register).…”

“…For example, when presenting a line, a presentation might begin with the formula y = 2x + 3 (symbolic register), proceed to a table of values associated with the formula (numeric register) and conclude with a graph of a line with slope two and intercept 3 (geometric register). McGee and Martinez-Planell [2] found that as a concept is beter understood, students would progress toward simultaneous awareness of the concept's representations which would be associated with the ability to perform treatments and conversions that are not in the initial semiotic chain. An example of this evolution is shown in Figures 1 and 2.…”

“…Based on Duval's assertion that the understanding of mathematical concepts can only be achieved through simultaneous awareness of associated representations, McGee and colleagues [2,3] implied, without an explicit presentation, that an operational framework might become accessible by associating the comprehension of a mathematical object with the ability to luidly move between its associated registers of representations. It was found [2,3] that promoting the ability to move luidly across three registers of representation throughout topics of integration and diferentiation signiicantly improved students' problem-solving abilities.…”

“…It was found [2,3] that promoting the ability to move luidly across three registers of representation throughout topics of integration and diferentiation signiicantly improved students' problem-solving abilities. McGee and MooreRusso [4] also found that a similar multi-representational perspective on conceptual understanding appears to positively impact teaching and learning with preservice teachers as well.…”