The ability of the civil engineering students to represent partial derivative symbols as metonymy and metaphor

Symbolic representation is a form of one's ideas interpretation to ease the problem-solving. The representation of symbols is an important thing in mathematical learning because it reflects the definition of a concept. Symbolic representation involves metonymy as the symbol scheme and metaphor as the denotation of the symbol. Metonymy and metaphor are related to each other and are involved in a symbolization system to discover new symbols in mathematics. The Civil Engineering students have to deal with a number of new symbols in Calculus II, such as the symbol of a function of two or more variables and its derivative. This symbol, needless to say, is nothing like the symbol of a function of one variable and its derivative which the students had learned in Calculus I offered in the previous semester. This study aimed to describe the ability of the Civil Engineering students to represent symbols as metonymy and metaphor through partial derivative problem-solving. This study was designed as a case study to detect the difficulties faced by the students in solving partial derivative problems. The students were provided with a worksheet containing partial derivative problems which focused on symbolic representation as metonymy and metaphor. The students' answers were analyzed based on how they denoted the partial derivative, both from the notation and the definition of the notation. Interview and observation were conducted to support worksheet findings. The results showed that the students had a poor ability in representing the partial derivative symbol of f with respect to x and y. The students' analogy was that the derivative symbol can be expressed with the d and prime notations such as in the derivative of functions of one variable. Therefore, this symbol was used in the partial derivative. The students were able to provide a correct solution to the partial derivative problems, but less careful in determining the partial derivative symbol. The error in using the partial derivative symbol was not noticed by the students because they focused more on the problem-solving procedure rather than the symbolization.