Quadratic functions and equations (QFE) are fundamental concepts in secondary school mathematics as well as essential in other fields such as Physics, Engineering, and Design mainly for its practicality in solving many word problems and for modelling real-life situations (Didis and Erbas, 2015). Although the role of multiple representations of concepts in learning mathematics has received a lot of attention in recent decades, there has been limited research on how and in what ways topic-specific multiple representations of mathematics concepts support understanding and learning. This qualitative study investigated Grade 10 students’ understanding of QFE and their different representations through a two-part task and a walk-through method that allowed the participants to verbally express what they were seeing, doing, or thinking as they worked on the tasks. The findings of this small study confirmed that both instrumental and relational understanding are important for success in mathematics education, as pointed out in literature (Skemp, 1976; Sajka, 2003; Wagner and Parker, 2003). Moreover, the findings suggested that procedural knowledge with limited conceptual knowledge gets in the way of moving flexibly between representations of QF and solving QE effectively. The study also revealed that the connection students made between verbal expressions and algebraic expressions was stronger than the connections between table of values, area diagrams, and graphs. Finally, evidence showed that previously learned knowledge can present obstacles to a relational understanding of QFE.

Authors:
Jose Miguel Oracion, Ateneo de Manila University, Philippines

About the Presenter(s)
Mr. Jose Miguel C. Oracion is currently a faculty member of the Junior High School unit of the Ateneo de Manila University.

See this presentation on the full schedule – Thursday Schedule

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