In the calculus, students can integrate functions that require procedures or algorithmic rules, but they grapple with contextual problems involving real-life motion of physical bodies. When undergraduate students learn the application of integration, they are expected to comprehend the concept of integration, make connections between particular constructs within integration and identify the coherence of these connections to kinematics. This study used the Triad theory to determine undergraduate students’ construction of connections and the underlying structures of these relationships as they learn calculus of motion. The research question was “To what extent do undergraduate students develop the knowledge of kinematics using the Triad theory?” This study was qualitative which involved a case study of 194 secondary mathematics students registered for a Bachelor of Education degree at a university in South Africa. Data was collected through an individual written test by all the students and semi-structured interviews with ten students. The ten students were selected purposively and the interview questions were meant to clarify some of the responses raised in test. The content analysis of the written responses was done to reveal the stages of students’ concept development of kinematics according to the Triad. The findings revealed that students had significant challenges in performing second and third level integration. These involve substituting the initial conditions at least once to find the constant of integration. Furthermore, students’ coherence of the connection among displacement, velocity and acceleration was weak, coupled by their failure to consider the point when the object was momentarily at rest.

Authors:
Benjamin Tatira, Walter Sisulu University, South Africa

About the Presenter(s)
Dr B TATIRA is a Senior Lecturer of mathematics education at Walter Sisulu University in South Africa. I am currently involved in pre-service teachers' development of mathematics knowledge for teaching using the APOS theory.

See this presentation on the full schedule – Thursday Schedule

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