The Elusive Slope

Abstract

In understanding upper secondary school students' interpretations of information in graphical representations of a distance-time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of interpretations of information in graphical representations of different situations. This paper integrates results from 2 studies and 3 theoretical perspectives: Tall and Vinner's theoretical perspectives on learning, Chi's ontological perspectives on conceptual development and Friel's theoretical perspectives on interpretation of graphical information. The findings provide evidence to support the conjecture that iconic interpretations could be stimulated and generated as a result of student categorisation of a distance-time graph as an event, when in fact the graph is being used to describe and communicate a process. The outcome further indicates that students found a resemblance between the ECG diagram and the periodic function of f(x) = sin(x).

Investigation of Learning Behaviors and Achievement of Simple Pendulum for Vocational High School Students with Ubiquitous-Physics App

“…The results demonstrated that interpreting graphs had an important role in physics learning as well as conceptual understanding. It is consistent with the results of studies (Lingefjärd & Farahani, 2017;Purba & Hwang, 2017a, 2017b which showed interpreting graphs could help improve better conceptual understanding. The knowledge of interpreting graphs can be very helpful in physics experiment and become an important step towards expertise in problem-solving (Beichner, 1994;Larkin & Reif, 1979;Supalo et al, 2016;Zebehazy & Wilton, 2014).…”

“…Students can extract most of their information content using graphs (Beichner, 1994). Besides, interpreting graphs can help improve better conceptual understanding (Lingefjärd & Farahani, 2017). However, information or content of knowledge is not often expressed using graph representations and pictures in mathematics, engineering and also science (Zebehazy & Wilton, 2014).…”

Motion, Velocity and Graphical Representations in GeoGebra

“…Students' alternative iconic interpretations of graphical representations are well known from research [2][3][4][5]. When students are asked to model a velocity-time graph, it often seems as if they are affected by the look of the distance-time graph.…”

Moving towards understanding: Reasoning about graphs in primary mathematics education

“…To validate our categorization into iconic reasoning, single, and multiple variable reasoning, we compared this process to the categories used in several other Provided at the end of studies on graphical reasoning. For example, Lingefjärd and Farahani (2017) identified three categories: (1) intuitive and iconic interpretations, (2) scientifically grounded interpretations and (3) a combination with influences from both 1 and 2. Similarly, Johnson et al (2019) included an iconic category and three other categories: motion of objects, individual quantities, and relationship between quantities.…”