Many students find it difficult to apply certain physics concepts to their daily lives. This is especially true when they perceive a principle taught in physics class as being in conflict with their experience. An important instance of this occurs when students are instructed to ignore the effect of air resistance when solving kinematics problems. To a student, this assumption disconnects from their everyday experience. Mathematically, ignoring the effect of air resistance is crucial, however, since it renders such problems tractable. However, this step is rarely, if ever, provided with justification in undergraduate texts, leading students to believe that what they are taught does not apply to their everyday experience. Taking the additional step of clarifying when it is reasonable to ignore air resistance makes students' reconciliation of their everyday experiences with the physics principle of free fall more likely. In this paper we develop a graphical tool intended to make this step as simple and effective as possible. We do this by summarising the results of a set of numerical simulations of various balls falling under the effects of both gravity and air resistance by means of a carefully chosen graph: a plot of an object's cross-sectional surface are versus its mass. We further use our numerical results to evaluate how these two variables relate to the effects of air resistance for balls dropped from varying heights.
The sequence of representations used to introduce new knowledge and the context in which this is done is critical to both effectively build on prior knowledge and establish conceptual coherence in physics. Ongoing reports indicate that current teaching activities fail address student difficulties to obtain conceptual understanding and-coherence between relevant physics representations and concepts. There is a need for fine-grained topic specific multiple representational teaching activities to enhance coherence in physics knowledge. In this paper we present a teaching activity for undergraduate physics, built on using motion diagrams to specifically relate the concepts and representations in kinematics, in particular for the concept of free fall. The teaching activity follows a conceptual qualitative approach to teaching kinematics concepts and is informed by the results of a broader Design Based Research study. In the teaching activity the concept of acceleration is introduced qualitatively as the net force to mass ratio followed by drawing motion diagrams to visualize the motion of the objects in free fall. The motion diagrams are implemented to support conceptual qualitative interpretation of mathematical representations such as graphs and equations, to enhance transfer of knowledge between representations and coherence between relevant concepts and representations. The contribution of this research lies in presenting an argument for a conceptual qualitative approach to teaching introductory mechanics and introducing a teaching activity based on the value offered of including motion diagrams in the teaching activity to enhance coherence between physics representations and between physics concepts.
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