In the last 25 years Physics Education Research has identified a number of fundamental ideas and concepts which beginning students have particular difficulty with, and found methods of instruction that are more effective than traditional pedagogy in helping students to understand the material. Here we discuss two of these ideas and concepts by two case studies. Case study 1 regards Newton’s 1st Law of motion, and case study 2 is about the uncertainty of physical measurements. The analysis is from the perspective of threshold concepts, troublesome knowledge, and liminality. For each case study we discuss the research-based pedagogy used in teaching the material. We then add another perspective on these issues from Piagetian taxonomy. We then discuss the results of interviews with students about concepts that they struggled with, and ways that they found helped them go through the threshold to gain a deeper understanding of those difficult ideas.
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