Derivatives, integrals and vectors in introductory mechanics: the development of a multi-representation test for university students

The use of mathematical concepts and formal reasoning is one of the main hurdles for students entering introductory physics courses at university. The ability to apply mathematical tools in the context of physics also relies on the use of multiple representations, i.e., the different forms in which a concept can be expressed, such as words, graphs, numbers and formal language. Based on these considerations, we have developed a multiple-choice test consisting in 34 items aimed at investigating students\u2019 understanding of derivatives, integrals and vectors and their application in the context of introductory classical mechanics. The items were constructed using multiple representational formats and isomorphic items in mathematics, and in physics, in order to explore students\u2019 representational fluency and their ability to transfer knowledge and skills from mathematics to physics. The test has been administered to 1252 students enrolled in introductory courses at the University of Padova in Spring 2018. The results indicate that the test is a valid and reliable instrument and it provides interesting insight into students\u2019 difficulties in the use of mathematical concepts and methods in physics

Using Targeted Active-Learning Exercises and Diagnostic Question Clusters to Improve Students' Understanding of Carbon Cycling in Ecosystems

In this study, we used targeted active-learning activities to help students improve their ways of reasoning about carbon flow in ecosystems. The results of a validated ecology conceptual inventory (diagnostic question clusters [DQCs]) provided us with information about students' understanding of and reasoning about transformation of inorganic and organic carbon-containing compounds in biological systems. These results helped us identify specific active-learning exercises that would be responsive to students' existing knowledge. The effects of the active-learning interventions were then examined through analysis of students' pre- and postinstruction responses on the DQCs. The biology and non–biology majors participating in this study attended a range of institutions and the instructors varied in their use of active learning; one lecture-only comparison class was included. Changes in pre- to postinstruction scores on the DQCs showed that an instructor's teaching method had a highly significant effect on student reasoning following course instruction, especially for questions pertaining to cellular-level, carbon-transforming processes. We conclude that using targeted in-class activities had a beneficial effect on student learning regardless of major or class size, and argue that using diagnostic questions to identify effective learning activities is a valuable strategy for promoting learning, as gains from lecture-only classes were minimal