This study describes the process of defining a hypothetical learning progression (LP) for astronomy around the big idea of Solar System formation. At the most sophisticated level, students can explain how the formation process led to the current Solar System by considering how the planets formed from the collapse of a rotating cloud of gas and dust. Development of this LP was conducted in 2 phases. First, we interviewed middle school, high school, and college students (N = 44), asking them to describe properties of the current Solar System and to explain how the Solar System was formed. Second, we interviewed 6th-grade students (N = 24) before and after a 15-week astronomy curriculum designed around the big idea. Our analysis provides evidence for potential levels of sophistication within the hypothetical LP, while also revealing common alternative conceptions or areas of limited understanding that could form barriers to progress if not addressed by instruction. For example, many students' understanding of Solar System phenomena was limited by either alternative ideas about gravity or limited application of momentum in their explanations. Few students approached a scientific-level explanation, but their responses revealed possible stepping stones that could be built upon with appropriate instruction.
We previously proposed a hypothetical learning progression around the disciplinary core idea of the Solar System and its formation as a first step in a research program to begin to fill this gap and address questions of student learning in this domain. In this study, we evaluate the effectiveness of two dimensions within the learning progression, dynamical properties and gravity, in describing change in how student reason in the domain across the course of their 14‐week astronomy unit. A sample of sixth‐grade students (N = 24) were interviewed before and after instruction. We compared changes in how students explained the dynamic properties of planets and the role of gravity in the Solar System to their experiences during instruction. Our findings provide evidence for the usefulness of this learning progression in describing how students' explanations may progress, offer insight into how instruction may support that progress, and highlight the challenges in drawing conclusions on how students' explanations may progress when limitations are identified in instructional experiences. We also discuss the connection between these two construct maps but also point out what appears to be a missing element in our original definition of the learning progression: inertia.
Quantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science (QIS) and quantum computing (QC). The book is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and trigonometry. While broadly accessible, the book provides a solid conceptual and formal understanding of quantum states and entanglement—the key ingredients in quantum computing. The authors give detailed treatments of many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book provides a solid explanation of the physics of QC and QIS and then weds that knowledge to the mathematics of QC algorithms and how those algorithms deploy the principles of quantum physics to solve the problem. This book connects the physics concepts, the computer science vocabulary, and the mathematics, providing a complete picture of how QIS and QC work. The authors give multiple representations of the concept—textual, graphical, and symbolic (state vectors, matrices, and Dirac notation)—which are the lingua franca of QIS and QC. Those multiple representations allow the readers to develop a broader and deeper understanding of the fundamental concepts and their applications. In addition, the book provides examples of recent experimental demonstrations of quantum teleportation and the applications of quantum computational chemistry. The last chapter connects to the growing commercial world of QC and QIS and provides recommendations for further study.
Quantum state entanglement is a crucial ingredient in many quantum algorithms. This chapter introduces the description of multi-qubit quantum systems and then explains what it means to say the state of that system is entangled. If the quantum state of the system is an entangled state, none of the constituents of the system are described by their own individual states. For a two-qubit entangled state, measurements of one of the qubits apparently affect the measurement results of the other even though the two qubits may be far apart. The change in basis states, introduced in Chapter 8, is applied to a two-qubit system, which will be used to illustrate Bell’s theorem. That theorem tells us that the quantum description of the world profoundly violates almost every concept we have about material properties and the measurement of those properties.
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