Decades of education research have shown that students can simultaneously possess alternate knowledge frameworks and that the development and use of such knowledge are context dependent. As a result of extensive qualitative research, standardized multiple-choice tests such as Force Concept Inventory and ForceMotion Concept Evaluation tests provide instructors tools to probe their students' conceptual knowledge of physics. However, many existing quantitative analysis methods often focus on a binary question of whether a student answers a question correctly or not. This greatly limits the capacity of using the standardized multiplechoice tests in assessing students' alternative knowledge. In addition, the context dependence issue, which suggests that a student may apply the correct knowledge in some situations and revert to use alternative types of knowledge in others, is often treated as random noise in current analyses. In this paper, we present a model analysis, which applies qualitative research to establish a quantitative representation framework. With this method, students' alternative knowledge and the probabilities for students to use such knowledge in a range of equivalent contexts can be quantitatively assessed. This provides a way to analyze research-based multiple choice questions, which can generate much richer information than what is available from score-based analysis.

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Since its introduction, the normalized gain or the g-factor has been widely used in assessing students’ performance in pre- and post-tests. The average g-factor can be calculated using either the average scores of the class or individual student’s scores. In general, these two calculations produce different results. The nature of these two results is explored for several idealized situations. The results suggest that we may be able to utilize the difference between the two results to extract information on how the population may have changed as a result of instruction.

In problem-solving situations, the contextual features of problems affect student reasoning. Using Newton's Third Law as an example, we study the detail of the involvement of contexts in students' uses of alternative conceptual models. Through research, we identified four contextual features that are frequently used by students in their reasoning. Using these results, a multiple-choice survey was developed to probe, in large classes, the effects of the specific contextual features on student reasoning. Measurements with this instrument show that the different contextual features can affect students' conceptual learning in different ways. We compare student data from different populations and instructions and discuss the implications.

Education goals have evolved to emphasize student acquisition of the knowledge and attributes necessary to successfully contribute to the workforce and global economy of the twenty-first Century. The new education standards emphasize higher end skills including reasoning, creativity, and open problem solving. Although there is substantial research evidence and consensus around identifying essential twenty-first Century skills, there is a lack of research that focuses on how the related subskills interact and develop over time. This paper provides a brief review of physics education research as a means for providing a context towards future work in promoting deep learning and fostering abilities in high-end reasoning. Through a synthesis of the literature around twenty-first Century skills and physics education, a set of concretely defined education and research goals are suggested for future research, along with how these may impact the next generation physics courses and how physics should be taught in the future.