We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

The vagaries of market forces are presenting a financially challenging environment for the higher education sector in England. Intense competition is leaving those overly dependent on tuition fee income in an exposed position. Despite a strong narrative for the need to diversify funding in the available higher education literature, empirical…

Contrary to its typical presentation in scientific publications as a certain and linear process, in reality, the experimental method, not least the design aspect of it, requires a great deal of trial-and-error and ad hoc decision-making on the part of the researchers. This uncertain and contingent aspect of research, although little known outside…

The Programme for the International Assessment of Adult Competencies (PIAAC) assesses key skills in literacy, numeracy and problem-solving in technology-rich environments, as well as their relationship to other social outcomes for adults. PIAAC's developers claimed to better account for adults' literacy practices than earlier international studies…

Standard setting is arguably one of the most subjective techniques in test development and psychometrics. The decisions when scores are compared to standards, however, are arguably the most consequential outcomes of testing. Providing licensure to practice in a profession has high stake consequences for the public. Denying graduation or forcing…

A common belief is that the Bookmark method is a cognitively simpler standard-setting method than the modified Angoff method. However, a limited amount of research has investigated panelist's ability to perform well the Bookmark method, and whether some of the challenges panelists face with the Angoff method may also be present in the Bookmark…

In this digital ITEMS module, Dr. Jacqueline Leighton and Dr. Blair Lehman review differences between think-aloud interviews to measure problem-solving processes and cognitive labs to measure comprehension processes. Learners are introduced to historical, theoretical, and procedural differences between these methods and how to use and analyze…

Factorial surveys use a population of vignettes to elicit respondents' attitudes or beliefs about different hypothetical scenarios. However, the vignette population is frequently too large to be assessed by each respondent. Experimental designs such as randomized block confounded factorial (RBCF) designs, D-optimal designs, or random sampling…

High attrition and dropout rates are common in introductory programming courses. One of the reasons students drop out is loss of motivation due to the lack of feedback and proper assessment of their progress. Hence, a process-oriented approach is needed in assessing programming progress, which entails examining and measuring students' compilation…

Rapid automatized naming (RAN) is associated with children's arithmetic performance, which is multifactorial by nature and consists of arithmetic fluency, arithmetic procedure, and word problems. Yet, it is unclear whether RAN can predict all key aspects of arithmetic skills independently and what cognitive mechanisms may explain this relation.…

Standard models for network meta-analysis simultaneously estimate multiple relative treatment effects. In practice, after estimation, these multiple estimates usually pass through a formal or informal selection procedure, eg, when researchers draw conclusions about the effects of the best performing treatment in the network. In this paper, we…

Through reflection, learning experiences that students most-frequently valued during open-ended, scaffolded problem solving in a bioengineering two-course sequence were identified in this study. Reflective knowledge of this type can inform instructors in orchestrating experiences to scaffold problem solving of this kind and were useful in directly…

In the age of litigation, teachers have a responsibility to protect students in their care from injury, to act as a reasonably prudent teacher would act to prevent loss or damage to their students, and to exercise sound judgement and authority over students, to correct misbehavior and to provide for their orderly instruction. Whenever a teacher is…

This chapter describes an evolving narrative inquiry into the use of formative sustainability assessments in teacher education for elementary and secondary level education. Framed within a postmodern approach to education, we describe the efficacy of using experiential, performative, discursive, graphic, and reflective assessments to bolster…