A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

In this article, Mark Colyvan argues that formal mathematical notation is more than just the language of mathematics. He gives examples of where notation plays a role in extending mathematical theory and in delivering explanations. He concludes that good mathematical notation, in both mathematics and empirical domains, helps us to think,…

An overview of the evolution of career information in light of the changing nature of the world of work is presented. Owing to the constant fundamental changes in the labour market, the distribution of paid work has been also constantly changing. In this article, a more dynamic and -- often temporary -- interplay between citizens and their…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Validity, reliability, and fairness are three prominent indicators for evaluating the quality of assessment processes. Each of the indicators is most often written about and applied in the context of large-scale assessment. As a result, the technical properties of these indicators make them limited in both their practicality and relevance for…

In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict…

Selecting courses in an open-curriculum education program is a difficult task for students and academic advisors. Course recommendation systems nowadays can be used to reduce the complexity of this task. To control the recommendation error, we argue that course recommendations need to be provided together with "statistical" confidence.…

Grades serve as one of the primary indicators of student learning, directing subsequent actions for students, instructors, and administrators, alike. Therefore, grade validity--that is, the extent to which grades communicate a meaningful and credible representation of what they purport to measure--is of utmost importance. However, a grade cannot…

For many years, scholars have investigated instructional design expertise and described the difficulty defining it. A lack of a clear definition, inclusive of primary components, poses a measurement problem for those seeking to evaluate the development of expertise. An overarching aim of this study is to gather evidence to support a definition of…

To explore the psychometric properties of the Greek version of the World Health Organization Disability Assessment Schedule (WHODAS 2.0-12 item) in adult patients suffering from motor disabilities. The questionnaire of WHODAS 2.0-12 item was officially translated and cross-culturally adapted into Greek (WHODAS 2.0-12Gr). 136 adult patients with…

Learning progressions (LPs) are "descriptions of the successively more sophisticated ways of thinking about a topic that can follow one another as children learn about and investigate a topic over a broad span of time" (National Research Council, 2007). One challenge that arises in LP research is the collection of evidence to ensure that…

A tension raised in recent scholarship is that between numeracy as a social practice and numeracy as a functional skill set. Such frameworks for conceptualizing numeracy pose a challenge to assessment because what individuals do with numeracy is not the same as what individuals can do (or express) in an assessment setting. This study builds on…

We develop the Trait Sources of Spirituality Scale (TSSS), which assesses experiences of closeness to the sacred, within and outside a religious tradition. After using factor analysis to finalize the scale, we examine evidence of construct validity, including latent profile analysis that reveals 5 patterns of how spirituality is experienced.

The development and deployment of STEM education in every continent and country are different. An instrument to access the current situation of the application, knowledge, as well as attitude towards STEM education, is necessary. This research aimed to design and develop a valid instrument that can be used to assure the quantitative degree of…

Considerable past classroom learning environment research has focused on the primary and secondary levels of education and the subject areas of science and mathematics. The current study is distinctive in its focus on university business statistics learning environments. For the first time, we validated and applied the widely-used What Is…