Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

Drawing upon phenomenological and arts-based approaches, the author explores everyday encounters with landscapes that call attention to the potential of place as sites for evoking mindfulness and transformative learning experiences. Theoretical perspectives within and across art education, aesthetics, contemplative education, holistic education,…

Collapsing categories is a commonly used data reduction technique; however, to date there do not exist principled methods to determine whether collapsing categories is appropriate in practice. With ordinal responses under the partial credit model, when collapsing categories, the true model for the collapsed data is no longer a partial credit…

The aim of this study was to create a model which describes the main elements for improving schools with digital technology and helps to reveal differences between schools and identify their best practices and challenges. The innovative digital school model (IDI school) offers a framework for research but also a research-based model for schools to…

Educational leadership is facing a need for change; this change requires innovative approaches such as Universal Design for Learning (UDL) to transform teacher practice. Principled modelling by these leaders is integral to sustained change. In addition, to initiate this change, traditional practices such as group work can be used with a UDL focus…

Technology Education was introduced and rolled out in South African schools in 1998. It has been twenty years since its implementation, yet it is being confused with other traditional subjects. Therefore, even though it is expected that Technology Education should be known for what it is exactly, it is still misunderstood, misconceived and…

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered…

Within caring science, the concept of caring leadership is well established. The aim of this study is to introduce Bondas's theory of caritative leadership into education. The theory of caritative leadership is a theory of caring leadership with the 'caritas' thought of human love and mercy at its core. The article considers a hypothetical testing…

The authors argue that nonfiction reading and writing instruction in K-12 settings must include authentic opportunities for students to seek information online. To that end, the authors provide two frameworks for thinking about information acquisition in the 21st century. The first, the intentional and incidental information continuum, describes…

Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a…

The community of inquiry (COI) model identifies elements which are fundamental to a successful online learning experience, namely, teaching presence, cognitive presence, and social presence. The model has received empirical support as a useful framework for understanding the online learning experience. A limitation of the model is its…

We offer a brief history of the study of excellence in college and university teaching. We review major examinations of teaching excellence and summarize key characteristics of model teachers.

Attribute structure is an explicit way of presenting the relationship between attributes in diagnostic measurement. The specification of attribute structures directly affects the classification accuracy resulted from psychometric modeling. This study provides a conceptual framework for understanding misspecifications of attribute structures. Under…

An important aspect of qualitative research is reaching saturation--loosely, a point at which observing more data will not lead to discovery of more information related to the research questions. However, there has been no validated means of objectively establishing saturation. This article proposes a novel quantitative approach to measuring…