Bramlett and Drake (2013) suggest that the ability of teachers to teach proof is crucial for students to learn and develop formal and informal proofs. Teachers need to be involved in the process of proving and have a firm understanding of the critical role of proofs in order to effectively engage their students in proving activities. It is…

Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive…

When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)."…

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

Mobile commerce has provided extended business opportunities for online organisations and made it easier for customers to purchase products on-line from anywhere at any time. However, there are several risks associated with it, especially the identity theft. Online organisations commonly use electronic commerce approaches; however, these have some…

What are the challenges faced by a mid-south liberal arts college teacher education program, in its attempt to successfully meet the new Council for the Accreditation of Educator Preparation (CAEP) accreditation requirements? The Investigator studied the Educator Program Provider (EPP) during academic year 2015-2016. The challenges faced by the…

This study aims at putting forth the reasons preventing teachers from acting ethically, acting within the framework of ethical principles and having an ethical tendency. This study featuring a qualitative research model taking as a basis the case study approach followed a path of selecting people that can be a rich source of information for…

Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper…

The development of the creative potential of individuals is considered to be one of the requirements of modern education. As in all areas, the development of students' creative potential is also among the objectives of education programs in music education. The ability of music teachers to achieve this objective and create creative learning…

As lines between research paradigms continue to blur with the ever-increasing popularity of mixed methods research, there are useful, and occasionally oxymoronic, opportunities for educational researchers to juxtapose tools from opposing methods. The gold standard is just not possible in so much of what we do with small-scale research, nor is it…

Cut scores are used in a variety of circumstances to aid in decision making through the establishment of a clear cut line between adjacent categories. Community colleges regularly use cut scores on placement tests to decide the appropriate course for each beginning student: the first college-level course or a developmental course, depending on…

This study describes the steps taken to measure the integrity of an intermediate concept measure and test the assessment strategy of a well-validated dental ethics curriculum. Because this curriculum, which had been in place for 15 years, had consistently been shown to influence moral judgment, it was posited that a cross-sectional comparison…

The predictive validity of the National Association of Secondary School Principals (NASSP) assessment center evaluation process for principals is compared with the perceived effectiveness of a selected population of principals. The NASSP assessment center approach includes a case study, a personal interview, two exercises, and a scholastic…

The construct of validity has received considerable attention in qualitative methods literature (Denzin, 1989; Erickson, 1986; Geertz, 1973; Goetz & LeCompte, 1984; Howe & Eisenhart, 1990; Maxwell, 1992; Smith & Glass, 1987). Much of the attention has been focused upon the issue of whether qualitative results and interpretations accurately reflect…

Assessment of clinical performance is intended to make generalizations about a physicians competence. Performance assessments involve three interacting components: the candidate, the cases, and the raters. Confidence in generalizations depends on reliability of the measurements and whether the cases represent the competence domains of interest.…