This paper gives a very elementary, essentially visual proof of Viete's product. We employ only the Pythagorean theorem, similarity of triangles, and exhaustion.

Alternating series have the simplest of sign patterns. What about series with more complicated patterns? By inspecting the alternating series test closely, we find a theorem that applies to more complicated sign patterns, and beyond.

If a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false. We provide examples of rational series that illustrate this point. The Cantor set appears in connection with one of the examples.

A visual proof of Ptolemy's theorem.

Previous studies have shown that both creativity and emotional intelligence (EI) were related to children school performance. In this study, we investigated the incremental validity of EI over creativity in an elementary school setting. Seventy-three children aged from 9 to 12 years old were recruited to participate in the study. Verbal and…

During the first decade of the twenty-first century, neopositivist claims made about the nature and validity of knowledge in the debates about scientifically based research were countered by educators who, decades earlier, had made various turns away from positivism and were surprised by its resurgence. In those debates, positivists often used…

The authors examined the psychometric properties of a clinician-rated measure of sex offender denial. Convergent and discriminant validity for the measure was supported, and given its relationship to treatment attitudes, the measure demonstrated utility for assessing treatment change and readiness. (Contains 3 tables.)

A new application of logarithmic differentiation is presented, which provides an alternative elegant proof of two basic rules of differentiation: the product rule and the quotient rule. The proof can intrigue students, help promote their critical thinking and rigorous reasoning and deepen their understanding of previously encountered concepts. The…

This study investigates the internal structure and construct validity of Complex Problem Solving (CPS), which is measured by a "Multiple-Item-Approach." It is tested, if (a) three facets of CPS--"rule identification" (adequateness of strategies), "rule knowledge" (generated knowledge) and "rule application"…

For a given positive integer k [not equal] 4, let "P[subscript k,n]" denote the "n"-th "k"-gonal number. We study "k"-gonal triples ("a", "b", "c") satisfying P[subscript k,a] + P[subscript k,b] = P[subscript k,c]. A "k"-gonal triple corresponds to a rational point on the rectangular hyperboloid x[squared] + y[squared] = z[squared] + 1. The simple…

Students is a very specific population according to their manner to cope with stress. A coping questionnaire for students was developed and administered to 1100 French students at the beginning of the term (T1). Principal Component Analysis of responses, followed by varimax rotations, yielded three factors accounting for 50.5% of the total…

The increased capabilities offered by digital technologies offer new opportunities to evaluate students' deeper knowledge and skills and on constructs that are difficult to measure using traditional methods. Such assessments can also incorporate tools and interfaces that improve accessibility for diverse students, as well as inadvertently…

The aim of this study is to adapt SIPPY (social interaction practices for the preschool years) scale into Turkish. The SIPPY is a tool designed to assess teachers' judgments of the acceptability and feasibility, as well as their current use of literature-supported strategies for promoting the development of young children's social competence in…

Standardizing aspects of assessments has long been recognized as a tactic to help make evaluations of examinees fair. It reduces variation in irrelevant aspects of testing procedures that could advantage some examinees and disadvantage others. However, recent attention to making assessment accessible to a more diverse population of students…

Despite the importance of work values in the process of career adjustment (Dawis, 2002), little empirical research has focused on articulating the domains represented within the construct of work values and the examination of evidence of validity for the construct has been limited. Furthermore, the larger number of work values measures has made it…