While significant progress has been made in recent years on technology enabled assessments (TEAs), including assessment systems that incorporate scaffolding into the assessment process, there is a dearth of research regarding psychometric scoring models that can be used to fully capture students' knowledge, skills and abilities as measured by…

Three unheralded results, two in Coordinate Geometry and the other in Plane Geometry, provide three proofs of a theorem dubbed by this author as "The Fundamental Theorem". The above theorem offers a uniform proof establishing the positive integral nature of the radii of the incircle and the three escribed circles associated with the right triangle…

Many models of cognitive diagnosis, including the "least squares distance model" (LSDM), work under the "conjunctive" assumption that a correct item response occurs when all latent attributes required by the item are correctly performed. This article proposes a "disjunctive" version of the LSDM under which the correct item response occurs when "at…

A differential amplifier composed of an emitter-coupled pair is useful as an example in lecture presentations and laboratory experiments in electronic circuit analysis courses. However, in an active circuit with zero input load V[subscript id], both laboratory measurements and PSPICE and LTspice simulation results for the output voltage…

We demonstrate how to assess the potential changes to a test's score scale necessitated by changes to the test specifications when a field study is not feasible. We used a licensure test, which is currently under revision, as an example. We created two research forms from an actual form of the test. One research form was developed with the current…

The concurrent validity of the KBIT-2 Nonverbal IQ and Leiter-R Brief IQ was evaluated for two groups of children: those with high functioning autism and those with language impairments without autism. Fifty-three children between the ages of 4 and 13 years of age participated in the study. The correlation between the scales was large (r = 0.62)…

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"…