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Advances in Social Sciences Research Journal – Vol.7, No.7

Publication Date: July 25, 2020

DOI:10.14738/assrj.77.8556.

Osler, J. E. (2020). Transformative Psychometric Research Trioengineering Modeling: Triangulating Digital Instrumentation,

Implementation, and Data Analysis for Effective, Efficient, and Engaging Classroom Inquiry. Advances in Social Sciences Research Journal,

7(7) 58-74.

Transformative Psychometric Research Trioengineering Modeling:

Triangulating Digital Instrumentation, Implementation, and Data

Analysis for Effective, Efficient, and Engaging Classroom Inquiry

James Edward Osler II

North Carolina Central University

ABSTRACT

This monograph provides an in–depth discourse on “Research

Engineering” in the field of “Educational Science” first detailed in a 2012

Journal on Mathematics article. Research Engineering involves the

methodology and the metrics used to conduct in–depth research

investigations via the innovative Total Transformative Trichotomy–

Squared [Tri–Squared] Test. The triangulation of this test aids in the

comprehension of how the Tri–Squared calculation is a mixed methods

research design based upon “Trichotomous Psychometrics”.

Trichotomous Psychometrics involves the development, deployment,

and analysis of “Trifold Assessments” for the holistic transformation of

qualitative outcomes into quantitative data. This paper is a continuation

of the published article entitled: The Psychometrics of Educational

Science: Designing Trichotomous Inventive Investigative Instruments

for Qualitative and Quantitative for Inquiry.

Keywords: Algorithmic Model, Cartesian Coordinates, Educational Science,

Geometric Vectors, Models, Psychometrics, Research Engineering,

Triangulation, Trichotomous Psychometrics. Trichotomy, Trioengineering,

Trifold Assessment, and Tri–Squared.

INTRODUCTION

One of the most challenging areas of research in education involves the construction of specific

instruments that are designed to measure qualitative outcomes and data. Although there are a great

many measurement tools that analyze the cognitive and psychomotor domains, there remains a

vacuum in the number of instruments especially designed to accurately measure the affective

domain (the learning domain that contains attitudes, opinions, emotions, perception, and

perspectives). This void is further expanded when the specific event under investigation is unique,

specialized, has specific characteristics, serious legal constrictions, and issues regarding time. This

often requires the research investigator to design an instrument that ideally measures the variables

under investigation (Osler, 2013b).

The process of designing instruments for the purposes of assessment and evaluation is called

“Psychometrics”. Psychometrics is broadly defined as the science of psychological assessment (Rust

& Golombok, 1989). The Tri–Squared Test pioneered by the author in 2012, factors into the

research design a unique event–based “Inventive Investigative Instrument”. This is the core of the

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Advances in Social Sciences Research Journal (ASSRJ) Vol.7, Issue 7, July-2020

Trichotomous–Squared Test. The entire procedure is grounded in the qualitative outcomes that are

inputted as Trichotomous Categorical Variables based on the Inventive Investigative Instrument.

The specific assessment of the variables is completely dependent upon the outcomes determined

by the researcher’s instrument. The creation, production, and deployment of the trichotomous

Inventive Investigative Instrument requires that the research investigator adopt the role of a

“Trichotomous Psychometrician”. A “Trichotomous Psychometrician” is an Educational Scientist

that uses trichotomous–based psychometrics to develop a qualitative Inventive Investigative

Instrument specifically designed capture qualitative responses during a specific event (Osler,

2013a). The design of Inventive Investigative Instruments is based on the mathematical “Law of

Trichotomy” (Apostol, 1967). Trichotomy itself is derived from historic discussions surrounding

higher cognition, general thought, and descriptions of intellect. Philosopher Immanuel Kant adapted

the Thomistic acts of intellect in his “trichotomy of higher cognition” — (a) understanding, (b)

judgment, (c) reason — which he correlated with his adaptation in the soul’s capacities — (a)

cognitive faculties, (b) feeling of pleasure or displeasure, and (c) faculty of desire (Kant, 2007). It is

important to note that in mathematics, the law (or axiom) of trichotomy is most commonly the

statement that for any (real) numbers x and y, exactly one of the following relations holds. Until the

end of the 19th century the law of trichotomy was tacitly assumed true without having been

thoroughly examined (Singh, 1997). A proof was sought by Logicians and the law was indeed proved

to be true. Mathematically, Trichotomous relations are irreflexive and antisymmetric (Sensagent,

2012). A description of the entire Tri–Squared research process follows and is described in detail

to provide the reader of the precise steps undertaken in the process of developing, designing, and

ultimately implementing an Inventive Investigative Instrument (Osler, 2013a). “Trioengineering”

is a novel term coined by the author and defined here as “the process involved in designing solutions

by actively using the mathematical law of trichotomy to produce a measurable, scalable, and

tangible results”.

DEFINING THE FIELD OF EDUCATIONAL SCIENCE

The field of “Education Science” is also represented by the term “Eduscience” which is a

portmanteau of the two terms “Education” and “Science”. Similar to the field of “Bioscience”,

Eduscience is the study of education wherein applicable sciences (such as ergonomics, statistics,

technology, etc.) are applied to enhance and improve learning. The primary purpose of the field of

Eduscience is the study and application of solutions to improve and enhance the learning

environment and learning in general. Eduscience is solution–driven and is actively concerned with

the transfer and dissemination of knowledge. Education Science is a broad field and its professionals

are directly involved in the field. Those who are actively involved in Eduscience can be referred to

as “Education or Educational Scientists”. Educational Scientists or “Eduscientists” are multifaceted

professionals who have a variety of areas of expertise. They can assume multiple roles in the

educational environment and can serve in a variety of offices and in a multitude of capacities. The

primary positions that Eduscientists assume are in the following areas: Administration (as Leaders,

Organizational Heads, and Organizational Management Professionals), Instruction (as Teachers,

Professors, and Facilitators), Practice (as Practitioners in a variety Specified Areas and Arenas), and

Technology (as Educational Technologists, Instructional Technologists, and Information

Technologists). In these positions Eduscientists effectively use, analyze, study, and deploy novel

instructional learning theories, methodologies, strategies, solutions, tools, and techniques in both

traditional or virtual (pedagogical and andragogical) settings to bring about learning (Osler, 2012a).

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URL: http://dx.doi.org/10.14738/assrj.77.8556 60

Osler, J. E. (2020). Transformative Psychometric Research Trioengineering Modeling: Triangulating Digital Instrumentation, Implementation, and Data

Analysis for Effective, Efficient, and Engaging Classroom Inquiry. Advances in Social Sciences Research Journal, 7(7) 58-74.

TRANSITIVE TRANSFORMATIVE KNOWLEDGE TRANSFER: THE ULTIMATE GOAL OF

EDUCATION SCIENCE

Educational Scientists strive to make the process of knowledge transfer both transitive and

transformational. A transitive and transformative knowledge transfer process is as seamless and as

harmonious as possible in an effort to empower, enhance, and improve learning. Eduscientists are

masters of teaching who also are also highly proficient practitioners who are able draw from

personal and professional experiences to make the learning environment more viable (Accessible),

usable (Ergonomic), teachable (Instructional), engaging (Relevant), approachable (Adaptive),

exploration–based (Discovery), and inspirational (Transformative). The Total Transformative

Trichotomy–Squared Test is a comprehensive multi–step research methodology that is employed

by Eduscientists. It is especially designed to conduct qualitative and quantitative investigations in

educational settings and the learning environment (Osler, 2013b).

Education–Based Inquiry: Using the Tri–Squared Research Methodology as a Four Step

Process to determine an appropriate research Effect Size, an ideal Sample Size, and an

effective Alpha Level for Education–Based Experiments in the Learning Environment

The Tri–Squared research procedure (Osler, 2013c) consists of a four step approach designed to

provide the researcher with a clear and precise set of data to conduct research, analyze data, and

determine the level of significance required to either validate or reject the initial research

hypothesis. The four Tri–Squared steps are as follows:

1. Design of an Inventive Investigative Instrument that has Trichotomous Categorical Variables

and Trichotomous Outcome Variables.

2. Establish the Research Effect Size, Sample Size with associated Alpha Level.

3. Establish Mathematical Hypotheses.

4. Use the Tri–Squared Test as the Data Analysis Procedure following implementation.

The Upright Right Triangle Testing Model for the Tri–Squared Test

The Algorithmic Model of Triangulation (Osler, 2013c) is of the form:

Where,

Vertex a = Ða = form “Vector [a→b]” as “[)*++++⃗]” = “authoring” = a ratio of a measurement metric of

4 (used to convey information) = The Initial Tri–Squared Instrument Design;

Vertex b = ∟b = = form “Vector [b→c]” as “[+

*-+++⃗]” = “building” = a ratio of a measurement metric of 3

(as the Triostatistics: Tri–Squared Test) = The Tri–Squared Qualitative Instrument Responses