The Regular Quadrilateral Function of E–Learning Engineering: The Mathematical Conjunction of Accumulation and Advancement that Defines The Logic, Rationale, and Active Infometrics of Information Delivery in the Digital Age

James Edward Osler II*
Associate Professor, Department of Allied Professions, North Carolina Central University, USA.
Periodicity:January - March'2018


This monograph provides in-depth mathematical logic as the foundational rationale for the novel and innovative online instructional methodology called the 4A Metric Algorithm. The 4A Metric has been designed to address and meet the meta-competency-based education challenges faced by 21st century students who must now adapt to and learn in a multitude of educational settings (face to face, hybrid, and online). The 4A Metric has a geometrically-spatial infrastructure that mathematically defines its unique online “E–Learning Engineered” methodology for online information delivery. This methodology is defined as a “Quadrilateral Function of E–Learning Engineering” that is grounded in neuroscience of mathematical trichotomy and the “neuromeasurement” of the “Bi-coordinate Scale of Learning”. The 4A Metric as an instructional methodology detailed in this narrative also provides an active solution that when implemented via an institutional Learning Management System (LMS)/Content Management System (CMS) uses virtual methods to achieve maximized information delivery in terms of meta-competence-based education for online learning. The explicative nature of the “Quadrilateral Function” also adds further mathematical value to online learning investigative inquiry through measurement, the efficacy of digital instrumentation, and information gathered through tools developed specifically for eduscientifically–engineered (Osler, 2013a and 2013b) research designs (Osler, 2013b and 2015a).


4A Metric ©, Brain-Based Learning, Cohesive Statement, Logic, Cognition, Cognitive Science, E–Learning Engineering, Eduscience, Emotional Intelligence, Epigenetics, Instructional Design, Inventive Investigative Instrument, Learning, Mathematical Model, Mechatronic Online Learning Model, Meta-Competency-Education, Online Learning, Outcomes, Neuroscience, Quadrilateral Function, Research, Tri–Squared Test, Trichotomy, Trioinformatics, Triple–I.

How to Cite this Article?

Osler II, J. E. (2018). The Regular Quadrilateral Function of E–Learning Engineering: The Mathematical Conjunction of Accumulation and Advancement that Defines The Logic, Rationale, and Active Infometrics of Information Delivery in the Digital Age. i-manager’s Journal of Educational Technology, 14(4), 36-52.


[1]. Adkins, S. S. (2004). Beneath the tip of the iceberg: Technology plumbs the affective learning domain. T + D, 58(2), 28-33.
[2]. American Academy of Neurology (AAN). (2012). Working with Your Doctor. American Academy of Neurology. Retrieved 28 October 2012 from
[3]. Atta, H. M. (1999). Edwin Smith Surgical papyrus: The oldest known surgical treatise. The American Surgeon, 65(12), 1190-1192.
[4]. Beane, J. A., Toepfer, C. F., & Alessi, S. J., (1986). Curriculum Planning and Development. Boston, MA: Allyn and Bacon.
[5]. BrainAge (2006). Nintendo Company of America. Based on the work of Ryuta Kawashima, M.D.
[6]. Careersinpsychology. (2015). Retrieved August 19, 2015 from
[7]. Carrero, M. D. (2011). One vital organ: Heart is more than a pump. The Morning Call. Retrieved February 12, 2011 from neurocardiology-20110212_1_heart-disease-unitedstates
[8]. Cherry, K. (2014). What is cognition? About Education. Retrieved from g/def_cognition.htm
[9]. Cobarrubias, S. (2014). What is neuroplasticity? – Definition, depression & quiz. Education Portal. Retrieved from what-is-neuroplasticity-definition-depression-quiz.html
[10]. Dettmer, P. (2006). New blooms in established fields: Four domains of learning and doing. Roeper Review, 28(2), 70-78. Retrieved from docview/206701165?accountid=458
[11]. Eagleman, D. M. (2011). The Brain on Trial. The Atlantic.
[12]. Feidakis, M., & Daradoumis, T. (2013). A Framework for Designing Computer Supported Learning Systems with Sensibility. International Journal of e-Collaboration, 9(1), 57-70.
[13]. Gage, N. L., & Berliner, D. C. (1988). Educational Psychology. Boston, MA: Houghton Mifflin Company.
[14]. Goodfriend, W. (2014). What is learning: Understanding effective classroom strategies. Education Portal. Retrieved from academy/lesson/what-is-learning-understandingeffective- classroom-strategies.html#lesson
[15]. Green, M. F. (1998). Schizophrenia from a Neurocognitive Perspective. Boston, Allyn and Bacon.
[16]. Güllü, A., Aki, O., & Ku?çu, H. (2015). Remote access for education and control of mechatronics systems. Procedia-Social and Behavioral Sciences, 176, 1050- 1055.
[17]. Hardcastle, A. (2016). Mechatronics in Washington State: Manufacturing, Energy and Marine Sectors. Social & Economic Sciences Research Center (SESRC).
[18]. Hidden Curriculum. (2014, August 26). In S. Abbott (Ed.), The Glossary of Education Reform. Retrieved from
[19]. Mandal, A. (2014). What is neurogenesis? Retrieved from What-is-Neurogenesis.aspx
[20]. Merrill, M. D., Drake, L., Lacy, M. J., Pratt, J., & ID2_Research_Group. (1996). Reclaiming instructional design. Educational Technology, 36(5), 5-7.
[21]. Natelson, B. H. (Feb 1985). Neurocardiology. An interdisciplinary area for the 80s. Arch Neurol., 42(2), 178–184.
[22]. Neuroscience. (1963). In Merriam-Webster online. Retrieved from dictionary/neuroscience
[23]. Nouri, A., & Mehrmohammadi, M. (2012). Defining the Boundaries for Neuroeducation as a field of study. Educational Research Journal, 27(1 & 2), 1-25.
[24]. Osler, J. E. (2010a). Infometrics™ ©: The Systemic Strategic Practice of Empowerment through the Creation of an Ideal Learning Environment via Optimal Instruction (First Edition). Lulu Publishing, Morrisville NC.
[25]. Osler, J. E. (2010b). Visualus™ © visioneering volumetrically: The mathematics of the innovative problem–solving model of inventive instructional design (First Edition). Lulu Publishing, Morrisville NC.
[ 2 6 ] . Osler II,J.E. (2012a). Introducing: Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists. i-manager's Journal on Mathematics, 1(3), 23-32.
[27]. Osler, J. E., & Waden, C. (2012b). Using Innovative Technical Solutions as an intervention for at risk Students: A Meta–Cognitive Statistical Analysis to determine the impact of Ninth Grade Freshman Academies, Centers, and Center Models upon Minority Student Retention and Achievement. i-manager's Journal on School Education Technology, 8(2), 11-23.
[28]. Osler, J. E. (2013a). The Psychometrics of Educational Science: Designing Trichotomous Inventive Investigative Instruments for Qualitative and Quantitative Inquiry. i-manager's Journal on School Education Technology, 8(3), 15-22.
[29]. Osler, J. E. (2013b). The Psychological Efficacy of Education as a science through Personal, Professional, and Contextual Inquiry of the Affective Learning Domain. i-manager's Journal on Educational Psychology, 6(4), 36- 41.
[30]. Osler, J. E. (2013c). The Triangulation Algorithmic: A Transformative Function for Designing and Deploying Effective Educational Technology Assessment Instruments. i-manager's Journal of Educational Technology,10 (1), 46–54.
[31]. Osler, J. E. (2014). Triostatistics: The application of innovative in–depth advanced post hoc statistical metrics for the assessment and analysis of statistically significant tri–squared test outcomes. Kentucky Journal of Excellence in College Teaching and Learning, 12(3), 27–39.
[32]. Osler, J. E. (2015a). Trioinformatics: The innovative and novel logic notation that defines, explains, and expresses the rational application of the law of trichotomy for digital instrumentation and circuit design. i-manager's Journal on Circuits and Systems, 3(2),1-7.
[33]. Osler, J. E. (2015b). AMOVA [“Accumulative Manifold Validation Analysis ”]: An Advanced Statistical Methodology designed to measure and test the Validity, Reliability, and overall efficacy of Inquiry–Based Psychometric Instruments. i-manager's Journal of Educational Technology,12 (3), 19-29.
[ 3 4 ] .Osler, J .E., & Mason, L.R.(2015) . Neuromathematical Trichotomous Mixed Methods Analysis: Using the Neuroscientific Tri–Squared Test Statistical Metric as a Post Hoc Analytic to Determine North Carolina School of Science and Mathematics Leadership Efficacy. i-manager's Journal on Educational Psychology, 9(3), 44–61.
[35]. Osler, J. E. (2016). The 4A Metric Algorithm: A Unique E–Learning Engineering Solution Designed via Neuroscience to counter cheating and reduce its recidivism by measuring Student Growth thorough Systemic Sequential Online Learning. i-manager's Journal on Educational Technology,12 (2), 44–61.
[36]. Petoft, A. (2015). Neurolaw: a brief introduction. Iranian Journal of Neurology, 14 (1), 53-58.
[37]. Posner, M. I., & Digirolamo, G. J. (2000). Cognitive neuroscience: Origins and promise. Psychological Bulletin, 126 (6), 873–889.
[38]. Research Network on Law and Neuroscience (2014). Neurolaw. Retrieved from http://www.lawneuro. org/
[39]. Royal Society (2011). Neuroscience: Implications for Education and Lifelong Learning (Brain Waves Module 2). London: The Royal Society. Retrieved from royalsociety. org/uploadedFiles/Royal_Society_Content/policy/public ations/2011/4294975733.pdf
[40]. Sabitzer, B. (2011). Neurodidactics–a new stimulus in ICT and computer science education. INTED 2011 Proceedings, 5881-5889.
[41]. Saleem, H., & Khan, M. S. A. (2014). Towards Generation of Alternate Electrical Energy via Paddling Impact: Protracted Design and Implementation. International Journal of Computer Applications, 107(2),1-6.
[42]. UC-Berkeley Molecular and Cell Biology Department (2014). Neurobiology. Retrieved from neuro
[43]. van der Wall, E., & van Gilst, W. H. (2013). Neurocardiology: close interaction between heart and brain. Netherlands Heart Journal, 21(2), 51-52.
[44]. Yale University (2010). Cognitive Science. Retrieved from
[45]. Yudofsky, S.C.; Hales, E.H. (2002). Neuropsychiatry and the Future of Psychiatry and Neurology. American Journal of Psychiatry, 159 (8), 1261–1264.
[46]. Zymo Research. (2014). What is epigenetics? Retrieved from epigenetics/what-is-epigenetics

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

If you have access to this article please login to view the article or kindly login to purchase the article
Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.