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

James Edward Osler II*, Letita R. Mason**
* Faculty Member, North Carolina Central University, USA.
** Student Mentor, National Consortium of Secondary STEM Schools (NCSSS), USA.
Periodicity:November - January'2016
DOI : https://doi.org/10.26634/jpsy.9.3.3772

Abstract

This study examines the leadership efficacy amongst graduates of The North Carolina School of Science and Mathematics (NCSSM) for the classes of 2000 through 2007 from a neuroscientific and neuromathematic perspective. NCSSM alumni (as the primary unit of analysis) were examined using a novel neuromathematic post hoc method of analysis. This study is grounded in the theoretical construct that non-cognitive psychological (also called motivational) factors are core components of leadership efficacy (self-efficacy), indicative of NCSSM graduates (who had high academic performance and attained STEM [Science, Engineering, Technology, and Mathematics] degrees). In this neuroscientific mixed–methods analysis, a quantitative phase was conducted to collect the data captured by the Mind Garden Leadership Efficacy Questionnaire. A Post Hoc qualitative analysis was conducted in the second phase of the data analysis, using the applied neuromathematic Trichotomous–Squared Test methodology (that has an associated qualitative researcher–designed Inventive Investigative Instrument (Osler, 2012a) embedded within the statistical methodology). An additional outcome of the research investigation was the development of a new assessment methodology called the “Mason Leadership Efficacy Model”.

Keywords

Analysis, Education Science, Inventive Investigative Instrument, Investigation, LEQ [Leadership Efficacy Questionnaire], Leadership Efficacy, Mathematical Model, Mind Garden, Neuromathematics, Neuroscience, North Carolina School of Science and Mathematics, Outcomes, Post Hoc, Research, STEM, Self-Efficacy, Static Test, Statistics, Trichotomy, Tri–Squared Test, Variables, Variance.

How to Cite this Article?

James Edward Osler II and Letita R. Mason (2016). 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. https://doi.org/10.26634/jpsy.9.3.3772

References

[1]. Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A Taxonomy for Learning, Teaching, and Assessing. New York, NY: Longman.
[2]. Apple, D. K., & Krumsieg, K. (2001). Teaching Institute Handbook. Lisle, IL: Pacific Crest.
[3]. Bandura, A. (1993). “Perceived self-efficacy in cognitive development and functioning”. Educational Psychologist, Vol. 28(2), pp.117–148.
[4]. Bandura, A. (1977). “Self-efficacy: Toward a unifying theory of behavioral change”. Psychological Review, Vol. 84(2), pp.191–215.
[5]. Bandura, A., Davidson, H. F., and Davidson, J. (2003). Bandura's Social Cognitive Theory: An Introduction. Davidson Films, Incorporated.
[6]. Bandura, A. (2010). “Self-efficacy ”. Corsini Encyclopedia of Psychology, pp. 1534–1536.
[7]. Bayer, (2010). “Bayer Facts of Science Education XIV: Female & Minority Chemists and Chemical Engineers Speak about Diversity and Underrepresentation in STEM”, Survey Findings.
[8]. Cano, J. (1993). “An assessment of the level of cognitive performance and critical thinking ability of selected agricultural education students”. Journal of Agricultural Education, Vol. 34(2), pp. 25–30.
[9]. Celuch, K., and Slama, M. (1999). “Teaching critical st thinking skills for the 21 century: An advertising principles case study”. Journal of Education for Business, Vol. 74(3), pp. 134–141.
[10]. Cherry, K. (2014). “What is cognition? ”, About Education. Retrieved from http://psychology.about.com/ od/cindex/g/def_cognition.htm
[11]. Davidson, J. (2005). Bandura's Social Cognitive Theory: An Introduction, pp. 209, #7.07.
[12]. Densten, I. L., & Gray, J. H. (2001). “Leadership development and reflection: What is the connection?” International Journal of Educational Management, Vol. 15(3), pp.119–124.
[13]. Dweck, C. S., Walton, G. M., and Cohen, G. L. (2014). “Academic tenacity: Mindsets and skills that promote long-term learning”. Bill & Melinda Gates Foundation.
[14]. Fredrickson, B. L. (2001). “The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions”. American Psychologist, Vol. 56, pp.218–226.
[15]. Gainen, J. (1995). “Barriers to success in quantitative gatekeeper courses”. In J. Gainen & E. W. Willemsen (Eds.), Fostering student success in quantitative gateway courses, New Directions for Teaching and Learning, Vol. 61. San Francisco, CA: Jossey-Bass.
[16]. Gréhaigne, J. F., Godbout, P., and Bouthier, D. (2001). “The teaching and learning of decision making in team sports”. Quest, Vol. 53, pp.59–76.
[17]. Hannah, S. T., Avolio, B. J., Luthans, F., and Harms, P. D. (2008). “Leadership efficacy: Review and future directions”. The Leadership Quarterly, Vol. 19, pp. 669–692.
[18]. Hannah, S. T., Avolio, B. J., Walumbwa, F. O., and Chan, A. (2012). “Leader self and means efficacy: A multicomponent approach”. Organizational Behavior & Human Decision Processes, Vol.118(2), pp.143–161.
[19]. Hannah, S. T., & Avolio, B. J. (2013). Leadership Efficacy Questionnaire. Menlo Park, CA: Mind Garden, Inc.
[20]. Hidden Curriculum. (2014, August 26). In S. Abbott (Ed.), The Glossary of Education Reform. Retrieved from http://edglossary.org/hidden-curriculum
[21] Hughes, M., and Demo, D. H. (1989). “Selfperception of Black American: Self-esteem and personal efficacy”. The American Journal of Sociology, Vol. 95, pp.132–159.
[22]. Ingold, K. (2014). “Impact of participation in the Shelton Leadership Challenge on Youth Leadership Development (Doctoral dissertation)”. Available from ProQuest Dissertations and Thesis Database, UMI No. 3623715)
[23]. Mason, L. R. (2015). “The leadership efficacy of graduates of north carolina school of science and mathematics: a mixed-methods analysis”. Doctoral Dissertation. North Carolina Agricultural and Technical State University.
[24]. McCormick, M. J., Tanguma, J., and Lopez- Forment, A. S. (2002). “Extending self-efficacy theory to leadership: A review and empirical test”. Journal of Leadership Education, Vol.1(2), pp.34–39.
[25]. Mindgarden. (2013). “Welcome to Mindgarden, Inc!”. Retrieved from http://www.mindgarden.com
[26] Myers, B. E., & Dyer, J. E. (2006). “The influence of student learning styles on critical thinking skill”. Journal of Agricultural Education, Vol. 47(1), pp. 43–52.
[27]. Nash, D. H. (2014). “Perception analytics of an inth depth observational analysis of 6 grade african american male students' personal agency”. Doctoral Dissertation. North Carolina Agricultural and Technical State University.
[28]. National Student Clearinghouse, (2015). “National Student Clearinghouse”. Herndon, VA: Author. Retrieved from http://studentclearinghouse.org
[29]. NCSSM Course Catalogue, (2012). Retrieved fromhttp://www.ncssm.edu/academics/docs/course catalog.pdf
[30]. NCSSM Institutional Research, (2013). “Report to Admissions Rubric Committee/Instructional Council: Secondary Outcomes for NCSSM Graduates 2000–2007”.
[31]. Natelson, B. H. (Feb 1985). “Neurocardiology: An interdisciplinary area for the 80s”. Arch Neurol. Vol.42 (2), pp.178–84.
[32]. Neuroscience. (1963). In Merriam-Webster online. Retrieved from http://www.merriam-webster.com/ dictionary/neuroscience
[33]. Osler, 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, Vol. 1(3), Jul - Sep 2012, Print ISSN 2277-5129, E-ISSN 2277- 5137, pp. 23-32.
[34]. 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 Educational Technology, Vol. 8(2), Sep-Nov 2012, Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 11-23.
[35]. 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 Educational Technology, Vol. 8(3), Dec-Feb 2013, Print ISSN: 0973- 2217, E-ISSN: 2230-7133, pp. 15-22.
[36]. Pryor, J. H., Hurtado, S., DeAngelo, L., Palucki Blake, L., and Tran, S. (2010). “The American freshman: National norms fall 2010”. Los Angeles, CA: Higher Education Research Institute, UCLA.
[37]. Sedlacek, W. E. (2004). Beyond the Big Test: Noncognitive Assessment in Higher Education. San Francisco, CA: Jossey-Bass.
[38]. Wagner, T. (2008). The global achievement gap: Why even our best schools don't teach the new survival skills our children need-And what we can do about it. New York, NY, Basic Books.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

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

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.