John J. Edgell Professor of Mathematics Office: Math/CS 462 Phone: 512-245-3416 Fax: 512-245-3425 Email: je02@txstate.edu Home Page

Research Interests: Mathematical Education, specialized in elementary education.

Professor Edgell received his Ph.D. from University of Texas at Austin in 1973. For the past fifteen years, Dr. Edgell has been conducting formative field research at all levels of public schools on discovering ideas of mathematics, which are accessible to students and how to enhance such accessibility. In the process he has presented and published several papers on such research nationally and internationally. Also, in the process, Dr. Edgell has discovered original aspects of mathematics and has presented several papers and publications on such mathematics. The ideas of accessibility have tended to focus upon: applications of trigonal arrays to various aspects of mathematics including number theory, geometry, algebra, discrete probability/statistics, combinatorics, etc.; understanding geometry from a measurement (cube)/tessellation/simplex perspective, including understanding the idea of 2-D and 3-D angles; applications of alpha-numeric modulo structures to arithmetic of rational numbers in various numeral bases and checking such arithmetic in corresponding cast out structures; understanding irrationals such as $x^{m/n}$ in terms of Euclidean geometry and graphically in terms of spirals. It is from these same ideas and mathematics educational pursuits that some of Dr. Edgell's original mathematics and the creation of an angle ruler, mathematically correct and accurate, for measuring angles in international units have evolved. Such formative field research is an important aspect of mathematics educational research for a source of innovative ideas for others to do comparative analysis and for curriculum revisions of the future.

 

Selected Publications

• J. Edgell; "Heronian Simplexes and Constructs - Teaching: Simplexes-Technology Connection.", reviewed and published Proceedings/Tagungsband DES-TIME-2006, 23 pp.
• J. Edgell; "Transcending the Boundary of Geometrical Ideas into Abstract Number Theoretic Ideas.", co-authors Kyle Seipp and Eric Janssens, The Lamar University Electronic Journal of Student/Faculty Research, 03/05/05, 14 pp.
• J. Edgell, Gena Orth; Trevor's Problem.", Tempo, Vol. XXIII, Issue 2, Spring 2003, published by the Texas Association for the Gifted and Talented, 12 pp.
• J. Edgell; Impact of Formative Field Research With Children on Applications of Modulo Structures Upon Preparation of Teachers.", Proceedings of the Ninth International Conference on the Teaching of Mathematics, ICME-9, Japan, July, 2002.
• J. Edgell; "A Formative Field Study with Second, Third, Fourth Grade Chinese-American Students on Accessing Geometry from Measurement: Tessellation, Cube, Simplex, Construct Perspective", (Complete Study Report), reviewed Topic Study Group-Two Committee on the Teaching and Learning of Geometry, CO Maria Alessandra Marotti, mariotti@dm.unipi.it, ICME-9, Japan, Aug. 1, 2000, 31 pgs.
• J. Edgell; "A Formative Field Study with Second, Third, Fourth Grade Chinese-American Students on Accessing Geometry from a Measurement: Tessellation, Cube, Simplex, Construct Perspective" (Focused Upon Two Episodes ) reviewed Topic Study Group-Two Committee on the Teaching and Learning of Geometry, CO Maria Alessandra Marotti, mariotti@dm.unipi.it , ICME-9, Japan, Aug. 1, 2000, 4 pgs, cited Proceedings of the Ninth International Congress on Mathematical Education, Kluwer Academic Publishers, The Netherlands, 2004. p. 229.
• J. Edgell; "An Academic Year Field Research Study at the Kindergarten Level on Geometry from a Measurement: Tessellation, Cube,Simplex-Construct Perspective in a Constructivist Mode.", reviewed Working Group for Action-One, WGO-1, on Mathematics Education in Pre- and Primary School Committee, CO Linda Sheffield and CO Ann Anderson, http://www.nku.edu/-sheffield/pbyd.html, ICME-9, Japan, Aug 2, 2000, 4 pp.
• J. Edgell; "An Example of a Child Becoming Mathematically Empowered and An Example of a Group of Children Not Becoming Mathematically Empowered", reviewed WGO-1 Committee, CO Linda Sheffield and CO Ann Anderson, http://www.nku.edu/-sheffield/pbyd.html , ICME-9, Japan, Aug 2, 2000, 4 pps., cited Proceedings of the Ninth International Congress on Mathematics Education, Kluwer Academic Publishers, The Netherlands, 2004, p. 225.
• J. Edgell; "Implications of an Academic Year Field Research Study a t the Fifth and Sixth Grade Levels on Checking Arithmetic of Rational Numbers Via the Cast Out Structure", reviewed Committee on Short Presentations ICME-9 chaired by Eizo Nagasaki, Science Education Section, National Institute for Educational Research, Japan, abstract published Abstract of Short Presentations of ICME-9, Japan, Aug. 5, 2000, 22 pp.
• J. Edgell, Michael Brown; "Impact of Mentor - Field Research Programs.", Proceedings of the Conference - Partnerships in Education - Voices from the Field: Impact of School Partnerships., Northern Arizona University's Center for Excellence in Education, October 21-23, 1998, p. 112-124.
• J. Edgell; "Generating JE(3) With Some Elementary Applications.", The AMATYC Review, Volume 13, Number 2 Spring 1992, 6 pp.
• J. Edgell; "Cover Design - JE(3)M2.", The AMATYC Review, Vol. 13, No. 2, Spring 1992.
• J. Edgell; "Trigonal Spaces with Applications.", Proceedings Third International Conference on Teaching Statistics, Vol. 1, International Statistical Institute - Publications in Statistical Education, January 1992, p. 70-74.