**Mathematics Education**

Jim Wilson's Home Page/Server!

My e-mail is

jwilson@uga.edu. - - - - - - - Last modifiedJanuary 14, 2013

Situations Project(password required)

Let Us Teach Guessing-- 60 minute video of George Polya

## Using the Arithmetic Mean-Geometric Mean Inequality in Problem Solving

The Arithmetic Mean-Geometric Mean (AM-GM) inequality is a very useful algebraic tool for reasoning about many maximization and minization problems without calculus. Yet, this tool gets very little attention in modern mathematics curriculum. I have presented basic information and definitions about the Arithmetic Mean-Geometric Mean Inequality, showed a range of proofs and demonstrations for the cases with 2 positive numbers and a range of problem solving episodes where the AM-GM inequality is used.

A presentation for the Annual Meeting of the School Science and Mathematics Association, Birmingham, November 8-10, 2012, was prepared using parts of this paper.

## Courses, J. Wilson, Instructor

EMAT 6600- EMAT 4600/6600 Problem Solving in Mathematics.Spring 2014

Technology Enhanced Instruction in School MathematicsEMAT 6690-.Spring2014EMAT 6680- Technology and Secondary School Mathematics. Fall 2013.

EMAT 7050 -Mathematics Instruction. Fall 2013.

EMAT 6450- Mathematics in Context. Course developed and taught in Summer 2013.

EMAT 6500- Connections in Secondary Mathematics. Course developed and taught in Summer 2013.

EMAT 6600- EMAT 4600/6600 Problem Solving in Mathematics.Spring 2014

EMAT 8990- Doctoral Seminars in Mathematics Education

MATH 7200- Foundations of Geometry I

MATH 7210- Foundations of Geometry II

EMAT 6700- Advanced Explorations with Technology in Mathematics Instruction.

EMAT 6990 -Research Seminar in Mathematics Education.No longer required nor available.

Research Council on Mathematics Learning -- 2009 Keynote

2008 NCTM Illuminations Institute

## Papers.

## Taxi Cab Geometry Investigations with Technology

This is a set of materials exploring the use of technology to visualize and understand the geometric consequences of using a TCdistance metric. Geometric constructions of the TCcircle, TCellipse, TChyperbola, TCparabola, TClines, and TC distance are included.## Comment on Triangle Center Investigations.

## The Fibonacci Sequence and the Golden Ratio in Stock Market Theories

This technical analysis introduces the use of the Fibonacci Sequence and the Golden Ratio in Elliott Wave Theory. Elliott Wave Theory is a useful technique for trading Forex -- foreign exchange.## Taking Some Mystery Out of the Nine Point Circle with GSP

## This paper examines the nine point circle as the common circumcircle of three special triangles of any given triangle -- the triangle formed by the midpoints of the segments from the orthocenter to the vertices, the medial triangle, and the orthic triangle.

## RESA August 23 Presentation

## SMSG: A personal perspective

## Mathematics Education Web Course Development on a Shoestring

## Middle School Mathematics and Technology -- Project InterMath

MATHEMATICS PROBLEM SOLVING USING GEOMETER'S SKETCHPAD and GRAPHING TECHNOLOGY

Technology in Secondary School Mathematics. A presentation for the Department of Mathematics, University of Kansas, December 7, 2000.

An Elementary Application of Similar Triangles. This note derives from a comment inon how a logger estimates the height of a tree.Workbench

Prospective Elementary Teachers' Conceptions of Rational Numbers.A paper by Dina Tirosh and Efraim Fischbein, Tel Aviv University, Anna O. Graeber, University of Maryland, and James W. Wilson, University of Georgia, from aprojectsupported by theUS-Israel BSF.

The Teaching Module on Rational Numbers for Prospective Elementary Teachers. A Teaching module by Dina Tirosh and Efraim Fischbein, Tel Aviv University, Anna O. Graeber, University of Maryland, and James W. Wilson, University of Georgia, from aprojectsupported by theUS-Israel BSF.

Implementing Mathematics Reform: The Challenges Within. A paper by Azita Manouchehri of Maryville University and Terry Goodman of Northwest Missouri State University.

Technology in Mathematics Teaching and Learning. Paper by J. Wilson, University of Georgia. This draft reflects some of the considerations I have implemented in the courses tied to this web site.

Technology Experiences for Prospective Secondary Teachers, a paper in progress by Azita Manouchehri, Maryville University.

Problem-Solving Using Graphing Calculators, a paper in progress by June Jones, University of Georgia. This study reports on the problem solving performance of 56 college freshman in a college algebra course.

Toward a Theory of Teaching-In-Context,a paper by Alan H. Schoenfeld, University of California at Berkeley. The Mathematics Education Student Association invited Dr. Schoenfeld to visit the University of Georgia on May 14 and May15, 1997. Preliminary versions of this paper and supporting documents were read in preparation for his visit.

Envelopes of Lines and Circles.This paper was constructed for a presentation/demonstration to Elbert County High School Mu Alpha Theta club. The paper examines the curves formed by sets of lines or circles that move along some defined paths.

Trisecting the Area of a Triangle. This is an investigation of the constructions required to divide the area of a triangle into three regions of equal area, under different initial conditions.

Squares. What is the ratio of areas of the two squares? This is a discussion of some exploration and extensions of this problem.

Capturing Area and a Solution. This paper by Pagnucco and Hirstein also explores the Squares problem with a somewhat different route.

Curve Building. When two relations are multiplied, points (x,y) on either will appear on the product graph. Characteristics of the graph are described to tell whether a relation is factorable.

Roots 2 and 5. This paper examines familes of curves that pass through 2 and 5 on the x-axis.

Orthotravels. What is the locus of the orthocenter when one side of a triangle is fixed and the third vertex is moved along some path?

Tangents Problem. Find two linear functions f(x) and g(x) such that the product h(x) = f(x).g(x) is tangent to each of the original lines.

Alternative Approach to Tangents Problem

Explorations with Heron's Formula. Heron's formula for finding the area of a triangle given the lengths of its three sides is a nice tool for problem solving explorations.

Exploration of a Triangle Ratios Problem. Given a triangle ABC and an interior point M. Extend a segment from each vertex through M to its intersecion with the opposite side creating segments AD, BE, and CF. The exploration will evaluate some ratios of segments within the triangle.

Multiple-Application Medium for the Study of Polygonal Numbers

This article is an expanded version of the paper presented at the 1994 International Symposium on Mathematics/Science Education and Technology, San Diego, CA, and published as: Abramovich, S., Fujii, T., & Wilson, J. (1994). Exploring and Visualizing Properties of Polygonal Numbers in a Multiple-Application Computer-Enhanced Environment. In G.H. Marks (Ed.), Proceedings of the 1994 International Symposium on Mathematics/Science Education and Technology. Charlottesville, VA: AACE.

Witch of Agnesi. This is an essay by two students in my 1995 EMT669 class.Some

Comments on the GLaD construction.

The SaRD Construction: An Elegant Solution for Euclid's Partitioning Problemby SriRanga S. Dattatreya (with help from Ravi E. Dattatreya).

An Interesting Ratio Result for Triangles.This paper by SriRanga S. Dattratreya and Ravi E. Dattratreya shows a construction and general ratio result for triangles that can be used to segment a line segment into parts.

Some Explorations with Lemniscates. This paper suggests some investigations with the Lemniscate of Bernoulli and the Lemniscate of Gerone.

Discussion of an Equal Segments Problem. Given thre points A, B, and C. Construct a line intersecting AC in the point X and BC in the point Y sucht that AX = XY = YB. The problem is from Polya'sMathematical Discovery, Vol. 1, pp. 7-8.

## Geometer's SketchPad Material

See also many of the papers, course materials, and problems throughtout the Site.

## Links

Some Mathematics Links.

Other Mathematics Resources

Megan Davenport's Mathematics and Mathematics Teaching Resources

## Local Links

Mathematics Education Program Page

University of Georgia Home Page

UGa College of Education Home Page

LPSL Home Page

Graduate School

## Personal Information

## POST TENURE REVIEW

Back## Application for Reappointment to Graduate Faculty

My Brief Resume.For the longer, more boring, versionclick here.First Version, NSF Proposal Format Biographical SketchSecond version, NSF Proposal Format Biographical Sketch.A Professional Bio IA Professional Bio IIA Professional Bio IIIA Professional Bio IVCommencement 1995My Wife, Corene.Corene and our daughters.Our House.The Mandolin.The Fiddle.The DulcimerPhoto AlbumNew Photo AlbumMy current and former doctoral students

St. Louis NCTM Meeting, October 26-29, 2011

Problems my Students and I have found Challenging

The Brain on Music -- A Roundtable DiscussionOn Wednesday, November 17, at 4 p.m. in 148 Miller Learning Center, the Willson Center sponsored a roundtable discussion on “The Brain on Music.” The lecture and discussion focused on the relationship of early music training to intellectual achievement in other areas. Roy Martin (Professor Emeritus of Educational Psychology and a violinist) gave the opening lecture. Panelists for the roundtable discussion included Jean Martin-Williams (Hugh Hodgson School of Music), Jed Rasula (English) and James W. Wilson (Mathematics Education). Martha Thomas (Hugh Hodgson School of Music) moderated the discussion. Following the Panel discussion, questions and comments were contributed by the audience.

Professor Martin's paper is provided here since many people who could not attend the discussion have expressed interest in the paper.

Workshop on Mathematics Problem Solving

Mastery Project, Mathematics and Science Teacher Education in Yemen

May 16-21 2009

## NATIONAL PINGTUNG UNIVERSITY OF EDUCATION

## Visit December 5 - 19, 2006

## Contemporary issues in the use of computer technology to improve mathematics teaching and learning

## Pictures from our visit.

EMAT Commencement August 2008

Disclaimer

The content and opinions expressed on this Web page do not necessarily reflect the views or nor they endorsed by the University of Georgia or the University System of Georgia.