Mathematics Education

My e-mail is jwilson@uga.edu. - - - - - - - Last modified June 27, 2018

 Intermath Project Web Site   Interactive Dictionary for Middle School Level   CONTEXTUAL TEACHING AND LEARNING -- EMAT   CPTM

# 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 I taught prior to May 2016, J. Wilson, Instructor (last time taught indicated).

EMAT 4600/6600 - EMAT 4600/6600 Problem Solving in Mathematics (2015)
EMAT 4680/6680 - Technology and Secondary School Mathematics (2016)

EMAT 4650/6450 - Mathematics in Context (2013)
EMAT 7050 - Mathematics Instruction (2014)
EMAT 6690 - Technology Enhanced Instruction in School Mathematics (2014)
EMAT 4500/6500 - Connections in Secondary Mathematics (2014)
EMAT 4000/6000 - Special Problem in Mathematics Education (2014)
EMAT 8990 - Doctoral Seminars in Mathematics Education
(2009)
MATH 7200 - Foundations of Geometry I (2010)
MATH 7210 - Foundations of Geometry II (2010)
EMAT 6700 - Advanced Explorations with Technology in Mathematics Instruction
(2009)

## 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.

## 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.

## Middle School Mathematics and Technology -- Project InterMath

MULTIPLE SOLUTIONS

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 in Workbench on how a logger estimates the height of a tree.

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 a project supported by the US-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 a project supported by the US-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.

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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.

The SaRD Construction: An Elegant Solution for Euclid's Partitioning Problem by 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 three points A, B, and C. Construct a line intersecting AC in the point X and BC in the point Y such that AX = XY = YB. The problem is from Polya's Mathematical Discovery, Vol. 1, pp. 7-8.

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Jim's GSP Library

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

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Other Mathematics Resources
Megan Davenport's Mathematics and Mathematics Teaching Resources

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## Application for Reappointment to Graduate Faculty

My Brief Resume.
.
First Version, NSF Proposal Format Biographical Sketch
Second version, NSF Proposal Format Biographical Sketch.

Third Version, NSF Proposal Format Biographical Sketch 2015
Professional Bio I
Professional Bio II
Professional Bio III
Professional Bio IV

My current and former doctoral students

Hooten Award 2015

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

Problems my Students and I have found Challenging

The Brain on Music -- A Roundtable Discussion

On 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

# Pictures from our visit.

Taiwan Welcome

Taiwan Visit Part 1

Taiwan Visit, Part 2

Taiwan, Pictures from class

Pictures from Talk

Pictures fron Tainan University Visit

Taiwan Farewell Party

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.