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 Presentation 2006. Problem solving for middle school level.
This paper has links to the Intermath web site and draws on examples from the web site.
SMSG: A personal perspective. A presentation, rather than a paper.
Mathematics Education Web Course Development on a Shoestring
This paper presented to a non-mathematics technology demonstrated the web-page development I had done. This work was done early in the "on-line" discussions and represented a hybrid approach -- regular meeting classes but utilizing web based material. These web pages did not have built in components for interaction with students. Of course, many fully on-line courses do not incorporate a discussion or interactive component. Key points were that this work was NOT funded, had limited professional support from colleagues, and was driven by model of learning mathematics via exploration of problem situations
Synthesis of Research on Problem Solving.
This paper was published as Chapter 4 in Wilson, P. S. (Ed.) (1993). Research Ideas for the Classroom: High School Mathematics. New York: MacMillan.
The book was part of the National Council of Teacher of Mathematics Research Interpretation Project, directed by Sigrid Wagner.
The bibliographic reference for the published version is
Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research Ideas for the Classroom: High School Mathematics (pp. 57-78). New York: MacMillan.
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.
What is the ratio of areas of the two squares? This is a discussion of some exploration and extensions of this problem.
Roots 2 and 5.
This paper examines sets of second degree equations that have graphs crossing the x-axis only at 2 and 5. For a preview on one family of such graphs, click here.
Problem Solving with Heron's Formula.
This is a paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides. Problems and explorations are included for using Heron's formula.
Alternative Developments for Heron's Formula for the area of a triangle, given the lengths of its sides.
The explorations include approaches that are algebraic, geometric, trigonometric, and complex number application.
A Different Geometric Development of Heron's Formula
This approach exploits the relationships of the incircle and excircle tangent on one triangle segment.
An Investigation with Parametric Equations.
This paper examines the movement of triangles when one vertex is moved along the x-asis and another is moved along the y-axis. We trace trace the movement of the thrid vertex.
Extended Concurrencies of the Triangle
Paper presented at the 1996 MAA Annual Meeting, Orlando, Florida. This investigation examines the locus of the point of concurrency of lines from vertices of the triangle to the non-base vertices of similar isosceles triangles constructed on each of the sides of a triangle.
Envelopes of Lines and Circles.
This paper was constructed for a presentation/demonstration to Elbert County High School Mu Alpha Theta club on March 18, 1997. 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.
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.
What is the locus of the orthocenter when one side of a triangle is fixed and the third vertex is moved along some path?
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.
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.