## Mathematics problem solving is the core of any ideas of functionality with mathematics. Appropriate uses of technology tools can enhance mathematics learning and teaching, support conceptual development of mathematics, enable mathematics investigations by students and teachers, and influence what mathematics is taught and learned. This talk focuses on a particular technology tool, Geometer's Sketchpad, for problem solving, inquiry, and exploration in mathematics. Demonstrations with Geometer's Sketchpad will predominate, but we may slip in some related explorations with Graphing Calculator 3.0 and Excel. I will make extensive use of links to my web site at Http://jwilson.coe.uga.edu.

## Good mathematics teaching, meaningful reform, and genuine improvement of mathematics inststruction will result only if it is manifested within mathematics classrooms.

## The role of the teacher is essential.

## The growing nearly universal availability of technology tools provides a grand opportunity to assist teachers in teaching well and in improving the mathematics experiences of students.

## Mathematics Education Web Course Development on a Shoestring

## Technology in Mathematics Teaching and Learning

## Project InterMath

## Material from courses I teach for inservice mathematics teachers

## Technology and secondary school mathematics

## Problem solving in mathematics

## Middle School Mathematics and Technology: Project InterMath

## Promote better mathematics learning.

## Build conceptual understanding

## Doing mathematics

## investigations

## problem solving

## applications

## exploration

## Communication within/about mathematics

## New look at some "old" stuff

## Doing mathematics not likely to be encountered without technology

## Doing mathematics that incorporates technology (e.g. iterations)

## Self-Confidence about one's mathematics

## Generative tools for constructing one's further mathematics study.

Centroid, Orthocenter, Circumcenter, Incenter, Euler line

Medial triangle, Orthic Triangle, Triangle from Midpoints of Orthocenter/vertex segments

Nine Point CircleLocus Explorations

Travels in 1992 with Bill (Orthocenter), George (Centroid), and Ross (Circumcenter)

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?

Extended Concurrencies of the TriangleFermat points, Napoleon points, and others.

Kiepert hyperbola.

Pedal Points and Pedal Triangles

Pedal.gsp. Open the file, hide the perpendiculars and move point P anywhere in the plane.

Trace the lines defining PQR as P is moved in a circle.

Trace the lines defining PQR as P is moved around the Circumcircle of ABC. (Pedal1.gsp)

Trace the center points of PQ, QP, and QR as P is moved in a circlular path.

Squares. What is the ratio of areas of the two squares?Conics

Parabola, Ellipse, Hyperbola: Directrix is a line or circle.

Second order conics: Directrix is a conic.

Inscribe a parabola in a triangle. GSP Sketch.

Problems. The Web Site for my Mathematical Problem Solving Course.

Folium of DeCartes -- and what if?

Translationto (x - a, y - b)

Transformto (sin x, siny)

Solve: ABC = 4; 3A + 2B - C = 3

Investigate

Graph PacMan

**About Problem Solving**

Research into PracticeAn article on a Synthesis of Reaseach on Mathematics Problem Solving prepared by me, Nelda Hadaway (a classroom teacher) and Maria Fernandez (an experienced teacher and doctoral student).