Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.

Principles and Standards for School Mathematics, NCTM, 2000

Today's math classroom is not a safe place for the teacher dependent upon textbooks, overheads, chalkboards and lesson plans written in the time of Nixon's presidency. With today's technology, the math classroom is an environment that allows interaction between the student and the subject. Through software programs, internet access, and powerful calculators, the student has the opportunity to explore many areas of mathematics without the restrictions previously experienced with visualization of diagrams, lengthy or complicated algebra and arithmetic computations, or uninteresting math problems.

Technology allows students to work at their own pace and not a pace set by others. By allowing the student time to process the information, the opportunity of ownership of the material is presented to each individual. At the same time, technology can facilitate individual instruction to each student's needs by allowing the teacher to address questions raised by each student while working through the activities.

The purpose of this project was to design an instructional web page that my geometry students could use in class. The topics presented cover various AKS objectives (Gwinnett County's curriculum) as well as enhancement activities that are not readily available in the textbooks or supplemental materials.

This project allows for student centered learning with varying levels of instructions. Problems contained in this project are applicable to all students from those who struggle in school to those gifted in mathematics. The topics and ideas presented can be used for review as well as enrichment for those students who need additional challenges to remain engaged in geometry.

The problems and activities were written and/or included with my Gifted Geometry students in mind. Although the students are labeled as gifted, it is important to understand that their "giftedness" may not be in mathematics. The prerequisites for Gifted Geometry (other than being classified as gifted) is an 85 average or higher test average in Honors Algebra and the teacher's recommendation. Students taking this class are either gifted in mathematics or have demonstrated the ability and work ethic to be successful in math. Even if a student is placed in the gifted geometry class, it would be a mistake to assume that all of the students in the class are ready for higher levels of learning. Sometimes it is necessary to review very basic material in order to have a foundation ready for more complex ideas. This project facilitates those needs in my classroom.

In my classroom instruction, I attempt to design lesson plans that address the Van Hiele Model of Learning, a linearly ordered model of geometric understanding. The Van Hiele theory asserts that there exist five hierarchal levels of thinking beginning with the basic level, visualization, analysis, abstraction, deduction and finally rigor. According to research, 57% of high school students prior to geometry class in high school are at the visualization level. At this level, students recognize the figures only by their appearance and are able to distinguish figures from others that may have similar characteristics. Unfortunately, many geometry textbooks are written at level four (4) - deduction. Although most gifted children have the ability to skip levels, it is necessary to address the previous levels, avoiding making the assumption that the students can construct proofs prior to recognizing properties and making meaningful relationships between figures and properties.

Through the use of technology, the following activities are written in accordance with the Geometry goals published by the National Council of Teachers of Mathematics in Principals and Standards for School Mathematics in 2000. These goals include but are not limited to the following: 1) analyze properties and determine attributes of two and three dimensional objects; 2) explore relationships (including congruence and similarity) among classes of two and three dimensional geometric objects, make and test conjectures about them, and solve problems involving them; and 3) establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.

In the instructional unit, the lessons begin with a review of basic area and perimeter concepts. Although these topics are covered in the middle school math classroom, some students need reinforcement in these areas. By lesson four, the unit moves into geometric probability which uses algebra and coordinate geometry in order to find the probability of an outcome. Throughout the lessons, practice problems are given for the student to complete with a link to the correct answers.

Most of the activities require Geometer's Sketchpad 3.05 and 4.0 either as a visual aid or as an instructional interactive tool. In some instances, directions are given so that the student can complete the activity on the computer by following along with the lesson. At other times, the students are instructed to attempt the problem and then given hints when necessary to complete the problem correctly either using GSP or pencil and paper. There are also web links that allow the student to research the concept in more detail.

This project has been used at various times with my students either in the classroom projected on the monitor or in the computer lab with each student having access to the pages. Students are encouraged to attempt the problems without the hints if at all possible. When using the web page in the computer lab, the teacher has the opportunity to circulate the classroom and give any help or hints that might prompt the student to full understanding of the objective addressed.

Bell, Ellen and Bell Redrick. Solving Geometry Mysteries Book 2. Wilinsbury, PA: Hayes School Publishing Co. 1983

Bennett, Dan. Exploring Geometry with Geometer's Sketchpad. Berkeley, CA: Key Curriculum Press, 1999.

Campbell, William. Notes from Exeter Math Institute. Exeter NH. 1992.

Coxford, Arthur. NCTM Addenda Series Grade 9-12 Geometry from Multiple Perspectives. Reston VA: National Council of Teachers of Mathematics. 1991

Mason, M & Lane, F. Activities to Teach Geometry Based on the Van Heile Levels of Understanding. 75th Annual Meeting of the National Council of Teachers of Mathematics. Minneapolis-Saint Paul, Minnesota. April 19, 1997.

National Council of Teachers of Mathematics. Principal and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. 2000.

Woodward, Ernest and Hamel, Thomas. Visualized Geometry. Portland, ME: J. Weston Walch, Publisher. 1990.