Problem solving is the big part of the mathematics. A fundamental premise of the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM(1989) is the belief that "mathematical problem solving is nearly synonymous with doing mathematics" (p137). The ability to solve problems, we are told, is facilitated when students have opportunities to explore "connections" among different branches of mathematics.

Mathematics teachers can offer such opportunities to their students by highlighting the connections between different units of study in the curriculum. In doing so, they enable students to view techniques learned in one unit as tools that can be used to solve problems in other, even seemingly unrelated, units.

One of the most powerful of these tools involves the application of techniques of coordinate geometry to solving problems. The power of coordinate methods is made explicit in the Standards (p.161):
One of the most important connections in all of mathematics is that between geometry and algebra. Historically, mathematics took a great stride forward in the seventeenth century when the geometric ideas of the ancients were expressed in the language of coordinate geometry, thus providing new tools for the solution of a wide range of problems.

Unit 1 (3days) : Concept of coordinate geometry

Day1. Introduction to the coordinate plane & distance formula

Day 2. Equation for Circles

Day 3 The midpoint formula

Unit 2 (2days) : Proof and theorem using the coordinate geometry

Day 4. Proof with coordinates

Day 5. The Midpoint Connector Theorem

Unit 3 (1 day) : Test

Unit 4 (1 day) : Explore of the test problem in the GSP

The popularity of low-cost calculators and low-cost computers has raised serious questions concerning the teaching of mathematics. Obviously, technology has had a major impact outside the classroom. However, is the use of technology appropriate inside the classroom? Preparing children to function successfully in the real world is a promary goal of mathematics instruction. Since technology is part of the real world, schools systems and teachers have an obligation to teach children how to use that technology.

Unit 5 (2 days) : Project

DAY 8. Flip Image in the Coordinate Geometry

Day 9. Flip Image in the GSP

This project is based on the cooperative learning. In a cooperative learning, students are grouped together in some manner and asked to work together to a complete a task, such as to master a instructional material, develop a presentation on a creative project. Through the group project, students will be leaded to both academic and social gains.

When students work together to search for better methods, they each share their own methods and listen to those of others. Through discussing the methods and comparing the advantages of each, student can lift themselves out of their rut and see the problem in a new way. Students can increase their understanding of the problem and of different methods that work.

Unit 6 (1 day) : Presentation

The Web presentation provides the opportunity to share the group work with the other student, teacher and even parents. And e-mail makes it possible to communicate between students and teacher or between students in informal way. In each group presentation site, comment section is provided to get other students' opinion. Communication works together with reflection to produce new relationships and connections. Students who reflect on what they do and communicate with others about it are in the best position to build useful connections in mathematics. Thus the group work as a cooperative learning with technology can increase the effectiveness of learning for student achievement.

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