ENTRY FOUR

Education today is in a constant state of change. This is greatly due to the advancements in electronics, technology, and media. Geometer’s Sketchpad is one computer programme that will change the way that mathematics is taught. Geometer’s Sketchpad can be used to teach many units in mathematics. The United States of America Survey of Mathematics Teachers (2009) states that Geometer’s Sketchpad is the most valuable software for students. It is also viewed as the award – winning Dynamic Geometry mathematics visualization software that has ever been created.


Geometer's Sketchpad is a popular commercial interactive geometry software programme that is utilized for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created by Nicholas Jackiw. It is designed to run on Windows 95 or Windows NT 4.0 or later and Mac OS 8.6 or later (including Mac OS X). The Geometer's Sketchpad is a dynamic construction and exploration tool that adds a powerful dimension to the study of mathematics. Across the United States and in countries around the world, Geometer’s Sketchpad™ helps students to better understand a range of mathematical subjects and has been an educational technology leader for almost twenty years.


Geometer's Sketchpad is used in many secondary mathematics classrooms throughout the United States and Canada. NCTM (National Council of Teachers of Mathematics) had identified one of its six principles as a Technology principle, stating that "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." Geometer's Sketchpad is one of these examples. The program comes with program files to help deepen students' understanding of such concepts as slope, geometric transformations and arithmetic on integers.


The Geometer’s Sketchpad can be used in classrooms at all levels of the mathematics curriculum. It has a scope that spans of the mathematics curriculum from elementary school to university. Topics and activities designed specifically for use in elementary and middle school classrooms include counting by grouping, measuring, balancing equations, similarity, adding integers, areas of triangles and circle vocabulary.


This software is very useful as it brings a powerful dimension to the study of mathematics. It is a dynamic construction and exploration tool that enables students to explore and understand mathematics in ways that are simply not possible with traditional tools—or with other mathematics software programs. Geometer’s sketchpad embodies dynamic visualization, enhances learning across the curriculum and is very easy and versatile to use.


Another use of Geometer’s Sketchpad is that students can construct an object, then explore its mathematical properties by dragging the object with the mouse. All mathematical relationships are preserved, allowing students to examine an entire set of similar cases in a matter of seconds, leading them by natural course to generalizations. It encourages a process of discovery in which students first visualize and analyze a problem, then make conjectures before attempting a proof.


Geometer’s Sketchpad brings its full dynamic power to the study of Euclidean and non-Euclidean geometries, algebra, trigonometry, precalculus, and calculus. Additionally, Geometer’s Sketchpad has a dynamic and visual approach that allows younger students to develop the concrete foundation they need to move ahead to more advanced levels of study.


Further to this, Geometer’s Sketchpad is designed with an intuitive interface for ease of use, so your students will be focused on the activity, not the navigation. It is also is suitable in a variety of classroom settings - with an overhead projector, with one or two classroom computers, or in a computer lab. Students can work on independent explorations, and they can solve assigned problems collaboratively or alone. Teachers can use Geometer’s Sketchpad to create worksheets, exams, and reports by exporting Sketchpad figures and measurements to spreadsheets, word processors, other drawing programs and on the internet.


Geometer’s Sketchpad is relevant in a variety of subjects—not just geometry. This hands-on, visual approach benefits students of all ages. Younger students develop the solid foundation they need for more advanced mathematical studies, and older students clarify their understanding of abstract concepts in algebra, geometry, and calculus.


I am always looking for ways to implement different technology into my lessons (especially Geometry). I had no idea what opportunities existed just in using Geometer's Sketchpad. I would have liked to have known about so many of the things I have learned prior to teaching but I totally intend in implementing this software into my teaching.


Geometer's Sketchpad is an interactive software program that allows teachers and students alike to represent so many graphic designs and geometric shapes. The software is appropriate as it is user friendly and a little bit of exploring can go a long way. As a teacher, I highly recommend this software to any other teacher who is looking for ways to appropriately and effectively integrate technology into a lesson plan. For someone like myself who is "artistically challenged", I am able to quickly and easily represent many concepts rather quickly with exceptional accuracy.


There are many other topics that make Geometer’s Sketchpad relevant and worthwhile to adopt into anyone’s teaching career. Transformations are difficult topics for students to grasp because it is difficult to teach visual topics in a non-visual way. Thus, Geometer’s Sketchpad can be an effective tool to teach these topics. Teachers can also use this programme to teach the equation for the length of a line segment. Geometer’s Sketchpad is equipped with a function, which measures the length of any line segment in inches or centimeters. Area, perimeter, and circumference can also be taught using this program. Geometer’s Sketchpad is also equipped to measure circumference of circles, as well as area of closed figures. By using the length of a line segment feature, students can also calculate perimeters. Trig function are difficult for some to understand. Geometer’s Sketchpad can help in the comprehension of these ratios by using the calculator feature. Students can also learn about the “special triangles” (30, 60, 90, and 45, 45, 90) and the trig functions relating to each angle of these triangles by using the “calculate angle” command.


An example of the use of Geometer’s Sketchpad in a lesson : “Measuring Circles, Angles, and Arc. This investigation concentrates on:
(1)Measuring the circumference and radius of a circle and calculating their ratio
(2) Constructing an arc on a circle and measuring its arc angle and arc length
(3) Measuring and comparing central and inscribed angle.
(4) Constructing a section and comparing its area to the area of the circle.


If I qualify for Secondary teaching in the future, I would use Geometer’s Sketchpad in all my high school mathematics and economics classes. However, for Form One and Form Two, it is suitable as an introductory tool to basic algebra, and trigonometry. I would use it as an exploration or introduction into a new topic. This would give the students an idea, especially visually of what this new topic is about and also a chance to play with it before studying the topic. In the higher level classes from Form Three to Form Six, it would be appropriately used as a teaching and assessment tool. I think the greatest use would be in the areas of trigonometry, geometry.


Geometer’s Sketchpad is also suitable for students who have different learning styles and preferences. The typical mathematics environment is where tests and quizzes are given randomly. With Geometer’s Sketchpad it is suited for students who may have test anxiety and for those who have a preparation issue as it assists students to solve problems on their own. This will motivate students and allow them to be more productive. Maslow (1969) states in his hierarchy of needs that these self – esteem needs will eventually give rise to self – actualization need which is the highest potential that an individual can reach and as such they would gained the confidence in solving the various problems given to them.



With Geometer’s Sketchpad, the teacher will be using direct learning when he is demonstrating a problem on the board for the class and guiding the class through a common practice problem. The teacher will be using constructivist activities when he or she gives the students general instructions and asks them to find a solution on their own using the tools and assistance in the classroom. The teacher will assess student learning through problem – solving practice and through hands – on projects. Therefore, students will be developing higher order skills : analysis, comparison, inference and evaluation.


To use Geometer’s Sketchpad effectively in a mathematics course, you need a plan for how you will use the software and how you will assess you students (based on both their work in class and in the computer lab). I am not one hundred percent certain of when each aspect of geometry is taught so to place a specific application of the program to particular Form will be difficult. Some may argue that it is not relevant as it is very costly to implement but it is my belief that the benefits outweigh the difficulties encountered in implementing this software into our curriculum. However, regardless of which class it is being introduced to, one of the most important things teachers can do is to familiarize the students with the program so that future lessons will allow more time for learning and less time for orientation.



I have listed some of the advantages for using the Geometer's Sketchpad software. As a teacher, here are some benefits to the Geometer's Sketchpad software:
• More accurate geometric shapes than drawing examples out by hand.
• Colour and labelling add clarity to work and concepts.
• Measurements are easily calculated for you if needed.
• Animation allows for students to see geometry in motion.
• Manipulation can be done effortlessly without the need for time consuming
redraws.
• Technology allows the students to become more interactive in their lessons.
• Technology skills will enhance the student's motivation and willingness to explore
new concepts!
• Work can be saved, printed, and/or edited later as newer concepts emerge!
Here are also some advice for teachers who are new to the software:
• Enjoy learning to use the software : play, experiment and explore.
• Lessons can be saved to check for correct student constructions and not just
a final picture
• Multiple drawings can be made by you before class and sent to your students
as a way to save time.
• When making a lesson on Geometer’s Sketchpad, just be careful when clicking
on a diagram as this can be frustrating if you're not paying attention.
• Calculations will still continue to work as pictures and diagrams are
manipulated!
• Paper and pencil drawings are still drawn on the computer with better
accuracy from yourself and students and it helps to eliminate a paper trail.



Online websites are also available for ideas, lessons, and how-to's for Geometer's Sketchpad. Some of these websites include: http://www.dynamicgeometry.com/Instructor_Resources/Professional_Development.html,http:// e-z geometry.com, http://www.dynamicgeometry.com/ and http://www.keypress.com/x5521.xml.


The geometer’s sketchpad is a valuable tool that can be used in the classroom to meet the technological requirements of the Trinidad and Tobago’s curriculum. It is therefore relevant to the educational system internationally and regionally in the Caribbean. In my future classes, I would definitely incorporate geometer’s sketchpad into my lessons. Most teachers avoid geometry but in reality mathematics is a form of communication and so too is geometry. The overall expectation states: Students will formulate conjectures and generalizations about geometric relationships involving two dimensional figures, through investigations facilitated by geometry software where appropriate. This is further reiterated as “ Mathematics reveals its secrets only to those who approach it with pure love, for its Inductive logic and even beauty”.



BIBLIOGRAPHY


Key Curriculum Press (1995). The Geometer’s Sketchpad: Dynamic
Geometry for the 21st Century. CA:Key Curriculum Press.


Maslow,A.(1969).Psychology Essentials Two. (2nd ed.). New York:
Mc Graw Hill Higher Education.


NCTM (1989). Curriculum and Evaluation Standards for School Mathematics.
Reston,Va.:The National Council of Teachers of Mathematics, Inc.


NCTM (2000). Principles and Standards for School Mathematics. Reston,
Va.:The National Council of Teachers of Mathematics,Inc.


Van Hiele, P. M. (1989). Structure and Insight: A Theory of Mathematics Education.
Orlando: Academic Press