# Geometer's Sketchpad

Published by Chartwell-Yorke

Maths

KS 3 & 4 (Years 10 &11)

### KS3 Content Evaluation by Linda Culm

**Description**

Geometer's Sketchpad is a very useful tool for teaching geometrical concepts and more, in an exciting and meaningful way. Students can construct geometrical figures onscreen and save them for future use, making them more dynamic than they would achieve by simply using a pencil and paper or a geometry set. The program's main strength, however, lies in its function as an exploratory tool that allows 'concrete operations' in many areas of maths and especially those associated with geometry and algebra. The program gives students a clearer idea of how a number of mathematical concepts work and what happens if you change certain aspects of them. Students can 'play' with the figures and gain real insight into how they operate on their own and in relation to others. This dynamic experimentation is not something that can be achieved by using the traditional tools of construction or a textbook where diagrams are static.

Teachers can use the graphics and animations in the program to make presentations to the class, enabling them to present mathematical concepts in a new and exciting way.

The content is mainly aimed at teachers and older students, although quite a few of the basic activities are suitable for Key Stage 3 students. However, the software is so versatile it could be easily adapted for use with students of any age and all levels of ability and could be a tremendous resource to use with able students.

The program also has applications across the Curriculum in any subject which relies on the production or manipulation of visual material, for example, Art, Design and Technology and Science and has a valuable part to play in the construction of technical illustrations in a variety of fields.

*Supporting Documentation*

The software comes with a comprehensive set of documents conveniently located in a sturdy ring binder. There is a large reference manual that takes the reader through every element of the program, from basic to advanced concepts. A shorter Learning Guide contains a number of tutorials covering all the basic functions and there is also a six-page Quick Reference booklet. Other supporting materials appear in the form of a booklet of 101 project ideas for using the program which is aimed at students, and a 96-page manual for teachers containing notes and sample activities. Other booklets supporting the software are available from the publishers although they are US-based. A dedicated website also provides a great deal of supplementary material.

*Technical Support*

A considerable amount of help is available via an online help system within the program (which reproduces what is in the Reference Manual). There are also some sample documents to browse on the CD-ROM and an online Sketchpad Resource Centre on the Internet, at the Keypress website. From here, it is possible to email for technical support.

**Curriculum Relevance** *Purpose of the Program*

Geometer's Sketchpad enables complicated geometrical figures to be produced quickly and efficiently by the student and makes the modelling process dynamic instead of static. Figures can be manipulated whilst keeping all their mathematical properties intact, making it possible to explore mathematics in a far more meaningful way than in the past. It is also a powerful tool for classroom presentations, bringing geometrical figures alive and presenting them in a dynamic and interesting way.

*Curriculum Relevance*

The program is mainly relevant to the Mathematics Curriculum as a tool to explore the possibilities of geometry, algebra and other aspects of Maths. It could also be used to enhance many other subjects, for example Art, Design and Technology and Science, although these areas are not really covered in the documentation.

*Extent*

The extent of this program is as wide as the imagination of the student and the expertise of the teacher. Key geometrical and algebraic principles are covered in depth. Key Stage 3 students can learn about constructing polygons and other figures, Pythagoras' theorem, transformations of all kinds, tessellations and straight line graphs. Students can use the diagrams already provided to learn about the properties of various mathematical constructions and how they can be manipulated.

**Analysis of Contents**

*Appropriateness*

This program was first devised for high school students in the United States and I feel that this age group is where it is most appropriate. Key Stage 3 students will need quite a lot of help to use the program effectively and what they can get from it will depend on the skill of the teacher, i.e. how they present the tasks and extrapolate their students' discoveries. Some of the language in the Help files is quite advanced although teachers could easily provide their own instructions.

*Quality*

The program is of very high quality. The only link to the Internet is to the dedicated website for the program which worked faultlessly each time I tried it.

**Differentiation**

This program has a lot to offer the more able Key Stage 3 student, who could undertake individual projects using this resource. It could also be used with less able students, as long as they were carefully guided by the teacher. Students could have a lot of fun creating drawings with this program: the tutorial on String Art would be a good place to start, producing 'Sketchograph' type diagrams. It also provides an opportunity for endless concrete operations practice – often very necessary for those with learning difficulties. Students are able to get a real feel for how geometrical and algebraic figures work, which is not possible with a static text or exercise book.

**Summary**

It is difficult to fault Geometer's Sketchpad in terms of its design and flexibility and it is a valuable creative tool for students and teachers. Although it is primarily aimed at students above Key Stage 3, a skilful teacher at this level will find it possible to manipulate the program to enable students to construct and experiment with geometric and algebraic figures in a meaningful way. Teachers will also find it invaluable as an explanatory presentational tool for teaching purposes. Geometer's Sketchpad has additional cross-curricular possibilities and I would recommend it as a worthwhile whole-school resource.

### KS3 Classroom Evaluation by Peter Halfpenny

**Installation & Access**

Initially the software was installed onto a standalone PC and this was found to be a quick and painless operation, achieved by simply following the onscreen instructions. Once the installation was complete there was no need to reboot the computer and the program immediately worked perfectly. The software was then installed onto a Research Machines Connect 3 Network. The program was installed onto one machine and then, using the RM Connect wizard, distributed as a 'package' to the other network machines. After the installation, the software worked first time on all the network machines. The installation of the software onto the standalone PC and the RM Connect 3 network computers took less than one hour to complete. The software proved suitable for all screen resolutions and worked at perfectly acceptable speeds on every computer tested (Pentium II to Pentium IV machines).

**Planning Classroom Use** *What This Product Offers*

Geometer's Sketchpad is a dynamic construction and exploration tool or, put more simply, a dynamic geometry package. In practical terms the software allowed me to draw accurately and quickly various plane figures on an interactive whiteboard. The software turned the interactive whiteboard into a very powerful demonstration tool for geometry. It was then possible for the pupils to construct their own shapes and explore the mathematical properties of the shapes by simply dragging the vertices with the mouse.

The visual approach of Geometer's Sketchpad allowed the students to easily change aspects of their construction and look at the resulting mathematical relationships and generalisations. In practice, my Year 7 students constructed triangles and quadrilaterals and the software measured individual angles and sides, together with the sum of the angles. The software then enabled the students to change the lengths of the sides of the plane shapes on their screens. It was possible for the students to generalise about the mathematical relationships of their constructions, for example, the sum of the interior angles of a quadrilateral is equal to 360 degrees.

I found that when Geometer's Sketchpad is used in conjunction with an interactive whiteboard it becomes an extremely powerful demonstration tool. However, when the software is used by pupils with individual computers then the software is even more powerful, since the program allows the teacher to create guided discovery lessons in which the students produce mathematical relationships and generalisations.

*Purpose of Using This Product*

The software was used with an able Year 7 group and an average ability Year 8 class. After I introduced the students to the main features of the program using an interactive whiteboard, they used the software to draw various plane figures. The program was then used to cover objectives from the Numeracy Strategy Sample Plans. In particular, the students used the software to investigate the following objectives: Classify triangles (isosceles, equilateral, and scalene), using criteria such as equal sides, equal angles, and lines of symmetry; Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals.

The software was evaluated in a computer room where every student was able to access and use the software individually. I asked the students to draw various plane figures and the students completed the task on grid lines using snap to grid points. The students were able to use the software to measure individual angles, calculate the total angles, measure lengths of sides and calculate the total length of the sides.

The software was then used to explore the Numeracy Strategy objectives: 'the sum of the angles of a triangle is 180 degrees and of a quadrilateral is 360 degrees' and 'the exterior angle of a triangle is equal to the sum of the two interior opposite angles'.

After the success of using the software with the two Key Stage 3 groups I then used the package with a Year 5 middle ability class. After a few minutes of instructions from me they were successfully drawing various plane figures. In the later lessons they used the software to 'Recognise properties of rectangles' and to 'Classify polygons using criteria such as number of right angles, whether or not they are regular, symmetry properties'.

*Differentiation*

The program is aimed at a wide audience, from possibly Key Stage 2 up to A-level and beyond. The software is a dynamic geometry package, so differentiation can be achieved by task, i.e. the teacher can select a task at an appropriate level for a student to complete. There are no specific built-in features for SEN students, but it is possible to alter the size and colour of text and use different scales on the axes to enable partially sighted pupils to view the package more easily.

**Classroom Experience**

*Classroom Organisation*

The software was mainly used in a computer room containing over thirty-five networked computers and an interactive whiteboard. This meant that the software was used in two ways: as a demonstration tool with the interactive whiteboard and as a program used on the networked machines that allowed the students to explore the geometrical properties of plane shapes. During class demonstrations it was necessary to blank out the students' monitors, since they were keen to experiment with the software rather than watch the program being used as a demonstration tool. The groups that used the software were a little noisier compared to classes that were taught using normal classroom methods, but this is due to the fact that students were discussing their work with neighbouring students.

*Context of Use*

No additional preparation was needed before the software was introduced to the class. With the more able pupils greater emphasis was placed on them exploring and discovering mathematical relationships and generalisations, rather than simply repeating work demonstrated on the interactive whiteboard. The software fitted exactly into the Key Stage 3 Numeracy Strategy Curriculum and many objectives, including key objectives, were addressed in the four-week evaluation period. Follow-up homework was set to assess the impact of the software and initial indications show that the students have a good grasp of the Numeracy Strategy objectives.

*Ease of Use - Design & Navigation*

Initially I found Geometer's Sketchpad's user interface a little daunting. However, after an hour or two of experimenting with the program and consulting the onscreen Help file and comprehensive user guides, I was in a position to use the software with a class. Most pupils on the other hand were able to use the program within a short space of time. In fact, a middle ability Year 5 group used the program successfully after five or ten minutes of instructions. The software has the normal Windows appearance, with nine drop-down menus, including the standard File, Edit, Window, and Help menus.

*Monitoring & Assessment*

Geometer's Sketchpad has no in-built tools for the monitoring and assessment of the student's progress. In practice, the easiest method of assessment was to observe and question the pupil as they used the software. It was discovered that a few pupils could use the software quite easily, but failed to explore the mathematical relationships that the package demonstrated. This was assessed in the plenary section of the lesson, when the pupils explained what generalisations they had discovered about each shape they has constructed using the software. On reflection, I would say that the majority of the students greatly benefited from using the software. In follow-up lessons the vast majority of the students remembered the results of the previous activities. They understood they were using ICT simply as a tool to explore the geometrical properties of plane shapes. The program has a Save feature which enables the user to save the work they have completed on Sketchpad. The pupils were encouraged to annotate their saved work with the mathematical relationships they had discovered. This was then used to assess their progress through the Numeracy Strategy objectives.

*Feedback from Pupils and Other Staff*

When questioned, many children said they enjoyed using the program and that it was easier and quicker than drawing the shapes on paper. They appreciated the fact that a drawing can be instantly altered by dragging its vertices to another position. As a homework exercise the students were asked to draw plane shapes onto one centimetre square paper and perform similar measurements and calculations as they had done using Geometer's Sketchpad. When the homework was collected several stated that the task would have been easier, quicker and more accurate using the The Geometer's Sketchpad software. The ICT technician who had initially installed the software made the comment 'it was one of the easiest installations that I have ever done'.

**Summary** *Ease of Use*

Geometer's Sketchpad has several features that make it easy to use in the classroom. The software relies on very simple commands that allow the user to effortlessly create, edit, and manipulate accurate geometrical constructions on the computer screen. This is simply achieved by selecting the appropriate tool from the left hand side of the display and then clicking the mouse at the desired position on the screen. This means that the package is an ideal demonstration tool for use with an interactive whiteboard and data projector. If students have access to computers then the software becomes a tool for the discovery of the mathematical relationships involved in geometrical constructions. There is a useful onscreen Help section together with comprehensive user documentation that is supplied with the software. The only feature that may hinder use by less able students is that the drop-down menus initially appear complicated and over- populated with commands.

*Classroom Experience*

The software was evaluated with Key Stage 3 pupils, but it should be noted that the program was successfully used to address Key Stage 2 Numeracy Strategy objectives with Year 5 pupils. There will always be a place for traditional pencil and paper constructions, but I found that using this software encouraged the students to comment on mathematical relationships and make important generalisations. Throughout the Key Stage 3 Numeracy Strategy there are many Shape and Space objectives that can be addressed by using this program. During the four-week evaluation period the software kept the students engaged and brought Geometry to life. In conclusion, I feel this software is an essential resource for any Secondary Mathematics Department.