Using Internet access devices in Mathematics lessons

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Adapted from material produced by the former Becta organisation - Contains public sector information licensed under the Open Government Licence v1.0.

Ruth Tanner teaches Year 9 maths. Her students have been using Geometer's Sketchpad, a dynamic geometry software program, to develop their understanding of circle theorems.

Ruth has found that learners of all ages seem to find geometric reasoning a challenge.

Using the software has deepened their understanding. By the end of the project, students were able to generate their own examples of circles and triangles. They formed conjectures that they could then begin to justify and prove.

**Name:** Ruth Tanner**Organisation: **
Wrenn School, Wellingborough**Address:** Doddington Road,
Wellingborough, Northants, NN8 2JJ

The project arose from a subject association working group in November 2007.

Wrenn School is a relatively large school located on a split site. The proportion of pupils with learning difficulties and disabilities is slightly above average. The number of pupils from minority ethnic groups and those identified as learning English as an additional language is average. The school was awarded specialist science college status in September 2004.

Ruth set out to investigate whether it was possible for students to use dynamic geometry software to develop their approach to geometric reasoning.

For this project, Ruth worked with a top set Year 9 class, about one third of whom had achieved a level 8 at KS3. She wanted them to deepen their understanding of isosceles triangles, which she hoped would deepen their understanding of circle theorems. She focused on some of the circle theorems included in the GCSE Higher Tier specification. The activity took place over seven lessons.

The students spent two lessons making isosceles triangles using paper, compasses and rulers. They also practised using the software. In this way, they revised constructions of triangles and learnt the properties of isosceles triangles. The software supported the questions that arose from this process.

The students next used the software to construct their own images. The visual approach of the software allowed them to continuously change aspects of their constructions and see the resulting mathematical relationships.

Ruth used three different approaches:

- Some students used a set of A4 cards that gave instructions on how to construct a series of dynamic images related to different circle theorems.
- A second group was given the same activities, but their instructions were about what to create, without any information on how to do this.
- A third group was given a pack of A4 cards with a theorem on it. They were asked to use the software to construct an example of the property given and to try to prove that the property is always true.

She put students in pairs so that they could benefit from collaborative working. She steered the higher-achieving students to the cards that focused on proof.

During the introduction, students were reminded about the need to take their time, to find out as much as they could for each activity card, to record their conjectures clearly and then to try to justify any conjectures they made.

Following these lessons, Ruth used a data projector to show the dynamic geometry images the students had created. They wrote a summary of the circle theorems they had discovered. This led to whole-class work on measuring and solving angle problems. By the end of seven lessons, students had improved their confidence and their understanding of circle theorems.

- Drawing and measuring circle diagrams, even if given a sheet of pre-drawn circles, can be time-consuming. With the software, students generated their own examples quickly and easily.
- By using the technology, students worked independently and made their own discoveries.
- Ruth was free to circulate around the class, encouraging students to express their conjectures.
- Students saved their work as they went along so that Ruth could check it after the lesson.
- It was a deliberate choice to get the students working in pairs so that they could help each other with these challenging tasks and enjoy the benefits of collaborative working.

Almost from the start there was a tremendous sense of engagement in the room. Those with the detailed instructions got started quickly and confidently. Some of the others were understandably more hesitant, but mostly seemed to enjoy the challenge. Students saved their work as they went along on the network in a shared area so that Ruth could access it after the lesson.

Towards the end of the lesson, some students felt confident enough to go to the front and use their own images to explain the properties they had discovered.

Ruth observed that some of the most interesting work was done by students who had previously found mathematics more difficult to understand than their peers.

The ICT resources used were fairly modest. A data projector and computer were in the classroom, and there was also some use of a computer suite. Because no interactive whiteboard was available, a graphics tablet and a gyro mouse that connected to the teacher's computer were helpful, but not essential. Ruth's department purchased the Geometer's Sketchpad, but the dynamic geometry software Geogebra is available as a free download.

The Geometer's Sketchpad software was new to the department and only one of Ruth's colleagues had ever used dynamic geometry before. However, by using the A4 cards from Ruth's lesson, the teachers were able to get started without any knowledge of the software. Several colleagues left feeling confident enough to use these resources again and made plans to do so. Hence, one reasonably expert user of dynamic geometry in a department can develop resources that can be used by colleagues who are less confident with the software.

On reflection after the first lesson, Ruth found that the outcomes had been variable. About three pairs of students had found it hard to understand what was expected from them. She believes they would have benefited from a mini-plenary - where one or two pairs of students share their work up to that point - earlier in the main part of the lesson. Interestingly, the students who seemed initially confused were the ones who went on to achieve the most in the second lesson.

An interactive whiteboard could have been used for whole class work, but Ruth found that using a relatively inexpensive graphics tablet to manipulate the images was almost as effective in promoting discussion and encouraging problem solving.

When asked whether the computers helped them, one of the students replied, "Using this software is really good - it lets us experiment - it's not that hard, but you can learn so much out of it."

At the end of these lessons, Ruth asked the students to write how they felt about the work they had done and the way they had worked. Although their assessment of their own understanding of the mathematics varied, their comments were overwhelming positive, for example:

"I can do it easily and confidently, every idea we have been learning and using was fun and creative. I really enjoyed it."

"I think I can do it quite well but I need to work on proof. I like using computers and it helped quite a lot."

At a time when the New Curriculum is urging teachers of mathematics to plan rich activities that develop students' ability to understand and use the key concepts and processes, Ruth believes that geometry software is one tool that can be used effectively. It can encourage creativity and help students to communicate mathematically.

**Links**

Geogebra geometry software is free to download.

Case studies from this project are currently available on Teachers' TV..

Do you have a case study that could be shared on these pages. Please let us know what you have found successful using ICT to support the teaching of topics that are "hard to teach" in Secondary Mathematics.p>

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