Adapted from material produced by the former Becta organisation - Contains public sector information licensed under the Open Government Licence v1.0.
Aishling Ryan teaches at St Angela Ursuline School for Girls. She used the computer software Cabri 3D to show how ICT can help students improve their visualisation and interpretation of a 3D geometrical problem situation. The Cabri 3D software encouraged students to 'get inside' the shape and understand the relative position of points both on the surface and within the shape.
Name: Aishling Ryan
Organisation: St Angela Ursuline School for Girls
Address: St George's Road, Forest Gate, London, E7 8HU
St Angela Ursuline School for Girls is a popular Catholic comprehensive school for girls in Newham. It has had Technology College status since 1995. It has a large sixth form that combines with the neighbouring boys' Catholic school. Well over four-fifths of students are from minority ethnic groups, with the largest group (about a third) from Black African backgrounds. A large number of languages are spoken by students, but few are at an early stage of learning English. The proportion of students with learning difficulties and disabilities is broadly average. Ofsted describes this as an outstanding school.
Aishling had observed that, although her students showed a confident understanding of the mathematical facts and skills relating to Pythagoras' Theorem and trigonometry, they were unable to apply this knowledge in real-life problem situations, particularly in 3D.
She used ICT to see if it would improve students' visualisation and interpretation of a 3D geometrical problem.
Aishling gave her Year 9 students the task of finding the length of the longest stick that would fit in a given closed box. She started by asking the students to discuss in small groups where they thought the longest stick would fit in the sealed box provided. This gave students the opportunity to manipulate the box and encouraged good discussion. It highlighted the need for good use of mathematical language when working in 3D.
She used Cabri 3D software to generate a representation of the physical box, which she displayed on the interactive whiteboard. She was able to demonstrate how to open the box and they could all see inside. It was easier for Aishling to describe the position of lines, as well as use colour to highlight identified triangles.
The software enabled students to spin the shape around so that they could see it from different positions. They opened the box to see its skeleton frame. They also drew and measured lines within the box.
Using the software, students could also label vertices and colourin triangles. This meant that they could see, for instance, the skeleton cuboid ABCDEFGH as a coherent 3D object, rather than as overlapping quadrilaterals°™as they would have appeared in a 2D diagram.
Students then worked in pairs using the software on laptops to discover the angle of incline of the longest stick in the box and then the longest stick that could fit within a square-based pyramid. Students identified more easily the right-angled triangles within the shapes and enjoyed using the software to help demonstrate their methods as well as to check their calculations.
The challenge for the most able students was to sort a selection of statements into those that are 'always true', 'sometimes true' and 'never true' in relation to the properties of cuboids. The aim was for them to predict what they thought would happen and then use the ICT to see if their predictions were correct.
This lesson began with practical work in groups using physical "hands-on" 3D objects. It then moved to whole-class work using the interactivity of the software and the whiteboard to respond to students' ideas and suggestions. It then returned to group work using paper-based techniques. After that, it moved to hands-on use of ICT by all students at their own tables using the same software and techniques to explore new configurations. It ended with the students reporting back on what they had learnt.
The challenge for the most able students was to sort a selection of statements into those that are 'always true', 'sometimes true' and 'never true' in relation to the properties of cuboids. The aim was for them to predict what they thought would happen and then use the ICT to see if their predictions are correct. The software gave students an opportunity to test their conjectures by allowing them to easily manipulate the lengths of lines or sizes of angles and to see how these changes altered the overall diagram. In this way, the use of ICT developed their deeper understanding of 3D properties.
Everyone was fully engaged, experiencing both enjoyment and satisfaction in the process. Aishling successfully demonstrated that, even with just a few of the Cabri 3D tools at her disposal, she could use ICT to teach those "hard to teach" aspects of 3D geometry.
The project is easily transferable provided that there is access to the software and that students have had time to get used to using it.
Using ICT helped Year 9 students visualise diagrams in 3D. The software helped students identify more easily the right-angled triangles within the shapes. Students also enjoyed using the software to help demonstrate their methods and to check their calculations.
Case studies from this project are currently available on Teachers' TV.
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