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Aims
The overall aim of this strand of the project was to examine the ways in which ICT can
be used in educational settings to enhance the learning of numeracy and mathematics.
Particular Aims were:
- for teachers, in partnership with researchers, to develop mathematics design initiatives
which focus on particular learning outcomes and use technologies appropriately;
- to investigate the process of teaching and learning mathematics within each of the
design initiatives;
- to identify learning outcomes with respect to the implicit assumptions and explicit
objectives of the mathematics design initiatives;
- to investigate the effects-with and the effects-of using ICT for learning mathematics.
Subject Design Initiatives
These are some of the subject designs of the mathematics teachers
Shape and space using dynamic geometry
(Pat Peel, Easton CEVC Primary School). Year 6 pupils learned about the properties of quadrilaterals and triangles (Numeracy Strategy, p
103). For six 'numeracy hours' spread over eight weeks pupils manipulated and
investigated the properties of particular quadrilaterals (square, rectangle,
parallelogram, kite, rhombus, trapezium) and triangles (isosceles, scalene, equilateral,
right-angled) in the dynamic geometry environment Cabri Geometry. Pat taught them in a
computer suite where they work both in pairs and as a whole class using an interactive
whiteboard.
Geometry and proof using dynamic geometry
(Marnie Weeden, Fairfield School).
Year 9 'Top set' students learned about the difference between mathematical proof and
practical demonstrations through work with Geometer Sketchpad and paper-and-pencil. Marnie
taught in her normal mathematics classroom with a set of portable computers and a video
projector connected to her own computer. Students used the dynamic geometry environment
to help develop conjectures and related proofs. There was also considerable emphasis on
'proof' as a particular mathematical practice.
Sequences and Series
(Leila King, John Cabot CTC).
Year 12 A/S level students learned about arithmetic and geometric sequences through using the power of
Excel (spreadsheets) to formalise rules to generate sequences and their sums. Leila
sometimes taught in her normal classroom and sometimes in a computer suite with an
interactive whiteboard. Students were already very confident with using spreadsheets
before they started this work and rapidly saw the links between inductive
definitions in mathematics and spreadsheet formalisms.
Understanding the graphing of functions
(Rob
Beswetherwick, John Cabot CTC). Using a combination of Omnigraph and paper-and-pencil the Year 9 students worked
towards a greater understanding and awareness of graphical representations of functions.
The students experimented with manipulating the invariant parts of linear and quadratic
equations in order to generate various families of graphs. They also investigateed negative
values and their effects on the graphical representations. Changes in graph behaviour such
as reflection, and translation were observed. From this they gained a greater insight into
the behaviours of the functions and developed a sense of being able to sketch graphs. The
Omnigraph software allowed students to represent a wide range of graphs very quickly which
is not possible with normal pen and paper plotting. Despite not having used Omnigraph the
students quickly adapted.
The golden ratio in art
(Jan Bovill, City of Bristol College) Jan worked with Intermediate GNVQ students in Art and Design. The content forms part of the Key Skills level 1 Application of
Number requirements. Students learned to construct the golden rectangle using pen and paper
techniques. Using the Internet and other software they then searched for examples of
paintings and investigateed whether aspects of the painting fitted within a golden rectangle
frame. They also investigated measurements within paintings, such as distances between the
various parts of the face. This enabled a comparison to be made between different artists.
Using Paintshop Professional students constructed a golden rectangle frame and attempt to
fit images within this frame thus assessing how much they conformed to the golden ratio.
Scaling was also explored within the Paintshop software with reference to different
measurement techniques.
Graphs of straight line functions and their equations
(Rachel Zewede, Filton High School). Working with graphics calculators Year 9 students focused on these
learning objectives: recognise that equations of the form y = mx + c correspond to linear
graphs; find the gradient of lines given by equations of the form y = mx + c; sketch and
interpret linear graphs. Rachel worked in her normal mathematics classroom using the
Texas Instruments OHP attachment and a set of graphics calculators. This work could be
extended to using other graph plotting packages such as Autograph or TI Interactive.
Functions and graphs from real-life problems
(Chris
Carter, Filton High School). Year 9 students used a motion detector and graphics calculator to solve distance-time
problems (Numeracy Strategy, p 173). In particular they focused on the construction and
interpretation of graphs of functions. This work drew on the classroom work of Phil
Hamilton.
Aspects of calculus
(Phil Hamilton, Sir Bernard Lovell School). Working with A Level students Phil Hamilton initially explored
the potential of using DERIVE with A-level students but then moved to using the relatively
new graph plotting package Autograph to teach A-level students key aspects of calculus.
Transformation Geometry
(Gary Handley, City of Bristol College). Working with a group of GCSE 'resit'
students in a Further Education College Gary used a dynamic geometry environment
to support students to engage with and learn about aspects of shape and space which
constitute 25% of the GCSE examination.
Similarity and transformations in geometry
(Heidi
Moulder, Cotham School). Working with Year 10 students and using a dynamic geometry environment Heidi developed a learning
initiative which focused on aspects of mathematical similarity as it links to
transformation geometry.
Trigonometry
(Aled Williams, Cotham School). Using Geometers Sketchpad with Year 9 students,
Aled taught aspects of trigonometry, with a focus on trigonometric
relationships and similar triangles.
Problem solving
(Jude Swailes, St Michael's CEVC Primary School). Jude worked with Year 4 pupils on
problem solving. She explored the potential of ICT environments
such as Logo and the Primary Numeracy Pack.
Working with Cabri-Geometre
(Ellie Coombs, John Cabot CTC) Ellie worked with a Year 9 class. Using Cabri-Geometre dynamic software she worked on discovering negative scale factors for enlargements.
This extract from video data of one of Ellie's lessons provides an example of a teaching and learning episode which gives evidence of how pupil-pupil talk, manipulation of the software on screen, dynamic visual representation and teacher intervention combine.
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Sam and Nabil construct Fig.1 in Cabri and start changing the scale factor. |
Nabil: |
Ehi Sam look at this! Sam, it turns around! ( Fig.2 )
Because it's going minus isn't it so it goes the other way .. so it? if say ..if we ? wow! |
Sam: |
Move that one. |
Nabil: |
This one? |
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Nabil changes the scale factor instead. The transformed figure disappears from the screen. |
Nabil: |
It's running away Sam! It's running away! ( Fig.3 ) |
Ellie: |
Oh, it's running away! That was an interesting thing. What happens when you do a negative? |
Nabil: |
It goes the opposite way. |
Ellie: |
It goes the opposite way. Cool. Yes, when it's negative. Do a negative again so that we can see it a bit better. It turns upside down, doesn't it?
So you can really comment on that. That's what I meant by orientation, because it does not stay the same way around. Well done boys! |
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Research on Teaching and Learning
Mathematics was one of the earlier subjects to make use of the computer in the
classroom and there has been substantial research in this area at both the primary and the
secondary level. The dynamic and symbolic nature of computer environments supports
students to generalise and make links between their intuitive notions of mathematics and
the more formal aspects of mathematical knowledge. Technology based environments can also
support students to think and reason about complex mathematical problems. However research
has shown that these understandings do not develop spontaneously and there is a need for a
teacher to support students to move between more informal knowing and the virtual world of
mathematics. Despite the wealth of knowledge about how to use ICT to enhance learning of
mathematics, research from a BECTa funded project showed that, at the start of the InterActive Education Project, mathematics
teachers use computers in the classroom less than any other subject teachers in UK
secondary schools.
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