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Enhancing Mathematics Teaching: Using Interactive Whiteboards with Compass, Ruler and Protractor Author(s): Dave Miller Source: Mathematics in School, Vol. 33, No. 4 (Sep., 2004), pp. 13-15 Published by: The Mathematical Association Stable URL: http://www.jstor.org/stable/30215714 . Accessed: 05/10/2013 16:27 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access to Mathematics in School. http://www.jstor.org This content downloaded from 157.182.150.22 on Sat, 5 Oct 2013 16:27:32 PM All use subject to JSTOR Terms and Conditions

Enhancing Mathematics Teaching: Using Interactive Whiteboards with Compass, Ruler and Protractor

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Enhancing Mathematics Teaching: Using Interactive Whiteboards with Compass, Ruler andProtractorAuthor(s): Dave MillerSource: Mathematics in School, Vol. 33, No. 4 (Sep., 2004), pp. 13-15Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215714 .

Accessed: 05/10/2013 16:27

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.

http://www.jstor.org

This content downloaded from 157.182.150.22 on Sat, 5 Oct 2013 16:27:32 PMAll use subject to JSTOR Terms and Conditions

Enhancing mathematics teaching: using interactive whiteboards with

compass, ruler and protractor

by Dave Miller

One of the most obvious advantages of an interactive whiteboard is to use it to help show pupils how to use a ruler, compass and protractor. This was one of the first things that came from our work with schools and has led to the development of the Toolbox in the Nelson Thornes EXP Maths year 7 interactive whiteboard resource developed by Dave Miller and Peter Sherran. From our experience as soon as teachers see and use this resource the wooden protractor and compass is relegated to the back of the store cupboard.

The diagram below shows a screen dump of the tools that can be easily used on any make of interactive whiteboard.

::::J 2!iiiiiiiix,; :.:~ i;xix:iiii;:ii iiiii!x

..... ...

\t

.::::.:: x,x ... ...:. : : x / -x:S:,,,xx . ...... .:i x'

.:;>. "

x:: ,,. , x , ..... .... .... .... . ..... ....... . . . ... ======= = ==== ;::::B :!

:: :::::::: ::::::::::::::::::

The protractor and ruler can be rotated and moved around the display; the pencil draws straight lines while the pen is used for freehand work. The compass works as illustrated below.

Click and drag here to move the compass (nothing else changes)

Click here to draw arcs about the compass point.

Click here rotate about the

compass point without

drawing.

Click here to change the radius.

The Toolbox shown allows you to work live with any year group to create constructions and consider locus problems, such as drawing a perpendicular bisector of a line. By pressing the Print Screen key on your keyboard any screen can be copied and put into a word document and printed for pupils.

However, when creating activities within EXP Maths other uses of the tools were also considered and are used in a number of other ways.

Measuring the Angles of a Triangle

Here a triangle is generated by marking and then labelling three points in the grey shaded area. The protractor is then provided so that the on-screen angles can be measured.

Use the protractor to measure the angles of the triangle. Click in each blue cell and use the keypad to enter the angle. Click ::i: i: to see if you are correct.

................... ::::::::::':::I-:: VA- 100 00LI

-ACF3=O I vO/

An On-Screen Animation to Show Constructing a Triangle given Side, Angle, Side

Here the protractor and ruler are used in an animation to show the construction of the triangle but are also left at the end so that angles and lines can be measured.

Use the ruler and protractor to check that: AB = 7 units, AC = 5 units and angle BAC = 40 degrees. Go to the Tools section to draw more triangles in this way.

S .. .. . .. .. .......... ......... .. . .. . ......... ...:.:...

........ .......s ..........

AB 1

1 2 3 4 5 6 7 8 9 10

ii.i.ixiii;i 3

Mathematics in School, September 2004 The MA web site www.m-a.org.uk 13

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Using the Tools to Show Rotation Properties

A protractor and rulers are used in this rotation example so that pupils and the teacher can consider the properties of a rotation.

If you join the centre of rotation to the same point..i-si!,i:th the object and the image then the angle between the lineS i:x.angle of'

..... rotation. Click i:::.:..... :start again . "

.........

.. .

" . . . x:xx"

..- '

...-.'i. .. .

x x : . . x .

- . . : . x . . . ..... .

:"x,x;,,: . x :x::x: :-" :-x .....x .......... x ............. =x ...........

.

.,..

. . . . . A n le o . . . . . . . .

i-x .::''"i: ;i. !x ! / x x

:i:xx. ro t.atio n

.

, ... .. . . . . . ... ...

...0 sA,

and

the. imag.........................between the

:::angle.....

xi:;;,: .:ix !...E ~i: ......................... ::::::::::::::::::::::::::: ,... ........

,.. ..:

Angle of rotation

j-90

O')

......................

2 3

The Advantages of using an Interactive Whiteboard Compass, Ruler and Protractor

Our work has clearly identified many advantages of using interactive whiteboards, including increased pupil and teacher motivation, improved classroom management, and greater on-time task and interest from pupils. We have also found that many teachers progress to an 'enhanced interactive' stage in which they use the technology as an integral part of most teaching in most lessons and look to integrate concept and cognitive development in a way that exploits the interactive capacity of the technology. Typically, at this stage of teacher development, the interactive whiteboard is used as a means of prompting discussion, explaining processes, developing hypotheses or structures and then testing these by varied application.

In order to get to this stage we believe that it helps to have appropriate material that will arouse interest and promote discussion. For example, consider the problem of drawing a triangle given side, angle, side. We think it is appropriate to give pupils scrap paper, compasses, protractor and ruler, to show the EXP Maths Toolbox with a blank screen and then await ideas, which can be tried out by pupils on the interactive whiteboard. The interactive whiteboard Toolbox is easy to use, rubbing out is simple and pupils are usually keen to try things. Once the process is complete, possibly with guidance from the teacher, the animation from one of the specific activities can then be used as necessary.

Other Resources

The DfES interactive teaching program Polygon also provides a protractor and ruler for measuring angles of assorted polygons.

Another DfES interactive teaching program, Ruler, provides a ruler for measuring lengths of assorted lines and polygons generated by the user.

-

I

BBC Bitesize Perpendicular Bisector

You can 'see' a compass at work on the BBC Bitesize web site as it shows how to construct a perpendicular bisector and again a teacher working at the 'enhanced interactive' level would look to collect ideas from pupils before showing the animation (that here sketches in the two arcs, but the compass is unseen).

A A

on.points of the. two arcs.

Postscript

The new toolbox to be found in EXP Maths for year 8 contains a 360' protractor as requested by a number of schools. In addition the protractors and ruler are used in a number of other activities. U

14 Mathematics in School, September 2004 The MA web site www.m-a.org.uk

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--------

Details of Resources Named Here EXP Maths http://www.nelsonthornes.com/secondary/maths/marketing/books_exp. htm

DfES Interactive Teaching Programs (ITP) http://www.standards.dfes.gov.uk/keystage3/publications/?template = do wn&pub_id=2535&strand=generic

BBC Bitesize perpendicular bisector example http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/locirev3.shtml

Keywords: Interactive whiteboards; Equipment.

Author Dave Miller, Keele University, Keele, Staffordshire. Over the last two years Dave Miller, Doug Averis and Derek Glover have been working on a Nuffield Foundation research project, Enhancing mathematics teaching through new technology : the use of the interactive whiteboard, with twelve schools looking at the use of interactive whiteboards in mathematics. Further details from http://www.keele.ac.uk/dept/ed/ian/

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Mathematics in School, September 2004 The MA web site www.m-a.org.uk 15

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