Intergrating Ict in the Teaching and Learning of Mathematics

PROGRAM BENGKEL ICT

DALAM PENGAJARAN DAN PEMBELAJARAN

MATEMATIKTahun 2008

23 FEBRUARI 2008

SIBER 1MAKMAL KOMPUTERSMK BUKIT GAMBIR

8.00 – 1.00 tgh.

ANJURAN:PANITIA MATEMATIK MENENGAH RENDAH

DAERAH MUAR

Jurulatih

En Lee Meow Choon

SMK Bukit Gambir

Guru Cemerlang Matematik

Pakar Perunding Mata Pelajaran Matematik dan Matematik Tambahan Negeri Johor

Pakar Perunding Pembinaan Item ( Matematik ) Negeri Johor

Jurulatih Utama Program MTDP, Bahagian Pendidikan Guru, KPM

Jurulatih Utama Geometer’s Sketchpad , Pusat Perkembangan Kurikulum, KPM

Integrating ICT in the teaching of Mathematics 1

MN

INTERGRATING ICT IN THE TEACHING AND LEARNING OF MATHEMATICS.

In the teaching of mathematics, we need to prepare exercises and tests that require us to draw diagrams. Thanks to the advancement made in MS Word , there are sufficient drawing features to address most of the drawing requirements. Rest assured that with a bit of practice , drawing is all but a breeze. Hope you will enjoy this session on drawing.

A. Drawing a circle and a triangle.

1. Locate your ‘Draw ‘menu bar as shown below. It may be docked at the top, bottom or The sides of the screen. If not, select the ‘View’, toolbar and click on the check box for Drawing.

3. To ensure a perfect circle or a square, hold down the shift key while drawing.

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2. When the mouse is over an icon, a pop up shows the function of the icon. Click on the oval icon to activate the drawing of a circle. A drawing canvas appears. Hit ‘Esc’ key to discard the canvas with ‘Create your drawing here’.( You can avoid the appearance of the canvas by highlighting the object drawn such as a line or a text box). The hollow N-E pointing arrow of the mouse turns into a solid hair-cross. Click on the right hand mouse to trigger off the drawing of a circle ( the centre), drag the mouse away from the center and release the right hand mouse to form the desired circle.

Similarly you may draw a Rectangle after you have activated the rectangle icon.

Without holding down the ‘Shift’ key while dragging the mouse

The ‘Shift’ key ensures a perfect circle and square

Hot Tips

To have a better control over the

smooth movement of points and lines,

hold down the ‘Alt –key ‘

1.Drawing with MS – Word

4. To enlarge the circle/square proportionally, select the object and

4.1 Drag the corner handle diagonally to increase or decrease the dimension of the circle /square. 4.2 Select format_autoshape then size. Under scale , check the locked aspect ratio ( it remains in proportion).Change the height only from the default of 100 % to the required change in size.

5. To extend or shorten a line in the same direction, highlight the line , hold down the shift key and drag the end handle ( the hollow small circle ) to extend its length.

Extend the length in the same direction

6. Click on Autoshapes _ lines and choose freeform Hit the right-hand mouse and release ( do not hold down ) to start the drawing and move the mouse to form the side of a triangle/ polygon and hit again to form the vertex and move to form the other side and finally close the triangle /polygon by double clicking.

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To ensure that all the lines remain parallel

3. Click the mouse to change direction

freeform

1. Click ONCE to start the drawing. Please do not hold down the right-hand mouse

2. Drag the mouse. It forms a straight segment

4. Double click to end the drawing mode

All these figures are drawn using freeform which can then be edited with edit points.

7. Draw a triangle in a circle as shown below.

It may not fit well. Highlight the triangle and select Draw_ Edit Point menu.( or select with left-hand click submenu). The vertices turn into little dark squares. Place the mouse arrow over the dark square and it turns into a net of a square shape. Drag it to perform the fine tuning of the vertices.

9. Select Draw, Autoshapes, More Autoshapes to get another collection of shapes.Locate the ¾ Sector of a circle ( at the bottom of the list )and click on it. A ¾ -sector is inserted into your document.

Select Shadow_ Style, No shadow , select Fill colour,_no_fill You may reduce the size by (a) Highlight the autoshapes, Format_autoshapes_Size to choose 30 % and checked the lock aspect ratio so that the shape remains the same. (b) Highlight the sector, drag the diagonal handle to reduce the size to the desired size.

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Vertices are touching the circumference accurately. It is best performed under 200 % view

Select Shadow Style_No shadow

Select Fill colour _No fill

Select format autoshape,_size,option lock aspect ratio

10. Move the sector to the vertex of a triangle . You may (a) Hold down ‘Alt’ key with right hand mouse to make ‘smooth’ movement. (b) Hold down ‘Ctrl’ key and move the arrow key ( nagging) to the desired direction.

11. Highlight the sector and drag the yellow handles to fit the arms of the angle. Fill with black colour.

B. Drawing a grid with x and y axes.

1. Highlight the rectangle icon and press ‘Esc’ to discard the canvas. Hold down ‘Shift’ key to draw a square. Select colour fill, no fill so that it is transparent.

2. While the square is still highlighted, hold down the ctrl key and move the mouse near the down right hand corner of the square. A small + sign appears. While holding down the right hand mouse, drag to make a duplicate and align it with the original square.

3. To select multiple objects you may(a) Highlight Select Object ( the arrow ) , hold down the right hand mouse and

drag diagonally to ‘box’ the objects. All objects in the box are highlighted.

(b) Hold down the shift key and click on the other objects. Multiple objects can be highlighted.

4. Repeat the process until you get the desired grid.5. Box to highlight all the grids and select Draw_ Group to group the grids into a

single grid. Now you can enlarge or shrink the grid proportionally and move the object freely ( Format_Autoshape_Layout_tight).

6. Highlight the grid, select line colour and pick the grey colour to tone down the grid.

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7. Select solid arrow to draw the axes on the grid.8. Select the Text box , the mouse arrow turn into a hair cross, hold down the right

hand mouse to draw a text box, type the labeling in the text box .Remember to select fill to no fill, line colour to no line such that the text box is transparent.

9. Duplicate the text box by holding ctrl key and the right hand mouse, retype the label.

10. The triangle is filled with 27 % transparency under the more fill colour mode.11. The y = x2 – 4 curve is drawn with Draw_Line , the curve line ( 4th selection ),

highlight it to edit points to get a smooth curve.12. The triangular shaded triangle under the curve y = x2 – 4 is drawn with freeform, edited by draw_ edit points, Draw_Order with send to back option.

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0 1 2 3 4

4

3

2 1

–1 –1 –2

x

y

y = x + 1

x

432

1

-3 -2 -1 0 1 2 3 4

y

y = x2 – 4

Curve to draw the curve

C. Drawing a 3-D solid

1. Use Autoshapes_Basics autoshapes as a guide, click on the autoshapes and drag with the right hand mouse to produce the autoshape . You may adjust the shape by moving the yellow handle.

2. Use autoshape_Lines_freeform to trace the object. Use Ctrl key + holding down the right hand mouse to duplicate the bottom layer. Change solid line to dashed line to indicate the hidden line.

3. You may transform the shape as shown.

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a b c

def

g h

i j k

Draw using freeform

Made transparent by 27 %

Draw_Order send to back

D Drawing a Globe.

1. Draw a perfect circle by holding down the shift key and the oval icon.2. Select Autoshapes_Basic shapes shape and pick the arc.3. Hold down the shift key and drag to draw a perfect arc. Drag the yellow

adjustment handle to form a 7/8 circle.4. Drag the bottom handle to squeeze the circle into a oval.

5. Drag the oval and adjust the size until it fits into a latitude.6. Hold the ctrl key and drag to make a duplicate.7. Drag the yellow adjustment handle to form the front latitude.8. Drag the duplicated oval onto the latitude, drag the handle in opposite direction to

form the posterior portion of the latitude.9. Select dash style to dashed style ( 4th selection ) to indicate the hidden latitude.

In the folder ‘Drawing with MS word’ , you are supplied with the drawings kept in different topic folder which are ready for use . Please browse through and try to explore how to draw each of them.

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SOME HELPFUL TIPS

1. Avoiding drawing canvas In MS word, a drawing canvas with “Create your drawing here” appears whenever you

start a new drawing.

If you don’t like the canvas ,you can uncheck the default. Select Tool_Options_General, the following dialogue box appears.

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Uncheck

2.Correcting spelling. In MS Word, if you misspelled a word, it will be underlined with red curvy line. (Assuming the check spelling is on ). To make the correction, just put the cursor on any of the character of the misspelled word, right click to get suggestions from the US-English dictionary, click on the word to get the necessary change.

Beware to ignore changes with US English spelling.

3. Use of format painter. Mathematical equations usually involve numerous superscript ( x 2) and subscript (mAB). It will be quite cumbersome to change variables to italic and the power to superscript.

(x + y) 2 – x2 –y2 = x2 + 2xy + y2 – x2 – y2

To change all variables x and y into italic x and y. highlight the x and select italic mode in the format toolbar, the x will be in italic. Look for the paint brush icon in the format toolbar and double click on the icon.(If you click once it will only work once.) When the cursor is in the writing area it change from a hollow NE pointing into a brush , just brush on any x and y and it will turn italic. Press ESC key to exit the italic mode.

(x + y) 2 – x2 –y2 = x2 + 2xy + y2 – x2 – y2

To raise the power to superscript, highlight 2, use the short cut key CTRL+SHIFT+”=” keys, use CTRL+”Z” to nullify the superscript mode. CTRL + “=” is the short cut keys for subscript.

(x + y) 2 – x2 –y2 = x2 + 2xy + y2 – x2 – y2

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The alternative way for superscript the character is by selecting Format_Font_effect_Superscript , check on superscript box .The character will turn superscript.

4. Layout of a picture or scanned object. Usually we insert a photograph, Graph image, scanned object into our text, it is quite often a nasty task to align with the text. Highlight the ‘picture’ and select Format_picture or right click when it is lighted and select format picture mode.

A dialogue box appearsand select layout , choosewrapping style as ‘Tight’, this enables you to movethe picture to any placeyou want. You may alsopaste into a text box suchthat you can move aroundin the document

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Check

mEAC

mEDC = 2.00

mEAC = 74.00mEDC = 37.00

Learning outcome : The angle subtended at the centre of a circle is twice the angle at the circumference.

1. Launch the Geometer’s Sketchpad Program.2. Use Compass tool to draw a circle with centre A and radius point B.3. Use Straightedge tool to construct segment CD. Note that when the mouse is

on the circumference, it is being highlighted. Click to make the end C ( snap to the circumference) and drag to a point D on the circumference.

A

BB

A A

BC

D

C

D

E

4. Continue to construct segments DE, EA and AC.5. Use Selection arrow tool to select points E, D and C (in anticlockwise direction) .

Select Measure_angle and a measurement of the angle is displayed as m EDC = 37.00o .

6. Repeat to select points E, A and C to measure the angle EAC. The measurement of the angle is displayed as m EAC = 74.00o .

7. Use Selection arrow key to drag point E along the circumference, note that both angles change accordingly.

8. Ask the pupils to guess the relationship between the angle at the centre and that at the circumference.

9. Select Measure_Calculate, a New Calculation pop up tool appear in the sketch.Click on m EAC = 74.00o and “÷” on the key pad and follow by clicking on m EDC = 37.00o, a computed value of the ration is displayed in the sketch.

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2.The use of Geometer’s Sketchpad in the teaching of Mathematics.

mEDC mEACmEAC

mEDC

37.00 74.00 2.00mEAC

mEDC = 2.00

mEAC = 74.00mEDC = 37.00

10. Use Selection arrow tool to select m EAC = 74.00o , m EDC = 37.00o and the ratio of the angles, select Graph_ Tabulate, the following table appears in the sketch.

11. Double click on the table will generate a new row of values. Use selection arrow tool to drag the point E. Notice that the values of the angles change accordingly but the ratio remains the same.

12. Repeat step 11 to generate a few more sets of values. It is obvious that the angle at the centre is twice of that at the circumference.

Based on the example above, we note that GSP is a very interactive and dynamic programme to use in the teaching of Mathematics. The easy tabulation of values in GSP make conclusion by induction a simple matter.

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1.To create a shortcut to Equation Editor 3.0 in the function toolbar.

1.1 Select Tools_Customize….a Customize dialogue appears as shown below

Click on Insert in Categories column and drag the slider to locate the Equation Editor and drag ( hold the right hand

mouse) the icon to the formula tool and release, the icon will remains at the formula toolbar.

2. When double clicked on the Equation Editor 3.0 icon , a floating toolbar and a blinking text box appears.In the editing mode - 2.1 No space is allowed in the formula, please insert empty element template of matrix. 2.2 The alphabets are italic by default, you may highlight and convert it into text ( non italic ), use the multiplication sign in the operator symbols . 2.3 Tap the Esc key to go back to MS word editing mode. 2.4 It is less time consuming if you duplicate the picture of Equation Editor by holding down ctrl key while highlighting the formula ( a small + sign appear near

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3.Microsoft Equation Editor 3.0

the formula )and drag and drop to the desired space. To edit it just double click on the formula to activate the editing mode.

3. Some frequently used templates

3.1 To insert a fraction or radical template and superscripts and subscripts.

Click on the fraction and radical template icon and select the required format.The template appears and type into the box as in MS word mode, use arrow key navigate or the mouse to navigate in the template. Similarly, use the super - sub scripts mode to insert power. Some examples are as shown below.

; ; ; ; ;

; ; ; ;

3.2 Fence template and Matrix template.

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Fraction and radical template

Superscripts and subscripts

Fence templateMatrix template

; ; ; ; ;

We can use matrix template ( 2 x 1) to insert spaces in between words in a formula.

3.3 Miscellaneous symbols and Greek characters ( Lower and Upper case)

; ;

3.4 Set theory symbols

; ; ; .

3.5 Summation or integral template

; ; ;

3.6 Relational operator

; ; ; .

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We can’t insert space in between

Highlight the word, select style_text

Use 2x1 matrix template to insert space

1. TC usually launched itself when we double click on the icon; OrTo highlight it, right-hand click on Autoplay to start when booted in the CD/DVD-ROM.Click on My Computer and Explore the disk

2. Double click to open the folder Lessons, the lesson folder leads to the Interactive folder and sub- subfolders of lessons.

3 Open the subfolder of the lesson, it contains a few clips of Flash files with .swf extension.

4 Look for .swf filesHighlight and copy to your intended lesson folder.

We need Flash8 or Flash9 ( Macromedia) to run the activeX file.If there isn’t any thing shown as its extension or the logo of Flash, chances are that it has no Flash program associated with it.1. First, install the Flash program and later highlight the .swf files, right click and select open with …. Browse to locate the installed Flash program.

5 It is advisable to rename the file so that it is

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Icon for the TC Autoplay

Explore

Lessons

Lessons

4. Integrating Teaching Courseware (TC)

easier to remember.

6 Launch the MS Powerpoint and open a new document.

7 To create an object –7.1 Draw a Text box7.2 Create a wordart7.3 Insert a picture7.4 Draw an Autoshape

Highlight the object and click on the icon of hyperlink

8 A dialogue box will pop-up. Locate the folder that was created. Click on the relevant

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.jpeg or picture file

To Create a new presentation

Create the hyperlink

files.

9 Save the presentation and in the Slide show mode ( You may launch with the F5 key )

When the mouse is on the “object”, a palm appears and when clicked, it will launch the Flash clip.

Here is another method of inserting the lesson video clip in MS Powerpoint.

1 You need to save a Powerpoint presentation in a folder that also contains the lesson Flash clips

Look for the control tool box; if it is not avalible in the task panel,Customise it or use View_Toolboxs_Task panel to open more control icons.

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An object to be associated with

Browse to the folder that was created.

2 The cursor in the slide become a hair cross, drag to enlarge the screen area; right click and a pop-up menu appears; select properties ,type the name of the Flash clip in the movie row that is to be inserted.

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More control

Select activeX objects