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TI-Time

TI-TimeSpring 2001

www.ti.com/calc/uk/

In this issue:• The CBL™ takes to the sky!

• Motivating Mathematics in Key Stage 3

• Control Experiments with CBL 2™

• Classroom Network Update

GENERAL INFORMATION: If you have general questions about using a product, to order products, or before returning a product for service:

CSC – Customer Support Centere-mail: ti-cares@ti.comPhone: 020 8230 3184Fax: 020 8230 3132Write to: Texas Instruments CSC, c/o SITEL · Researchdrive 4 · B-1070 Brussels, Belgium

EDUCATIONAL INFORMATION: For information on integrating hand-held technology and workshop ideas contact:

Guy Harris, your Educational Marketing Managere-mail: gharris@ti.comPhone: 01604 663 003Write to: Texas Instruments, 800 Pavilion Drive, Northampton, NN4 7YL

ContentsTest Flying the CBL . . . . . . . . . . . . . . . . . . . p. 3

Using the TI-83 Plus to solve problems in Higher Physics . . . . . . . . . . . . p. 6

Flash(ing) Technology – CBL 2 . . . . . . . . . . p. 8

A Christmas Postscript! . . . . . . . . . . . . . . . p. 9

The TI-83 Problem Page . . . . . . . . . . . . . . p. 10

Motivating Mathematics in Key Stage 3 . . . . . . . . . . . . . . . . . . . . . . p. 11

T3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 13

A Postcard from T3 Summer School . . . . . p. 14

Classroom Networks . . . . . . . . . . . . . . . . . p. 15

★ FREE★ Workshops & Demonstrations .p. 16

Instructional Dealer List / Credits . . . . . . .p. 16

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Introduction

Dear TeacherWelcome to the 16th issue of TI-TIME!

Numeracy is coming to secondary schools in England. The

National Numeracy Strategy has produced a draft document

"Framework for Teaching Mathematics: Years 7–9", which

runs to some 300 pages. This will be finalised and sent to

schools later this year.

The document makes it clear that the Y7–9 framework cannot

be taught without access to:

• calculators

• graphics calculators

• data-loggers

• dynamic geometry software

• graph plotting software

• spreadsheets

• Logo

• either Basic or the programming language in a

graphics calculator.

The document also covers issues like how the standards fund

can be used to buy additional equipment required, as well as

for training and software.

In parallel with this, T3 writers have been working hard on

new training materials over the last few months. They have

copies of the new draft framework, and are designing

training materials to reinforce the examples in the framework.

T3 has begun training KS 3/4 teachers in some leading

education authorities, and is looking for further authorities

to work with. Please see the article on page 13 for

further information.

There have also been some articles in the papers about a new

AS subject, "Use of Mathematics". This is apparently to be

based around the Free Standing Maths Modules, and will

require the use of technology in both teaching and

assessment. I hope it will also encourage more post 16 pupils

to continue their maths studies after GCSE.

National Training (in the use of technology) is moving forward

for maths teachers in Scotland. Materials are currently being

written, and reportedly bear a close resemblance to T3

Scotland training materials. Representatives of all Education

Authorities will be trained this summer. Those trained

will then develop plans to deliver further training to teachers

in their own authority.

THANKS to those of you who have contributed to this issue

with ideas and articles. Sharing articles in this way helps

bring new and creative ideas into other classrooms across the

United Kingdom and Ireland. If you have an activity that you

or your students have enjoyed, please share it with us!

You can send them to me at the address below.

Guy Harris

Educational Marketing Manager

Texas Instruments Limited

800 Pavilion Drive

Northampton

NN4 7YL

Phone: 01604 663003

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IntroductionOn 7 August 2000, T3 Scotland (Teachers Teaching with Technology™)began its third annual T3 Summer School in Perth. New this year was aseries of sessions for science teachers using the TI-83 Plus and CBL fordata logging and analysis. Since one of the great advantages of the CBLsystem is its portability, the science teachers1 wanted to take theirequipment ”in the field.” One of the authors, John Sharkey, who had justflown in from the Western Isles, agreed to make available his rented plane,a 4 seater Cessna 172 (with windows that can be opened in flight!) Weprepared two CBLs: one to take acceleration measurements, and the otherto record pressure, inside temperature, and outside temperature.

The Take OffWe used a low-g accelerometer probe made by Vernier Software2. Thisaccelerometer has an arrow printed on it that indicates the direction inwhich it measures the acceleration. As long as this arrow pointshorizontally the probe accurately reads the component of acceleration inthe direction indicated. But when the accelerometer is tilted, the reading isaffected by gravity. For example, when the arrow is pointed directly upwardthe probe will indicate an acceleration of one ”g” (9.8 m/s2) even when it is not moving. Knowing the actual acceleration requires that you know theangle of tilt of the accelerometer.

This was important in our experiment, because during take off an airplane’sangle of tilt (the pitch) changes as it climbs, and the plane banks during aturn. To avoid this tilt effect, the accelerometer was held horizontal duringall measurements by visually lining up the arrow with the earth’s horizon.During take-off, for instance, the accelerometer was pointed forward butkept horizontal so that the acceleration readings would be the actualforward acceleration. Of course, some allowances must be made for theoperator being a bit shaky at times.

Graph 1 shows the acceleration of the airplane during take-off. We tookmeasurements in intervals of 0.50 s for a total of 50 s starting when theplane began to move. The acceleration reaches about 1.9 m/s2 as theengines rev up and the plane begins to roll down the runway. As the planeapproaches take-off speed, the acceleration decreases to about 0.75 m/s2

until the plane lifts off about 30 s after the start. At this point much of theeffort of the engines goes into climbing rather than increasing forwardvelocity, so the acceleration shows a sudden decrease3. See Graph 1.

With the arrow pointed in the direction of motion the area under theacceleration curve is the total increase in speed. By summing therectangles represented by the acceleration for each time interval we founda total velocity change of 27.8 m/s. John tells us that take-off speed thatday was about 60 knots. 27.8 m/s is about 54 knots, so we are prettypleased with the agreement! See Graph 2 below.

Air PressureThe second CBL ran during the entire 30 minute flight, takingmeasurements with a pressure probe and two temperature probes. The pressure probe recorded the air pressure in kilopascals, kPa. Normalatmospheric pressure is about 101 kPa.

Richard L. Taylor, The Hockaday School, Dallas, TX, 75229. Email: rtaylor@tenet.edu

Test Flying the CBL™

Acc

eler

atio

n (m

/s2 )

time (s)

Graph 1:

Acc

eler

atio

n (m

/s2 )

time (s)

Graph 2:

z

Preparing for liftoff!

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Graph 3 shows the pressure through the trip. As we lifted off you can seethe air pressure drop. A plateau occurs as we reached a cruising altitude of 600 m (2000 ft). After flying at this level we began to climb to 900 m (3000 ft). The pressure doesn’t stay at a steady value because, to produceinteresting data for the accelerometer, John took the plane into a tight rightturn. To produce even more interesting data for the accelerometer, Johnthen took the plane, probes, and nervous passengers into a diving left turnthat quickly brought us down to about 300 m (1000 ft). You can see thesharp rise in the air pressure starting about 15 minutes into the flight. Wethen climbed back up to 600 m and flew at that altitude for a few minutesuntil another plane in the area induced John to drop to 450 m, from whichaltitude we began our landing back at Perth airport. Every altitude changeis tracked beautifully by the pressure probe.

Since we could use the graph to find the pressure at 0 m, 450 m, 600 m,and 900 m, we plotted the pressure against altitude, and the result was astraight line. The gradient of the line,

Pressure / altitude gradient5 -0.013 kPa m–1.

The International Standard Atmosphere4 (ISA) is a theoretical model of the Earth’s atmosphere in which pressure falls by 1mB per 30 ft (1000mB = 100 kPa), a gradient of -0.012 kPa/m. Not bad!

TemperatureWe also connected two temperature probes to the CBL, one for thetemperature inside the cabin and one for outside temperature. For thepassengers, who were more used to large pressurized cabins than theywere to small planes, sticking a probe out the window seemed an unusualexperience – but not nearly as unusual as other things that were to come!

You can see from Graph 5 that the temperature dropped as we rose inaltitude. In fact, it is astonishing how closely the temperature and pressure data track! It is almost as if you could measure altitude with a thermometer!

Shown in Graph 6 is the temperature of the inside of the plane. We had noair conditioning or heating turned on, so it’s perfectly reasonable that theinside temperature tracks with the outside temperature. The bumpsbetween ten and twenty minutes resulted from John opening the window(gasp!) to take pictures.

Relationship between Pressure and TemperatureThe similarity between the temperature and pressure graphs is so strikingthat it lead us to wonder how they might be related. We plotted a graph oftemperature versus pressure, and the result is shown in Graph 7 (at the topof the opposite page). Since the pressure went up and down together theyformed a graph that looks like a fuzzy straight line. We used the linearregression function on the TI-83 Plus to find the best fit line, and wegraphed the line to illustrate how close to the line most of the points reallyare. The regression coefficient is 0.964, indicating a strong positivecorrelation. Our best fit line had a gradient.

Pres

sure

(kPa

)

time (min)

Graph 4:

Out

side

Tem

p. (°

C)

time (min)

Graph 5:

Pres

sure

(kPa

)

time (min)

Graph 3:

Insi

de T

emp.

(°C)

time (min)

Graph 6:

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Temperature / pressure gradient = 0.61 ˚C / kPa.

Combining this with the pressure altitude gradient given in (1) producesanother interesting quantity,

Temperature4 altitude gradient = 0.61 }k°PCa}3 0.013 }

kmPa}5 0.0079 }

°mC}

The International Standard Atmosphere (ISA) is a theoretical model of theEarth’s atmosphere, and in it temperature falls by 2°C for each 1000 ft, a gradient of 0.0067 ˚C / m.

TurnsAbout 15 minutes into the flight, John warned us that he was about tobegin a level right turn. The accelerometer was kept level and pointed tothe right during the 10 second turn. After the turn (and after thepassengers thought they were through with that funny feeling), John began a diving right turn, dropping nearly 300 m and maintaining the turn for nearly 35 seconds. (Whew!) The initial positive acceleration for the right turn goes to an impressive 1.1 g, while the more leisurely left turn peaks at 0.82 g, see Graph 8 below.

Classroom RelevanceThe greatest part of all this, of course, is the new questions that arise. Whydoes the temperature fall as you go up? Could you really use a thermometerto measure altitude? What assumptions would be involved? Do therelationships that we found continue for higher altitudes? How would thisbe different if we were flying in a cloud?

While this is all great fun, interpreting graphs of this sort is an extremelyvaluable exercise for our science and maths students. If a student can lookat the pressure graph (without the notes on the graph!) and see where theplane is gaining altitude and where it is diving; if a student can look at thetemperature/time graph and the pressure/time graph and predict that atemperature/pressure graph will be a straight line; if a student cancorrectly interpret the meaning of the gradients and compare them tostandard values; if a student can see the area under the acceleration graphas accumulated velocity – then the student must have a real understandingof graphs.

For us these data and graphs are especially fun because we flew in theairplane, and we can use our personal experience to excite our students.But graphs like these can be found all over. Data can be taken riding a lift,on the playground, at an amusement park, or just riding in a car. No graphis as exciting and motivating as the one the students make for themselves.With the CBL™’s ability to take data anywhere, the entire world becomes the classroom.

Notes:1 Participants in the evening flight included pilot John Sharkey, Richard Taylor,

Gay Taylor, and Texas Intruments’ Guy Harris. Hamish Budge provided

ground support.2 Vernier Software is on the web at http://www.vernier.com.3 We have made an adjustment in the data for a 0.09 g bias in the accelerometer .4 For further information, and a really cute online calculator, see the Department

of Aeronautical Engineering, University of Sydney, Australia, at

http://aeroserver.aero.usyd.edu.au/aero/atmos/atmos.html

Author: Richard L. TaylorThe Hockaday SchoolDallas, TX, 75229USAEmail: rtaylor@tenet.edu

Photos: Gay Taylor

Out

side

Tem

p. (°

C)

Pressure (kPa)

Graph 7:

Acc

eler

atio

n (g

)

time (s)

Graph 8:

Interpreting the results (on terra firma!)

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John Sharkey

Using the TI-83 Plus to solve problems in Higher Physics

Many numerical problems in physics can be solved more easily with theuse of a calculator. Often the calculator is used to "do the sums" at the endof the problem. The TI-83 Plus is an advanced (Graphing) calculator whichcan be used to help solve physics problems at earlier stages of the solution.The notes that follow show how the calculator can be used in this way.Several typical numerical problems are solved.

ProblemA helicopter is rising vertically at 10 m s –1 when a wheel falls off. The wheel hits the ground 8 seconds later. Calculate at what height the helicopter was flying when the wheel came off.

This problem can be solved using the equations of motion and a competentstudent should be able to complete it in several minutes. However, thisparticular problem is one in which it is difficult to visualize the path of thewheel. The graphing facility of the TI-83 Plus is particularly helpful inunderstanding the problem. The student is likely to gain a betterunderstanding of the underlying physics.

STEP 1: Enter the information that is given in the problem

Enter the following into the calculator:® ÷ ß U ∏

This stores the initial velocity u of the wheel (and the helicopter) in thecalculator memory as U.

∑ o ∂ n ß A ∏

This stores the acceleration a of the wheel in the calculator memory as A.Note that the initial direction of the wheel is UP, so we define the positivedirection as UP. Gravity always acts DOWN, so the acceleration due togravity is entered as a negative number.

Also note that the "make negative" ∑ key is pressed rather than thesubtract key.

STEP 2: Enter the equation to be used into the calculator.

The equation to be used is s5 ut1 }12} at 2

Graphing calculators handle equations and can plot graphs of y against x.

The equation will be stored in the calculator memory as a variable Y1

which is a function of x.

Enter the following into the calculator:# U ´ µ ∂ z A

STEP 3: Use the calculator to solve the problem

Return to the Home screen by pressing 2

We now solve the problem to find the displacement s when the time is 8 seconds.

Enter the following into the calculator: ∏ ∏

ALPHA

ALPHA

VARS ˙

ALPHA ALPHAX,T,Θ,n X,T,Θ,n x 2

QUIT

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Now enter the time 8 s which will be the x variable by pressing c n d ∏

The answer, -233.6 m appears on the screen. Remember the negative signtells us that the displacement of the wheel is DOWN. The displacementcorresponds to the height of the helicopter when the wheel was released. The displacement of the wheel at any time can now easily be found.Try finding the displacement of the wheel in successive seconds afterrelease. A clearer picture of the motion of the wheel should now emerge.The table function can also be used to view multiple time values:

Press 2

A good idea would be to plot a graph of the displacement of the wheelagainst the time of flight. The calculator can do this for us.

Step 4:Solve the problem graphically

Press and you will probably get some kind of graph but it is unlikelythat it will be helpful. We need to set up the graph axes.

Press and set the axes as shown:

An alternative is to use the button to zoom into the significant part of the graph.

Press . The graph is of the displacement against time. The axescould be labelled but for the purposes of solving the problem it is not necessary.

Now we have a clear picture of the motion of the wheel. As it falls off,the helicopter it is still moving up. It decelerates (accelerates down) to a maximum height then accelerates down.

Press 2 ∏ n ∏ to calculate the value at time 8seconds.

The answer (-233.6m) is displayed.

Try finding the displacement of the wheel in successive secondsafter release.

Another way of exploring the motion of the wheel is to use the button.

Press and use the blue cursor buttons to move the flashing cursoralong the curve. (It may start off the curve to the right). The x and y values(s and t) are displayed at any point on the curve.

There are more ways yet of analysing the graph.

Press 2

Choose MAXIMUM and move the cursor to the left of the maximum, thenpress ∏. Next move to the right and press ∏. Lastly move thecursor close to the maximum. On pressing ∏ the calculator will findthe highest point reached by the wheel.

As a last example, try choosing }ddyx} from the CALC menu.

The calculator will display the gradient of the curve at any point. What is represented by the gradient of displacement / time graph?

John Sharkey is the secondary advisor for the Western Isles Council.

E-mail: jsharkey@cne-siar.gov.uk

ZOOM

GRAPH

TRACE

TRACE

TRACE

TRACE

GRAPH

WINDOW

GRAPH

CALC

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Adrian Oldknow

Flash(ing) Technology – CBL 2™

The CBL 2 differs from the original CBL™ in a number of ways. One of the big changes is that it has a huge amount of so-called Flash-ROM memory,which means that it can be used as a mass memory store, like a sort ofhard-disk, for graphic calculators. Externally, it no longer has a LCD screenwith which to communicate, but instead it has red, yellow and green LEDs,together with a buzzer. These can be programmed from whichever graphiccalculator is attached. So some of the simple control experiments familiarfrom some technology syllabuses can be tackled just using the CBL 2without any additional hardware. Here we will try to develop a traffic light simulation program using its built-in LEDs.

You control the CBL 2 by sending it lists. The list {1998,L,S} is used tochange the state S of one of the LEDs L. L can be: 1 for Red, 2 for Yellow or 3 for Green, and S can be 1 for On or 0 for Off. So we can write a verysimple program, ONRED, to turn the Red LED on, as in Fig. 1

Fig 1

Use the PRGM's I/O menu to find the command Send(, as in Fig. 2.

Fig 2

You will need to write similar programs called ONAMBER and ONGREEN. If we want to avoid draining the CBL 2's batteries completely we will also need to write programs to turn each LED off, such as OFFRED in Fig. 3 below.

Fig 3

In addition to the six On and Off programs we will also need a delayprogram, such as WAIT, which just uses a counted loop controlled by avariable W whose value will need to be set in the calling program. Byexperiment I found that a value of 10000 for W seemed to produce a delayof 30 seconds, so if we pass a value of W in seconds we will need tomultiply it by about 333 to control the loop, as in Fig. 4.

Fig 4

So we can now build up a main program, called SEQUENCE, to perform oneset of changes from Red, through Red/Amber to Green, and then throughAmber back to Red. We just need to decide on the values to use for W tokeep each combination of lights on at each stage. My version uses thefollowing values:

Red: 7 seconds

Red & Amber: 2 seconds

Green: 6 seconds

Amber: 2 seconds

Fig 5

8

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9

Fig 6

To call another program as a subprogram use the EXEC menu from PRGM as in Fig. 7.

Fig 7

Finally you could incorporate SEQUENCE as a subprogram of a mainprogram, such as TRAFFIC, Fig. 8. Here the sequence is performed 5 times. The list {0} is sent at the start to clear the CBL 2.

Fig 8

With any luck this might suggest other projects you could carry out withthe coloured LEDs, such as "disco lights", or using them to display the 3digit binary equivalent of numbers between 0 and 7.

You might also like to attempt projects using the CBL 2's tone generator,with or without lights. Here the basic technique is shown in thesubprogram TONE, Fig. 9. The list {1999,D,N} is used to make the CBL 2sound a tone whose semi-period is N, for a duration of D, where both aremeasured in units of 100 micro-seconds. TONE uses values L and H setoutside the program. L is the duration in seconds and H is the frequencyin Hertz.

Fig 9

Well, happy flashing and buzzing! I'm sure the editor would be glad to hearof any interesting projects which students develop using these techniques.

Adrian Oldknow is the Visiting Research Fellow, School of Education, King's College, University of London

Email: a_oldknow@compuserve.com

A Christmas Postscript!

Many thanks to Richard Smith for providing the following program whichshould put the CBL 2 into the Christmas spirit. The list L1 holds the relativedurations of the notes, which are multiplied by the constant K to convertthem into the CBL units of 100 microseconds. The list L2 holds thecorresponding frequencies of the notes.

{2,2,1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,1,1,1,1,2,2,1,1,2,2,2,2}→L1

{182,136,136,121,136,144,162,162,162,121,121,108,121,136,144,182,182,108,108,102,108,121,136,162,182,182,162,121,144,136}→L2

1500→KK*L1→L1

For(N,1,30,1)Send({1999,L1 (N),L1 (N)})End

yy

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Alan Graham

The TI-83 Problem Page

Time for a calculationQ How can I perform time calculations (involving in hours,

minutes, and seconds)?

A Like most graphical calculators, the TI-83 can perform anglecalculations in degrees, minutes, and seconds using the Angle menu.These can be easily adapted to perform time calculations.

For example, add 2 hr. 25 min. 15 sec. to 4 hr. 55 min. 55 sec. and display the result in DMS (degrees,minutes, seconds) notation by pressing:2 2 1 25 2 2 15

" ´ 4 2 1 552 2 55 " 2

4 ∏

Median-Median LineQ I see that Option 3 of the STAT CALC menu is the Median-Median

line. I presume that it is some sort of regression line for paired databut what exactly is it?

A Until recently I wasn’t too sure myself. I have always assumed that theMedian-Median line was formed by separating the points of thescatterplot into two equal halves (left and right) and joining themedians of these two sets of points. However, after checking the TIwebsite (dial up www.ti.com and then follow the TI&ME option toreach the TI-83 discussion group), I discovered that it is a bit morecomplicated. The algorithm to which the TI-83 is programmed can bebest understood by going through the following stages:

(a) The paired data are split into three equal sets of points – call them‘left’, ‘middle’ and ‘right’.

(b) A line is drawn to join the median of the ‘left’ points with themedian of the ‘right points.

(c) A second line is drawn through the median of the ‘centre’ pointswith the same slope as that of the first line.

(d) A third line is drawn one third of the way between the first andsecond of these lines, again with the same gradient. This is theMedian-Median line.

As the web-site entry observes, an advantage of the median-medianline over a least-squares regression line is that stray data points do notaffect the end result very much.

Same final digitsQ I’ve been working on number investigations with my class. One that

caught their and my interest was the following: ‘For what numbersdo X and X5 have the same last digits?’ Any suggestions for tacklingthis on the TI-83?

A Basically you need to generate two sequences, namely X (taking values0, 1, 2, 3, …) and, alongside, the corresponding values of X5. However,before rushing into creating lists or writing a complicated program, it isworth exploring how this can be done more simply on the Homescreen. Here is a possible first draft solution to the problem.

The first command stores 0 in X. The next two commands (linked by thecolon) increase the value of X by 1 andthen display, side by side, the currentvalues of X and X5.

Each press of ∏ generates thenext value.The user simply compares the final digits visually.

This solution may be sufficient for less experienced pupils but if they arelooking for something more challenging, here are two extra features theymight include.

(a) The final digitIt is possible to tweak out the valueof the final digits of the X and the X5

and let the calculator make thecomparison directly. The firstchallenge here is how to reduce a given integer to its final digit.Experimenting with the fPartcommand (which finds the fractional part of a division) using a divisorof 10 might suggest to them that the command 10*fPart(X/10) will dothe trick.

(b) The = commandNext they might like to use the Testmenu to compare the final digits ofX and X5. This will require use of theequality command from the Testmenu. If pupils are unfamiliar withthe Test menu, this is somethingthat would be well worth exploring.Where the given statement is true, the output value is 1, otherwise it is 0.

All that is required now is to apply the equality command to the final digits of X and X5, thus:

The first displayed output valueinside the curly brackets showswhether the equality is true. Thesecond and third values are,respectively, X and X5. It will quicklybecome apparent that the result isalways true. However, this solutionis easily adaptable to other questions of a similar form. For example:‘For what numbers do X and X3 have the same last digits?’

Alan Graham works at the Centre for Mathematics Education, The Open University, (e-mail: a.t.graham@open.ac.uk).In association with Barrie Galpin, he is author of the two ‘CalculatorMaths’ series of books written for the TI-80 and TI-83 respectively.

ANGLE ANGLE

ALPHA ANGLE

ANGLE ALPHA ANGLE

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Kerry Horstead and Roger Fentem

Motivating Mathematics in Key Stage 3

Aspiring secondary mathematics teachers in their first year oftraining on the B.Ed. (Hons) course at the College of St. Mark andSt. John (Marjon) spend four weeks in school at the end of theyear practising the theory they have covered in College. Some ofthe theory concerns the role of graphing calculators in teachingand learning mathematics. Kerry Horstead was just such astudent. She wrote the following of her teaching experience in aCommunity College.

"I have found the experience very enjoyable, hard work butextremely eye-opening to the policies in schools and theattitudes of staff and pupils alike. However I have decided towrite this report about the use of technologies as it seemed very appropriate, as the Community College has been grantedtechnology status from September.”

The Community College had just had a class set of TI-83 calculatorsdelivered along with a CBR™ (Calculator-Based Ranger™ – motiondetector) and ViewScreen™ for use on an over-head projector. When Istarted the practice at the school, mention was made of the delivery of thecalculators, but due to paperwork and other commitments there hadn’tbeen the time found for anyone to explore the new technology.

I decided to take in my own TI-83 (all students on the course at Marjon aregiven one for their use on the B.Ed. course) to show my professional tutorthe few programs we had explored in Marjon. I thought that they would beappropriate to use with Key Stage 3 pupils. I was very pleased by theresponse; my ideas on how to use the programs were greeted with muchenthusiasm. I was allowed to raid the storeroom and use whateverequipment I thought I would need. It was like Christmas, unpacking all thisbrand new technology and being allowed a free rein to set it up anddemonstrate how I thought it was appropriately used.

The program I chose to use initially was called APE. Children need toengage in problem solving and to know their tables (up to 9 by 9). Thisinvolves children reassembling two pictures of mixed up apes by use of a multiplying controlled grid system. The choice of tables provides for differentiation.

The first group where I used this program were a bottom set, year sevengroup. I wasn’t sure how they would respond as a calculator producingapes is not quite as exciting as a game boy or games console. Children, andadults alike, who are intimidated by mathematics and calculators, miss thepoint that programmable graphical calculators are capable of running quitesophisticated pedagogical programs.

I was stunned by the response of this group – they absolutely loved it. This group were struggling to make headway in mathematics and did not seem particularly interested in the subject, but they responded withenthusiasm and vigour. Even notorious individuals were captivated intoworking out strategies to solve the problem posed. I was extremely pleased with this as my first experience of introducing graphing calculatortechnology to pupils. I was encouraged to keep the activity alive andengage other groups with it.

The next group I attempted to use the ape program with was a differentexperience altogether. This was a middle set, year nine group, whoweren’t going to be so overly impressed by an ape-producing calculator.Although most individuals seemed to enjoy the descision making andproblem solving the program requires, a few individuals were obviouslybored by the whole process. I think the only attraction to those pupils inthe program was the lack of writing they had to do in this particular class.

I decided to switch tack and change the nature of the challenge. I chose touse the CBR and the ‘walk this way’ program. It was as though someonehad thrown a switch. As the challenge became more physically demandingthe entire class warmed to the experience and I had a hard job sorting outthe order in ‘who goes next?’ Although interpreting graphs is a big part ofthis program, which incidentally tied in well with their current topic, thepupils went ahead with great gusto at working out how to follow the lineson the graph first before walking it.

The memory of the day was when a particularly difficult young ladydecided she would have a go, but the graph changed from a walking awayfrom to a walking towards one, this pupil instantly recognised the changein tact and walked a near perfect graph. She was obviously quite pleasedwith herself but ‘street cred’ being what it is decided not to show it.

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The fact that this pupil had shown a glimmer of talent, and moreimportantly interest in the subject, was the breakthrough of the day at leastif not the week.

The next group I used the ape program with was a top set, year seven; they were enthusiastic at the start, although the ‘rules’ took someunderstanding. Once they had mastered the art of the rules they wereextremely quick in developing strategies to cope with solving both apes atonce. They had soon run through the program twice in a very short space oftime. Retrospectively that would have been the best time to stop, as thethird time round prove tedious as the children lost interest very quickly.

Even so, one usually disruptive child was extremely taken with the program– so much so that there was a risk of distracting others in the class.

This program certainly reaches the parts other mathssessions normally don’t!

Trying out this technology in school has been an interesting and thought-

provoking experience. I was extremely pleased to be able to introduce this

technology to a school in the first instance. My observation in schools

suggests that the children have become blasé if not complacent about the

use of computers and calculators in the classroom. It was incredibly

refreshing to see the reaction to the TI-83 and the CBR in action. The most

rewarding part of introducing the pupils to the technology was the

enthusiasm, on most parts, with which it was greeted and hopefully their

new relationship will thrive and prosper into the future.

CBR is an electronic device which measures distance using sound wavesand simultaneously records the times of the measurements. The CBR plugsdirectly into a TI graphing calculator which can then display the distancesmeasured. The display may be in graphical form or purely numerical. Itcomes with its own program called RANGER or you can use other tailor-made programs (as in Kerry‘s case – she used a suite of programs availableon the TI web site: www.ti.com/calc/uk

Kerry Horstead is a trainee teacher on the B.Ed. (Hons) course at theCollege of St. Mark and St. John, Plymouth.

Roger Fentem is a senior lecturer in Mathematics Education at the College of St. Mark and St. John, Plymouth

E-mail: Rfentem@marjon.ac.uk

CBR™ (Calculator-Based Ranger™)

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T3 – Teachers Teaching with Technology™

T3 ScotlandT3 Scotland delivers Hand-heldTechnology Courses that are :

• Delivered in partnership with Education Authorities• Delivered by current classroom teachers• Designed to meet the needs of Scottish Teachers • High quality content developed in Scotland

★ FLEXIBLE OPTIONS – half day, one day, two day, summer school

Teachers:• Become familiar and comfortable with Technology• Get help with introducing technology into

mathematics teaching

For more information about T3 Scotland courses, please contact Ian Forbes:

Phone: 0131 651 6034e-mail: ian_forbes@education.ed.ac.ukAddress: Faculty of Education

Dept of Curriculum Studies: S T M CMoray House Institute of EducationThe University of EdinburghHolyrood RoadEdinburgh EH8 8AQ

We are pleased to announce that T3 in England, Wales and NorthernIreland is now offered in partnership with the Mathematical Associationand co-ordinated by their Professional Development Officer, Rosalyn Hyde.

We are now offering the following courses:

• Mathematics at Key Stages 3 and 4• Data Handling in Maths and Science for Secondary Schools• Numeracy and Transition at Key Stages 2 and 3 (TI-73)• Data Handling in Science at Key Stage 3

The recently published draft national Numeracy Strategy for Key Stage 3makes it clear that graphics calculators have a key role to play in teaching and learning at Key Stage 3. All T3 materials are written byexperienced educators in line with the National Numeracy Strategy,National Curriculum and G.C.S.E. criteria. Training sessions are hands-onworkshops given by trainers experienced in using hand-held technology inthe classroom. The courses cover basic operation of the calculator anddata loggers, ideas and materials for use in the classroom across theattainment targets, practical help in managing the use of ICT in teaching

and learning, and discuss the impact of technology on teaching. We arealso able to offer short introductory sessions for teachers, as well as longercourses in a variety of formats.

A key part of our strategy for training and supporting teachers in usinghand-held technology is to work in collaboration with Local EducationAuthorities. An important way forward for this partnership is for T3 to traina team of local teachers to become trainers in their L.E.A. Those authoritiesalready working in partnership with T3 have been able to select anappropriate focus for their area from the list of available courses, teachersto act as trainers and to plan a strategy to develop the appropriate use ofhand-held technology in their area.

If you are interested in more details, please contact Rosalyn Hyde:

Phone: 023 8051 0674e-mail: hyde@tcp.co.ukAddress: 158 Dale Valley Rd

Southampton SO16 6QW

T3 England, Wales and Northern Ireland

14TI-TIME

We arrived by train,boat and plane – just as the song says, from all cornersof Scotland. From Wick in the far north to Lewis in the west, Lockerbie inthe South West to Elgin in the North East, from the Highlands to thecentral belt, Lothian, Strathclyde and the Scottish Borders. 30 of us in all,ready to work and play – hard.

The course was run in two groups:• Elementary for those with limited experience; and, • Intermediate for the more advanced.

This worked most effectively. The duplication of some classes allowed for a good mix.

A group of Scientists were on the course as well –some of these went airborne on the Mondayevening (two of them having flown in from Lewisthat day) to collect data on the CBL, which we allgot the chance to see at the workshop on theCBL™/ CBR™ the next evening. Amazing!

The sessions covered the use of the TI-83 Plus’s own facilities –MATRICES, DRAW, MATH, VARS, CALC and complex numbers as well as the chance to look at some of the vast array of programmes andworksheets available, from 5–14 Numeracy to NQ Statistics, thanks toMadMaths. Opportunities to link calculators and share programmes. There was an introduction to programming and a chance to see the CAS facility on the TI-89. Indeed something for everyone !

A visit to Perth College allowed us to gain experience in the downloadingof applications/programmes from the internet – one of the main benefits ofthe FLASH Technology inbuilt in the TI-83 Plus.

The social side of the course was every bit as much fun as the coursecontent, and allowed us to make some good friends.

Mention must be made of Stella's flying lesson! Since the course wastaking place at Perth Airport, Stella was determined to have a flying lesson.

Ruth and Jay were arm twisted to accompany her – but boy it was worth it.The views of the beautiful Perthshire countryside took our mind off the factthat Stella was indeed flying the plane for a while herself!

The Tuesday evening was Quiz Night!, the Grand Prize being two TI-83 PlusViewScreen™ kits. This was won admirably by a husband and wife team from West Lothian, teachers at St Margaret’s and Linlithgow. Ruth wasthouroghly delighted to know that she could remember the names of theAlexander Brothers! (Tom and Jack for those of you who didn’t know!!) By a strange coincedence when she arrived home it was to find that the said duo are to appear in the Macphail Centre in Ullapool, her home town, on September 8th!!!

See you next year!

����������������� ��������

The T3 Scotland Summer School was held at Perth Aerodrome, part of a Perth College, from 7–9 August 2000.

Ruth Clark, Jay Donald, Stel la McKague, Gi l l ian Pr ingle

A Postcard from T3 Summer School 8

N

★ 2001 Summer School will be held in the Perth area in late summer 2001 ★Please contact Ian Forbes at 0131 651 6034, or e-mail ian_forbes@education.ed.ac.uk for details.

15TI-TIME

Nevi l Hopley

Classroom Networks

I have been involved in delivering sessions for PGCE students since 1997 andearly in 2000 I became involved in the T3 (Teachers Teaching withTechnology™) programme that centres on developing teachers’ skills withgraphical calculators. I have also written a number of stand-alone tutoringprograms which are now extensively used within my department and now inseveral other schools in Scotland. This background made me a goodcandidate to get involved in a pilot project that links graphical calculatorstogether using the Internet in a similar way to existing computers.

The appropriate hardware was installed in my classroom last year. This wasone of the first calculator networks installed, although there are morerunning now, including some in England and other parts of Europe.

The classroom setup has TI-83 Plus’s connected to the Internet by cablessimilar to those used for TI-GRAPH LINK™. The school network also has a"Concentrator Gateway" utility running that allows direct communicationbetween these calculators and a web site in Texas. The teacher’s calculator isalso linked to this website and user-entered identity numbers and passwordshelp the site detect who is a "student" and who is a "teacher".

As well as other teachers in the USA, I have been writing programs that takeadvantage of the features that such a link up makes possible. Here is oneexample of what is now possible: First I send the class a set of configuredaxes so that their screen looks identical to mine. I then instruct them to sendme a point where "the y-coordinate is double the x-coordinate". Each studentmoves their arrow to a point on the plane which they think satisfies my statedcondition. This point is sent and all of the class’s points are displayed on theteacher calculator’s axes, which everyone can see via a viewscreen. Resultsvary from a random scattergram to a perfect straight line! It’s interesting tosee who strays into which quadrants, and who sticks near the origin! Usingthe Trace feature, the teacher can identify who sent which point. This really isa case when there is more than one answer!

However, the great strength of the system is that everyone in the class isinvolved and they each have their own unique identification number, whichonly they and the teacher knows. As a result, no-one knows what others sent in and so the class can respond to what it sees without bias or blame or shame.

The speed at which all the answers are collated and displayed make for a veryengaging lesson! In fact, any data can be sent to and from the teacher andstudent calculators – strings, lists, functions, single real variables, pictures –it’s use is limited only by the questions that can be put to a class.

It can also facilitate swift sharing of results. Have every student send in asingle number (or experimental result). These are then collated and stored inlists on the teacher calculator, which can then in turn be sent back to thestudents’ calculators. Each student then has the full class set of data withwhich they can do their own, independent statistical analysis.

We have regularly been told that open-ended questions that invite creativeresponses are the best to ask students who are learning mathematics, but ithas been very difficult to practically collect all the varied responses from aclass without the pace of the lesson being severely impaired. The ClassroomNetwork is excellent at quickly gathering everyone’s answers and allowingthem to be displayed and shared in a meaningful fashion – it really is making

me think long and hard about good questions to ask students that stimulateand support their understanding.

I am currently very much involved in the continuing development of this newprogramming environment and one of the programs that I have designed isgoing to be used to demonstrate the system’s capabilities at conferences forTeacher Trainers in the USA. The system will also be on show at the BETTExhibition, London in January 2001 and I shall be talking about it at the SMCStirling Maths Conference in May 2001.

This November, I took delivery of a new wireless hub system that uses radiowaves to send and receive the information with the Internet, instead of thelarge numbers of cables that it currently uses – this will greatly ease thesetup and use of the system with a large class of students – no cables forthem to stand on or trip over!

In conclusion, this is a fantastic opportunity to trial the next generation ofeducational technology that will help deliver our subjects, using hardwarethat we readily have at our disposal.

Nevil Hopley is Head of Mathematics at George Watson's Collegein Edinburgh.

E-mail: n.hopley@watsons.edin.sch.uk

Title page – from this you can choose many options....

teacher chose to send axes configuration

and it’s now been sent

student calcs show the retrieval process

and then they can plot a point to send back to the teacher

the teacher collects theclass’s points

and they are displayed (here we have a class of 3 students!)

EXAMPLE: The Link activity

All products available in Europe are manufactured to ISO 9000 certification. Calculator-Based Ranger, Calculator-Based Laboratory, CBR, CBL, CBL 2, DERIVE, EXPLORATIONS, StudyCards, TI-GRAPH LINK, TI InterActive!, TI-Presenter, T3, Teachers Teaching withTechnology and ViewScreen are trademarks of Texas Instruments Incorporated. Cabri Géomètre II is a trademark of Université Joseph Fourier. Mac and Macintosh are registeredtrademarks of Apple Computer, Inc. IBM is a registered trademark of International Business Machines Corporation. Windows is a trademark of the Microsoft Corporation. MS-DOS is aregistered trademark of the Microsoft Corporation. Texas Instruments reserves the right to make changes to products, specifications, services and programs without notice. Printed onrecyclable 100% chlorine-free paper by Thamesdown Colour Limited, UK. Desk Top Publishing – Cloud 9 Publishing Limited, UK.

©2001 Texas Instruments Incorporated

CL2001NLM1/UK

CSC

www.ti.com/calc/uk/ ti-cares@ti.com

Customer Service CentrePhone: 020 8230 3184 – For Teacher Express Service,

press 84 after calling the CSCFax: 020 8230 3132E-mail: ti-cares@ti.com

Instructional DealersAddex Limited (Ireland) 1460 0046 Comcal 0141 332 5147George Waterstons & Sons Limited 0131 553 1154 Jaytex 0161 831 7585Oxford Educational Supplies 01869 344 500 Science Studio Limited 01993 883 598Shaw Scientific Limited (Ireland) 01 450 4077

★ FREE★Workshops

and DemonstrationsWe can send an instructor to your school or education authority to help support the use of Texas Instruments technology in education!

Training courses are available from an introductory two hour session to full length in depth courses in a variety of curriculum areas.

In England, Wales or Northern Ireland:Ring Rosalyn Hyde on 023 8051 0674

COURSES INCLUDE:Mathematics at Key Stages 3 and 4

Data Handling in Maths and Science for Secondary SchoolsNumeracy and Transition at Key Stages 2 and 3 (TI-73)

Data Handling in Science at Key Stage 3

In Scotland:Ring Ian Forbes on 0131 651 6034

T3 SCOTLAND OFFERS HAND-HELD TECHNOLOGY COURSES:Delivered in partnership with Education Authorities

High quality content developed in Scotland Taught by current classroom teachers

Flexible options – half day, one day, two day, summer school