TI-Time. In this issue: The CBL takes to the sky! Motivating Mathematics in Key Stage 3 Control Experiments with CBL 2

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1 TI-Time In this issue: The CBL takes to the sky! Motivating Mathematics in Key Stage 3 Control Experiments with CBL 2 Classroom Network Update Contents Test Flying the CBL p. 3 Using the TI-83 Plus to solve problems in Higher Physics p. 6 Flash(ing) Technology CBL p. 8 A Christmas Postscript! p. 9 The TI-83 Problem Page p. 10 Motivating Mathematics in Key Stage p. 11 T p. 13 A Postcard from T 3 Summer School..... p. 14 Classroom Networks p. 15 FREE Workshops & Demonstrations.p. 16 Instructional Dealer List / Credits p. 16 GENERAL INFORMATION: If you have general questions about using a product, to order products, or before returning a product for service: CSC Customer Support Center ti-cares@ti.com Phone: Fax: Write to: Texas Instruments CSC, c/o SITEL Researchdrive 4 B-1070 Brussels, Belgium TI-Time Spring 2001 EDUCATIONAL INFORMATION: For information on integrating hand-held technology and workshop ideas contact: Guy Harris, your Educational Marketing Manager gharris@ti.com Phone: Write to: Texas Instruments, 800 Pavilion Drive, Northampton, NN4 7YL

2 Introduction Dear Teacher Welcome to the 16th issue of! 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. 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 T 3 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. In parallel with this, T 3 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. T 3 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. Guy Harris Educational Marketing Manager Texas Instruments Limited 800 Pavilion Drive Northampton NN4 7YL Phone:

3 Richard L. Taylor, The Hockaday School, Dallas, TX, Test Flying the CBL Introduction On 7 August 2000, T 3 Scotland (Teachers Teaching with Technology ) began its third annual T 3 Summer School in Perth. New this year was a series of sessions for science teachers using the TI-83 Plus and CBL for data logging and analysis. Since one of the great advantages of the CBL system is its portability, the science teachers 1 wanted to take their equipment in the field. One of the authors, John Sharkey, who had just flown 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!) We prepared two CBLs: one to take acceleration measurements, and the other to record pressure, inside temperature, and outside temperature. Graph 1 shows the acceleration of the airplane during take-off. We took measurements in intervals of 0.50 s for a total of 50 s starting when the plane began to move. The acceleration reaches about 1.9 m/s 2 as the engines rev up and the plane begins to roll down the runway. As the plane approaches take-off speed, the acceleration decreases to about 0.75 m/s 2 until the plane lifts off about 30 s after the start. At this point much of the effort of the engines goes into climbing rather than increasing forward velocity, so the acceleration shows a sudden decrease 3. See Graph 1. Graph 1: Acceleration (m/s 2 ) time (s) With the arrow pointed in the direction of motion the area under the acceleration curve is the total increase in speed. By summing the rectangles represented by the acceleration for each time interval we found a total velocity change of 27.8 m/s. John tells us that take-off speed that day was about 60 knots m/s is about 54 knots, so we are pretty pleased with the agreement! See Graph 2 below. Preparing for liftoff! The Take Off We used a low-g accelerometer probe made by Vernier Software 2. This accelerometer has an arrow printed on it that indicates the direction in which it measures the acceleration. As long as this arrow points horizontally the probe accurately reads the component of acceleration in the direction indicated. But when the accelerometer is tilted, the reading is affected by gravity. For example, when the arrow is pointed directly upward the probe will indicate an acceleration of one g (9.8 m/s 2 ) even when it is not moving. Knowing the actual acceleration requires that you know the angle of tilt of the accelerometer. This was important in our experiment, because during take off an airplane s angle of tilt (the pitch) changes as it climbs, and the plane banks during a turn. To avoid this tilt effect, the accelerometer was held horizontal during all measurements by visually lining up the arrow with the earth s horizon. During take-off, for instance, the accelerometer was pointed forward but kept horizontal so that the acceleration readings would be the actual forward acceleration. Of course, some allowances must be made for the operator being a bit shaky at times. Graph 2: Acceleration (m/s 2 ) time (s) Air Pressure The second CBL ran during the entire 30 minute flight, taking measurements with a pressure probe and two temperature probes. The pressure probe recorded the air pressure in kilopascals, kpa. Normal atmospheric pressure is about 101 kpa. z 3

4 Graph 3 shows the pressure through the trip. As we lifted off you can see the 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 produce interesting data for the accelerometer, John took the plane into a tight right turn. To produce even more interesting data for the accelerometer, John then took the plane, probes, and nervous passengers into a diving left turn that quickly brought us down to about 300 m (1000 ft). You can see the sharp rise in the air pressure starting about 15 minutes into the flight. We then climbed back up to 600 m and flew at that altitude for a few minutes until another plane in the area induced John to drop to 450 m, from which altitude we began our landing back at Perth airport. Every altitude change is tracked beautifully by the pressure probe. Temperature We also connected two temperature probes to the CBL, one for the temperature inside the cabin and one for outside temperature. For the passengers, who were more used to large pressurized cabins than they were to small planes, sticking a probe out the window seemed an unusual experience 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 in altitude. 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! Graph 5: Graph 3: Pressure (kpa) Outside Temp. ( C) time (min) time (min) 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 a straight line. The gradient of the line, Pressure / altitude gradient kpa m 1. Shown in Graph 6 is the temperature of the inside of the plane. We had no air conditioning or heating turned on, so it s perfectly reasonable that the inside temperature tracks with the outside temperature. The bumps between ten and twenty minutes resulted from John opening the window (gasp!) to take pictures. Graph 6: Graph 4: Pressure (kpa) Inside Temp. ( C) time (min) time (min) The International Standard Atmosphere 4 (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 kpa/m. Not bad! Relationship between Pressure and Temperature The similarity between the temperature and pressure graphs is so striking that it lead us to wonder how they might be related. We plotted a graph of temperature versus pressure, and the result is shown in Graph 7 (at the top of the opposite page). Since the pressure went up and down together they formed a graph that looks like a fuzzy straight line. We used the linear regression function on the TI-83 Plus to find the best fit line, and we graphed the line to illustrate how close to the line most of the points really are. The regression coefficient is 0.964, indicating a strong positive correlation. Our best fit line had a gradient. 4

5 Temperature / pressure gradient = 0.61 C / kpa. Graph 7: Outside Temp. ( C) Pressure (kpa) While this is all great fun, interpreting graphs of this sort is an extremely valuable exercise for our science and maths students. If a student can look at the pressure graph (without the notes on the graph!) and see where the plane is gaining altitude and where it is diving; if a student can look at the temperature/time graph and the pressure/time graph and predict that a temperature/pressure graph will be a straight line; if a student can correctly interpret the meaning of the gradients and compare them to standard values; if a student can see the area under the acceleration graph as accumulated velocity then the student must have a real understanding of graphs. Combining this with the pressure altitude gradient given in (1) produces another interesting quantity, C Temperature 4 altitude gradient = 0.61 } k } } k Pa } } m m Pa The International Standard Atmosphere (ISA) is a theoretical model of the Earth s atmosphere, and in it temperature falls by 2 C for each 1000 ft, a gradient of C / m. C } Turns About 15 minutes into the flight, John warned us that he was about to begin a level right turn. The accelerometer was kept level and pointed to the right during the 10 second turn. After the turn (and after the passengers 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. Graph 8: Acceleration (g) time (s) Classroom Relevance The greatest part of all this, of course, is the new questions that arise. Why does the temperature fall as you go up? Could you really use a thermometer to measure altitude? What assumptions would be involved? Do the relationships that we found continue for higher altitudes? How would this be different if we were flying in a cloud? Interpreting the results (on terra firma!) For us these data and graphs are especially fun because we flew in the airplane, 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 graph is 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 We have made an adjustment in the data for a 0.09 g bias in the accelerometer. For further information, and a really cute online calculator, see the Department of Aeronautical Engineering, University of Sydney, Australia, at Author: Richard L. Taylor The Hockaday School Dallas, TX, USA rtaylor@tenet.edu Photos: Gay Taylor 5

6 John Sharkey Using the TI-83 Plus to solve problems in Higher Physics Many numerical problems in physics can be solved more easily with the use of a calculator. Often the calculator is used to "do the sums" at the end of the problem. The TI-83 Plus is an advanced (Graphing) calculator which can 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. 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: # ALPHA U X,T,Θ,n µ z ALPHA A X,T,Θ,n x 2 Problem A 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 competent student should be able to complete it in several minutes. However, this particular problem is one in which it is difficult to visualize the path of the wheel. The graphing facility of the TI-83 Plus is particularly helpful in understanding the problem. The student is likely to gain a better understanding of the underlying physics. STEP 1: Enter the information that is given in the problem Enter the following into the calculator: ß ALPHA U STEP 3: Use the calculator to solve the problem Return to the Home screen by pressing 2 QUIT We now solve the problem to find the displacement s when the time is 8 seconds. Enter the following into the calculator: VARS This stores the initial velocity u of the wheel (and the helicopter) in the calculator memory as U. o n ß ALPHA 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 positive direction as UP. Gravity always acts DOWN, so the acceleration due to gravity is entered as a negative number. Also note that the "make negative" key is pressed rather than the subtract key. STEP 2: Enter the equation to be used into the calculator. The equation to be used is s 5 ut 1 } 1 2 } at 2 Graphing calculators handle equations and can plot graphs of y against x. 6

7 Now enter the time 8 s which will be the x variable by pressing c n d Press GRAPH. The graph is of the displacement against time. The axes could be labelled but for the purposes of solving the problem it is not necessary. TRACE The answer, m appears on the screen. Remember the negative sign tells us that the displacement of the wheel is DOWN. The displacement corresponds 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 after release. A clearer picture of the motion of the wheel should now emerge. The table function can also be used to view multiple time values: 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 TRACE n to calculate the value at time 8 seconds. Press 2 GRAPH The answer (-233.6m) is displayed. Try finding the displacement of the wheel in successive seconds after release. Another way of exploring the motion of the wheel is to use the button. TRACE A good idea would be to plot a graph of the displacement of the wheel against the time of flight. The calculator can do this for us. Step 4: Solve the problem graphically Press GRAPH and you will probably get some kind of graph but it is unlikely that it will be helpful. We need to set up the graph axes. Press WINDOW and set the axes as shown: Press TRACE and use the blue cursor buttons to move the flashing cursor along 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 CALC Choose MAXIMUM and move the cursor to the left of the maximum, then press. Next move to the right and press. Lastly move the cursor close to the maximum. On pressing the calculator will find the highest point reached by the wheel. As a last example, try choosing } d y } from the CALC menu. dx 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. jsharkey@cne-siar.gov.uk An alternative is to use the part of the graph. ZOOM button to zoom into the significant 7

8 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 of hard-disk, for graphic calculators. Externally, it no longer has a LCD screen with which to communicate, but instead it has red, yellow and green LEDs, together with a buzzer. These can be programmed from whichever graphic calculator is attached. So some of the simple control experiments familiar from some technology syllabuses can be tackled just using the CBL 2 without any additional hardware. Here we will try to develop a traffic light simulation program using its built-in LEDs. 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 delay program, such as WAIT, which just uses a counted loop controlled by a variable W whose value will need to be set in the calling program. By experiment I found that a value of for W seemed to produce a delay of 30 seconds, so if we pass a value of W in seconds we will need to multiply it by about 333 to control the loop, as in Fig. 4. You control the CBL 2 by sending it lists. The list {1998,L,S} is used to change 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 very simple program, ONRED, to turn the Red LED on, as in Fig. 1 Fig 4 So we can now build up a main program, called SEQUENCE, to perform one set of changes from Red, through Red/Amber to Green, and then through Amber back to Red. We just need to decide on the values to use for W to keep each combination of lights on at each stage. My version uses the following values: Fig 1 Use the PRGM's I/O menu to find the command Send(, as in Fig. 2. Red: Red & Amber: Green: Amber: 7 seconds 2 seconds 6 seconds 2 seconds Fig 2 Fig 5 8

9 With any luck this might suggest other projects you could carry out with the coloured LEDs, such as "disco lights", or using them to display the 3 digit binary equivalent of numbers between 0 and 7. Fig 6 To call another program as a subprogram use the EXEC menu from PRGM as in Fig. 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 the subprogram TONE, Fig. 9. The list {1999,D,N} is used to make the CBL 2 sound a tone whose semi-period is N, for a duration of D, where both are measured in units of 100 micro-seconds. TONE uses values L and H set outside the program. L is the duration in seconds and H is the frequency in Hertz. Fig 7 Finally you could incorporate SEQUENCE as a subprogram of a main program, 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 9 Well, happy flashing and buzzing! I'm sure the editor would be glad to hear of 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 a_oldknow@compuserve.com Fig 8 y A Christmas Postscript! Many thanks to Richard Smith for providing the following program which should put the CBL 2 into the Christmas spirit. The list L1 holds the relative durations of the notes, which are multiplied by the constant K to convert them into the CBL units of 100 microseconds. The list L2 holds the corresponding 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} L K K*L1 L1 For(N,1,30,1) Send({1999,L1 (N),L1 (N)}) End 9 9

10 Alan Graham The TI-83 Problem Page Time for a calculation Q How can I perform time calculations (involving in hours, minutes, and seconds)? A Like most graphical calculators, the TI-83 can perform angle calculations 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 ANGLE ANGLE 2 15 ALPHA " 4 2 ANGLE ANGLE 2 55 ALPHA " 2 ANGLE 4 Median-Median Line Q 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 data but what exactly is it? A Until recently I wasn t too sure myself. I have always assumed that the Median-Median line was formed by separating the points of the scatterplot into two equal halves (left and right) and joining the medians of these two sets of points. However, after checking the TI website (dial up and then follow the TI&ME option to reach the TI-83 discussion group), I discovered that it is a bit more complicated. The algorithm to which the TI-83 is programmed can be best 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 the median of the right points. (c) A second line is drawn through the median of the centre points with the same slope as that of the first line. (d) A third line is drawn one third of the way between the first and second of these lines, again with the same gradient. This is the Median-Median line. As the web-site entry observes, an advantage of the median-median line over a least-squares regression line is that stray data points do not affect the end result very much. Same final digits Q I ve been working on number investigations with my class. One that caught their and my interest was the following: For what numbers do X and X 5 have the same last digits? Any suggestions for tackling this on the TI-83? The first command stores 0 in X. The next two commands (linked by the colon) increase the value of X by 1 and then display, side by side, the current values of X and X 5. Each press of generates the next value. The user simply compares the final digits visually. This solution may be sufficient for less experienced pupils but if they are looking for something more challenging, here are two extra features they might include. (a) The final digit It is possible to tweak out the value of the final digits of the X and the X 5 and let the calculator make the comparison directly. The first challenge here is how to reduce a given integer to its final digit. Experimenting with the fpart command (which finds the fractional part of a division) using a divisor of 10 might suggest to them that the command 10*fPart(X/10) will do the trick. (b) The = command Next they might like to use the Test menu to compare the final digits of X and X 5. This will require use of the equality command from the Test menu. If pupils are unfamiliar with the Test menu, this is something that 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 X 5, thus: The first displayed output value inside the curly brackets shows whether the equality is true. The second and third values are, respectively, X and X 5. It will quickly become apparent that the result is always true. However, this solution is easily adaptable to other questions of a similar form. For example: For what numbers do X and X 3 have the same last digits? A Basically you need to generate two sequences, namely X (taking values 0, 1, 2, 3, ) and, alongside, the corresponding values of X 5. However, before rushing into creating lists or writing a complicated program, it is worth exploring how this can be done more simply on the Home screen. Here is a possible first draft solution to the problem. Alan Graham works at the Centre for Mathematics Education, The Open University, ( a.t.graham@open.ac.uk). In association with Barrie Galpin, he is author of the two Calculator Maths series of books written for the TI-80 and TI-83 respectively. 10

11 Kerry Horstead and Roger Fentem Motivating Mathematics in Key Stage 3 Aspiring secondary mathematics teachers in their first year of training on the B.Ed. (Hons) course at the College of St. Mark and St. John (Marjon) spend four weeks in school at the end of the year practising the theory they have covered in College. Some of the theory concerns the role of graphing calculators in teaching and learning mathematics. Kerry Horstead was just such a student. She wrote the following of her teaching experience in a Community College. "I have found the experience very enjoyable, hard work but extremely eye-opening to the policies in schools and the attitudes of staff and pupils alike. However I have decided to write this report about the use of technologies as it seemed very appropriate, as the Community College has been granted technology status from September. The Community College had just had a class set of TI-83 calculators delivered along with a CBR (Calculator-Based Ranger motion detector) and ViewScreen for use on an over-head projector. When I started the practice at the school, mention was made of the delivery of the calculators, but due to paperwork and other commitments there hadn t been 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 are given one for their use on the B.Ed. course) to show my professional tutor the few programs we had explored in Marjon. I thought that they would be appropriate to use with Key Stage 3 pupils. I was very pleased by the response; my ideas on how to use the programs were greeted with much enthusiasm. I was allowed to raid the storeroom and use whatever equipment I thought I would need. It was like Christmas, unpacking all this brand new technology and being allowed a free rein to set it up and demonstrate how I thought it was appropriately used. The first group where I used this program were a bottom set, year seven group. I wasn t sure how they would respond as a calculator producing apes is not quite as exciting as a game boy or games console. Children, and adults alike, who are intimidated by mathematics and calculators, miss the point that programmable graphical calculators are capable of running quite sophisticated 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 with enthusiasm and vigour. Even notorious individuals were captivated into working out strategies to solve the problem posed. I was extremely pleased with this as my first experience of introducing graphing calculator technology to pupils. I was encouraged to keep the activity alive and engage other groups with it. The next group I attempted to use the ape program with was a different experience altogether. This was a middle set, year nine group, who weren t going to be so overly impressed by an ape-producing calculator. Although most individuals seemed to enjoy the descision making and problem solving the program requires, a few individuals were obviously bored by the whole process. I think the only attraction to those pupils in the 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 to use the CBR and the walk this way program. It was as though someone had thrown a switch. As the challenge became more physically demanding the entire class warmed to the experience and I had a hard job sorting out the order in who goes next? Although interpreting graphs is a big part of this program, which incidentally tied in well with their current topic, the pupils went ahead with great gusto at working out how to follow the lines on the graph first before walking it. The program I chose to use initially was called APE. Children need to engage in problem solving and to know their tables (up to 9 by 9). This involves children reassembling two pictures of mixed up apes by use of a multiplying controlled grid system. The choice of tables provides for differentiation. The memory of the day was when a particularly difficult young lady decided she would have a go, but the graph changed from a walking away from to a walking towards one, this pupil instantly recognised the change in tact and walked a near perfect graph. She was obviously quite pleased with herself but street cred being what it is decided not to show it. 11

12 The fact that this pupil had shown a glimmer of talent, and more importantly interest in the subject, was the breakthrough of the day at least if 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 some understanding. Once they had mastered the art of the rules they were extremely quick in developing strategies to cope with solving both apes at once. They had soon run through the program twice in a very short space of time. Retrospectively that would have been the best time to stop, as the third 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 maths sessions normally don t! Trying out this technology in school has been an interesting and thoughtprovoking 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 (Calculator-Based Ranger ) CBR is an electronic device which measures distance using sound waves and simultaneously records the times of the measurements. The CBR plugs directly into a TI graphing calculator which can then display the distances measured. The display may be in graphical form or purely numerical. It comes with its own program called RANGER or you can use other tailormade programs (as in Kerry s case she used a suite of programs available on the TI web site: Kerry Horstead is a trainee teacher on the B.Ed. (Hons) course at the College 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 Rfentem@marjon.ac.uk THIS COULD BE YOUR LAST ISSUE OF... UNLESS YOU RE-SUBSCRIBE! We re updating our subscription list If you want to continue to receive your copy, either: Send an to: ticares@msn.com or Send a fax with your Name / Address / Contact numbers to: requesting re-subscription 12

13 T 3 Teachers Teaching with Technology T 3 Scotland T 3 Scotland delivers Hand-held Technology 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 T 3 Scotland courses, please contact Ian Forbes: Phone: ian_forbes@education.ed.ac.uk Address: Faculty of Education Dept of Curriculum Studies: S T M C Moray House Institute of Education The University of Edinburgh Holyrood Road Edinburgh EH8 8AQ T 3 England, Wales and Northern Ireland We are pleased to announce that T 3 in England, Wales and Northern Ireland is now offered in partnership with the Mathematical Association and 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 3 makes it clear that graphics calculators have a key role to play in teaching and learning at Key Stage 3. All T 3 materials are written by experienced educators in line with the National Numeracy Strategy, National Curriculum and G.C.S.E. criteria. Training sessions are hands-on workshops given by trainers experienced in using hand-held technology in the classroom. The courses cover basic operation of the calculator and data loggers, ideas and materials for use in the classroom across the attainment targets, practical help in managing the use of ICT in teaching and learning, and discuss the impact of technology on teaching. We are also able to offer short introductory sessions for teachers, as well as longer courses in a variety of formats. A key part of our strategy for training and supporting teachers in using hand-held technology is to work in collaboration with Local Education Authorities. An important way forward for this partnership is for T 3 to train a team of local teachers to become trainers in their L.E.A. Those authorities already working in partnership with T 3 have been able to select an appropriate focus for their area from the list of available courses, teachers to act as trainers and to plan a strategy to develop the appropriate use of hand-held technology in their area. If you are interested in more details, please contact Rosalyn Hyde: Phone: hyde@tcp.co.uk Address: 158 Dale Valley Rd Southampton SO16 6QW 13

14 8 Ruth Clark, Jay Donald, Stella McKague, Gillian Pringle A Postcard from T 3 Summer School N A visit to Perth College allowed us to gain experience in the downloading of applications/programmes from the internet one of the main benefits of the FLASH Technology inbuilt in the TI-83 Plus. We arrived by train,boat and plane just as the song says, from all corners of Scotland. From Wick in the far north to Lewis in the west, Lockerbie in the South West to Elgin in the North East, from the Highlands to the central 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 Monday evening (two of them having flown in from Lewis that day) to collect data on the CBL, which we all got the chance to see at the workshop on the CBL / CBR the next evening. Amazing! The social side of the course was every bit as much fun as the course content, and allowed us to make some good friends. Mention must be made of Stella's flying lesson! Since the course was taking 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 fact that Stella was indeed flying the plane for a while herself! The Tuesday evening was Quiz Night!, the Grand Prize being two TI-83 Plus ViewScreen kits. This was won admirably by a husband and wife team from West Lothian, teachers at St Margaret s and Linlithgow. Ruth was thouroghly delighted to know that she could remember the names of the Alexander 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 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 and worksheets available, from 5 14 Numeracy to NQ Statistics, thanks to MadMaths. 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! The T 3 Scotland Summer School was held at Perth Aerodrome, part of a Perth College, from 7 9 August Summer School will be held in the Perth area in late summer 2001 Please contact Ian Forbes at , or ian_forbes@education.ed.ac.uk for details. 14

15 Nevil Hopley Classroom Networks I have been involved in delivering sessions for PGCE students since 1997 and early in 2000 I became involved in the T 3 (Teachers Teaching with Technology ) programme that centres on developing teachers skills with graphical calculators. I have also written a number of stand-alone tutoring programs which are now extensively used within my department and now in several other schools in Scotland. This background made me a good candidate to get involved in a pilot project that links graphical calculators together using the Internet in a similar way to existing computers. The appropriate hardware was installed in my classroom last year. This was one of the first calculator networks installed, although there are more running now, including some in England and other parts of Europe. The classroom setup has TI-83 Plus s connected to the Internet by cables similar to those used for TI-GRAPH LINK. The school network also has a "Concentrator Gateway" utility running that allows direct communication between these calculators and a web site in Texas. The teacher s calculator is also linked to this website and user-entered identity numbers and passwords help 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 take advantage of the features that such a link up makes possible. Here is one example of what is now possible: First I send the class a set of configured axes so that their screen looks identical to mine. I then instruct them to send me a point where "the y-coordinate is double the x-coordinate". Each student moves their arrow to a point on the plane which they think satisfies my stated condition. This point is sent and all of the class s points are displayed on the teacher calculator s axes, which everyone can see via a viewscreen. Results vary from a random scattergram to a perfect straight line! It s interesting to see who strays into which quadrants, and who sticks near the origin! Using the Trace feature, the teacher can identify who sent which point. This really is a case when there is more than one answer! However, the great strength of the system is that everyone in the class is involved and they each have their own unique identification number, which only 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 very engaging lesson! In fact, any data can be sent to and from the teacher and student calculators strings, lists, functions, single real variables, pictures it s use is limited only by the questions that can be put to a class. me think long and hard about good questions to ask students that stimulate and support their understanding. I am currently very much involved in the continuing development of this new programming environment and one of the programs that I have designed is going to be used to demonstrate the system s capabilities at conferences for Teacher Trainers in the USA. The system will also be on show at the BETT Exhibition, London in January 2001 and I shall be talking about it at the SMC Stirling Maths Conference in May This November, I took delivery of a new wireless hub system that uses radio waves to send and receive the information with the Internet, instead of the large numbers of cables that it currently uses this will greatly ease the setup and use of the system with a large class of students no cables for them to stand on or trip over! EXAMPLE: The Link activity Title page from this you can choose many options... and it s now been sent and then they can plot a point to send back to the teacher teacher chose to send axes configuration student calcs show the retrieval process the teacher collects the class s points It can also facilitate swift sharing of results. Have every student send in a single number (or experimental result). These are then collated and stored in lists on the teacher calculator, which can then in turn be sent back to the students calculators. Each student then has the full class set of data with which they can do their own, independent statistical analysis. We have regularly been told that open-ended questions that invite creative responses are the best to ask students who are learning mathematics, but it has been very difficult to practically collect all the varied responses from a class without the pace of the lesson being severely impaired. The Classroom Network is excellent at quickly gathering everyone s answers and allowing them to be displayed and shared in a meaningful fashion it really is making and they are displayed (here we have a class of 3 students!) In conclusion, this is a fantastic opportunity to trial the next generation of educational technology that will help deliver our subjects, using hardware that we readily have at our disposal. Nevil Hopley is Head of Mathematics at George Watson's College in Edinburgh. n.hopley@watsons.edin.sch.uk 15

16 FREE Workshops and Demonstrations We 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 COURSES INCLUDE: 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 In Scotland: Ring Ian Forbes on T 3 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 ti-cares@ti.com CSC Customer Service Centre Phone: For Teacher Express Service, press 84 after calling the CSC Fax: ti-cares@ti.com Instructional Dealers Addex Limited (Ireland) Comcal George Waterstons & Sons Limited Jaytex Oxford Educational Supplies Science Studio Limited Shaw Scientific Limited (Ireland) 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, T 3, Teachers Teaching with Technology and ViewScreen are trademarks of Texas Instruments Incorporated. Cabri Géomètre II is a trademark of Université Joseph Fourier. Mac and Macintosh are registered trademarks 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 a registered trademark of the Microsoft Corporation. Texas Instruments reserves the right to make changes to products, specifications, services and programs without notice. Printed on recyclable 100% chlorine-free paper by Thamesdown Colour Limited, UK. Desk Top Publishing Cloud 9 Publishing Limited, UK Texas Instruments Incorporated CL2001NLM1/UK