Spring 2011

IN THIS ISSUE:

FRETBOARD MATHEMATICS

USING CAS: WHY NOT?

GREAT TEACHING MOMENTS

Welcome...We invite you to enjoy the Spring 2011 edition of (n)sight,

a termly magazine written by and for teachers who are

using TI technology to improve teaching and learning.

IN THIS EDITION

Fretboard mathematics 2Using modern technology to investigate the historical problem faced by

instrument makers –where exactly should those frets go?

Using CAS: why not? 6TI-Nspire comes in two versions one of which includes a Computer

Algebra System. But…to CAS or not to CAS? that is the question.

Great Teaching Moments 8Six teachers share experiences when TI-Nspire, students and teacher

came together to create magic mathematical moments in the classroom.

Support for TI technology 12Details of resources, loans and professional development to support your

use of TI technology.

COMPETITIONSMost people who entered our Summer 2010 (n)sight competition: Screen

Snap, correctly matched the nine screenshots to the activities on the Nspiring

Learning website (www.nspiringlearning.org.uk). David McDonald won the

tie-breaker by completing the sentence “I would like a new activity on the

website which...”, with the words “shows the curve of a football after David

Beckham has taken a free kick over the wall”. David will be receiving his prize,

a TI-Nspire ‘Teacher Bundle’ but will he be getting his wished for activity?

The Winter competition... “Round the wall”.Here’s your chance to win your own ‘Teacher Bundle’ consisting of a

TI-Nspire with Touchpad handheld and TI-Nspire Teacher Software licence

that you can use for yourself or in your school. Send us a tns fi le that

shows the curve of a football being bent around a defensive wall. Interpret

this as you will…

• perhaps it will allow the user to position the ball and the wall?

• perhaps it will allow the user to choose different functions to model the

ball’s fl ight?

• perhaps it will be in the form of a student activity?

• perhaps it will be a student-produced response to a challenge?

Send an email with the tns fi le attached along with any helpful

documentation to the editor, barrie.galpin@zen.co.uk, to arrive by 28

February 2011. The prizewinner and winning entry will be featured in the

next edition of (n)sight.

For a 90-day trial of TI-Nspire Teacher Software, visit our resources

website, nspiringlearning.org.uk. Our ETCs will be happy to help you get

started! Email etcuk@ti.com.

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Where do the frets on a stringed instrument need to be positioned? In this article Linda Tetlow

suggests ways in which TI-Nspire can be used to investigate the mathematics involved. There are

more musical activities in Perfect Pitch, part of STEM activities with TI-Nspire – Using Real World

Data (www.tinyurl.com/STEMactivities)

The frequency of the note produced by a particular

vibrating string just depends on the length that

vibrates: the longer the string, the lower the

frequency and the lower the note. Two common

labelling systems generally used in western countries

are shown on the piano keyboard. The repeating

pattern of 12 black and white notes (semitones),

such as from C1 to C2, makes up an octave.

Linda Tetlow

Stringed musical instruments have been in existence

for thousands of years. Pieces of three lyres and a

harp over 4,500 years old, were found in a tomb in

Ur in Ancient Mesopotamia (now Iraq).

The lute and the near-Eastern oud have similar origins

and both names derive from the Arabic for wood.

They have a soundboard attached to a deep round

back, a neck and varying numbers of strings.

To produce a particular note, the performer shortens

the vibrating part of the string by placing fi ngers on

the neck. To help the performer, lutes had frets at

fi xed intervals on the instrument’s neck. They were

very popular between the 14th and 18th centuries

and instruments such as guitars, mandolins and

banjos developed from them. Other instruments like

the violin, oud and the Japanese shamisen have no

frets and the Indian sitar has moveable frets. This

makes them more versatile for playing the different

scales used in world music.

How does the instrument maker determine where to

place frets to obtain the correct notes? Try measuring

the length of the vibrating part of a guitar string (from

the fret to the bridge) for different fret positions.

The guitar shown here measured 65.0cm from fret

0 (the white bar) to the bridge.

What might a scattergraph of fret number against string

length look like? What sort of function might fi t these

points? In TI-Nspire you could enter the data into

a Lists & Spreadsheet page and add a Data

& Statistics page. Then experiment with

commands in the Analyse menu such as

Plot Function or Regression.

Guitar Oud

*sight 3

If the length of the open string (F0 B) is 65.0cm,

to fi nd the other lengths we need to keep

multiplying by 17/18.

• Choose a Graphs page with suitable window setting.

• From the View menu select Show Grid.

• Select Point On and mark grid points on the x-axis.

• From the Graph menu select Function and

enter the function.

• Construct Perpendiculars to the x-axis from the

marked grid points.

Note: not all lines are shown in the image above.

• Mark the Intersection Points of the graph with the

perpendicular lines.

• Construct Perpendiculars to the previous lines

through the intersection points.

• Mark the Intersection Points of the new

(horizontal) lines with the y-axis. These points on

the y-axis give the position of the frets.

• From the Actions menu select Coordinates and

Equations and read off the measurements.

Now you can check whether fret 12 is exactly where

you would expect it, halfway along the open string.

Legend has it that Pythagoras discovered a

mathematical relationship between the frequencies

of harmonious sounding notes whilst listening to

the sound made by blacksmiths’ hammers. Notes

with frequency ratios of 2:1 sounded the same,

though an octave apart, and notes with ratios such

as 3:2 sounded particularly harmonious. From this

developed a 6-tone scale where moving up one tone

multiplied the frequency by 9/8. The system, known

as just intonation, is still used by some musicians

today. Frequencies of scale notes are related by

simple small-whole-number ratios because these

produce the most harmonious sounds.

These systems use the fact that doubling the

frequency of a note raises it one octave (12

semitones). This can be done by halving the length

of a vibrating string, so for instruments with frets, fret

12 (F12) must be half way between the bridge and

fret 0, the initial fret (F0). But what about all the other

frets used to produce the intermediate semitones?

How should these frets be positioned? Here are three

different methods all of which can be investigated

with TI-Nspire.

THE MASTER-LUTHIERS’ METHOD

A method used by master lute makers was to use a

ratio of 1:18.

The distance from F0 to F1 is 1/18

of the distance from F0 to the bridge (B).

The distance from F1 to F2 is 1/18

of the distance from F1 to B

and so on...

Since F0 F1 is 1/18 of F0 B it follows that F1B is 17/18

of F0 B, F1 F2 is 17/18 of F1 B, F2 B is 17/18 of F1 B,

and so on...

So each length is 17/18 of the length before.

TI-Nspire offers many ways to calculate these lengths.

Calculator pages, spreadsheets or short programs

could be used to do it numerically, but a graphical

method is shown below.

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Lute

4 *sight

The coordinates could be inserted or captured in a

Lists & Spreadsheet page, adding extra columns to

calculate the distance of each of the frets from the

neck of the guitar, point C (12,0) using:

distance = √(y2+(12-x)2).

EQUAL TEMPERAMENT METHOD

This tuning method enables a piece of music to sound

the same in any key, so musicians whose instruments

are tuned in different keys can play together. There

is a constant ratio (r) between the frequencies of

successive notes.

Since the frequency doubles when raised an octave

(12 semitones) then r12 = 2.

A similar approach to the master luthiers’ method could

be used to position the frets for equal temperament.

What would the function be? Why?

How close is fret 12 to halfway along the open string

using this method of tuning?

FURTHER INVESTIGATIONS

TI-Nspire makes it easy to compare the calculated fret

positions for the three different tuning methods. The

methods can be adapted for other instruments with

frets such as the mandolin shown where F0 B is 33.0cm.

Several ideas in this article were taken from Nuffi eld

Advanced Mathematics - Mathematics, Music and

Art––one book in a series published by Longman for

the Nuffi eld Foundation in 1994. Further information

from Wikipedia (http://en.wikipedia.org/) and the

Physics of Music website (www.phy.mtu.edu/~suits/

Physicsofmusic.html).

DANIEL STRÄHLE’S METHOD

In 1743 the Swede, Daniel Strähle, published the

following alternative method for placing frets 1 to 12.

• Draw an isosceles triangle ABC with sides

24, 24, 12.

• On BA mark the point D, 7 units from B and

draw DC––the neck of the guitar.

• C is fret 0, D is fret 12.

• Extend CD to E where ED = DC. E is the bridge

since DE is half of CE.

• Divide BC into 12 equal intervals and draw straight

lines from A to these points.

• Where these lines cross DC will represent the

position of the fi rst 12 frets.

• Scale up to fi t the size of the actual instrument.

One way to construct this using TI-Nspire is to set

up a Graphs page with the grid showing and to

mark points on the grid at (7,0), (12,0) and (24,0).

Construct circles as shown below to create the

isosceles triangle ABC and the point D.

Hide the constructions and draw segments joining A

to the grid points on the x-axis. Mark the intersection

points where these lines cross the line DC and fi nd

their coordinates.

Mandolin

�*sight 5

Many older teachers will not have come across

CAS in their professional lives but if they are recent

graduates of mathematics or engineering, they almost

certainly will have. CAS software is regularly used

by professional mathematicians, more commonly

in applied fi elds, and certainly by engineers and

scientists. MathCad, Maple and Mathematica, all CAS

systems, are very familiar in professional fi elds and

have been available and developed for many years.

Research suggests that their use in university teaching

is variable and that those academics who use CAS in

their research and development work tend also to use

it in their teaching (Lavicza 2008). Generally these will

be applied mathematicians and engineers whereas in

England, school mathematics has tended to be rooted

in pure mathematics. We learn the factorisation of

quadratics largely for its own sake: the skill is

the most important thing rather than solving

the problem in which it will be useful.

However this all looks set to change, as the

STEM (Science, Technology, Engineering,

Mathematics) agenda is beginning to

lead developments in what has come

to be known as ‘Using and Applying’ or

‘Functional Skills’.

So, what is CAS? From the early days

of computing, computer-programming

languages had built in mathematical

functions and commands that were capable

of evaluating mathematical expressions. CAS

is simply a collection of commands capable

of actually doing the mathematics. Early CAS

software consisted of additional commands

that would, for example, allow you to solve an

equation, simplify an expression, differentiate

or integrate a function.

Modern CAS does the same except that, with the

advantage of powerful graphical interfaces, the

algebra can now be correctly formatted. The data

can be looked at in sophisticated forms, notably with

powerful graphing facilities, and interfaces are now

much more user friendly. So, put simply, CAS provides

tools for evaluating and manipulating mathematical

expressions.

As such powerful tools were developed, it was natural

that they would be made available for school use.

Derive, the most common CAS software in schools,

was widely used throughout the 1980s and 1990s and

developed into a sophisticated graphical system. There

are many publications documenting the use of Derive

in schools (e.g. Kutzler & Boykett 1996). However, in

England there remained worries: will there be any point

learning mathematics manipulation at all if we make

machines available that will do it for us? There was a

residual worry that adults cannot add up because we

gave them calculators when they were at school. The

debate is well set out in the 2004 book ‘The Case for

CAS’. (Bohm et al. 2004) which you can download at

www.t3ww.org/cas.

Chris Olley

King’s College, London

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Using CAS: Why not?In some parts of the world there is a passionate debate about whether Computer

Algebra Systems (CAS) are a legitimate educational tool. For example, different

states in Australia have signifi cantly different mathematics examinations

because some states allow the use of CAS systems in the exams themselves

while others do not. In Scotland there has been considerable interest but,

curiously, in England there is no such debate.

6 *sight

However, in Europe and many other parts of

the world, where mathematics is taught from

a problem-solving perspective, sophisticated

tools used in developing a solution have

certainly been seen as appropriate and

reasonable. What is central is not the

manipulation of the algebra but the actual

doing of the mathematics––the setting up of

the relationships, data, functions, inputs that

will solve the problem.

We need to move towards this problem-

solving perspective, where we are not simply

using the problem as a vehicle to practise

mathematical manipulation. This naturally

mirrors the practice of applied mathematicians

and engineers doing the task for real in their

professional lives. In thinking through a

complex problem-solving activity, students

can struggle to persist, because there are

too many aspects to be profi cient in: the

symbolic mathematics can become a barrier

to developing their problem solving. CAS can

act to ease the fl ow of their thinking by carrying

the burden of the algebraic manipulation. That

is not to say that students should not learn

how to manipulate algebra for themselves, just

that this can be saved for another day, when

that is the focus of the task. Then the two

strands (Pure and Applied) can be developed

together, rather than delaying problem solving

(perhaps forever!) until students are secure and

confi dent algebraists.

A calculator can be seen as a threat to learning

when pupils are allowed to use it to do simple

arithmetic. However, generations of teachers

have developed activity-based learning

opportunities, which use the calculator as a

pedagogic tool to develop their pupil’s numeracy.

The same can be true with CAS.

For example, with non-CAS TI-Nspire we can

investigate how the machine adds fractions

together when one denominator is a multiple

of the other. Asking questions such as ‘how

does it do that?’ allows students to develop

their experience in structuring and organising

their investigation skills. Which type of fraction

should I try next? Does that support my rule

or do I need to modify and develop it further?

Why does the last example look different?

However, with T-Nspire CAS there can

be a logical extension to number-based

investigations of this kind.

Here are some more examples with the

powerful factor command. A favourite activity

is to investigate what it does to numbers and

using this to develop a method for prime

factorisation is very successful. However,

once this is done students are ready to

explore what it does to expressions of many

different kinds as in the example below.

Those using a non-CAS TI-Nspire would be

able to carry out the fi rst three steps but for

the fourth, most logical, of extensions you

would need TI-Nspire with CAS. The last

two examples are quite dramatic. Why does

one work fi ne and the next one not work at

all? Students will be fascinated and want to

explore which quadratics factorise and why.

CAS can help students to make sense of

algebra. For example, to solve an equation we

have to modify it, fi nding a series of simpler

versions, leading to a value of the unknown

which satisfi es the original statement. CAS has

the mathematical tools to do this as shown in

the following example. Students can experiment

with different approaches to see if they make the

statement simpler or more complicated. Finally

the CAS system can confi rm that the statement

is true when x=1. Having CAS available allows

students to explore ever more complicated

statements and hence see the need to

develop more sophisticated mathematics for

simplifi cation and hence, solution.

TI-Nspire has an integrated set of

mathematical tools: numeric, graphing,

geometric, statistical and the additional CAS

facilities complete the pedagogic toolkit.

Students can use this tool to manipulate a

wide range of algebraic expressions. Just

as with the other tools, they will need to go

back to pencil and paper and practise the

skills independent of the machine. And just

as with the other tools, students will then

be able to choose the right tool for the job:

brainpower, pencil and paper, or technology.

In England CAS technology cannot be

used in public exams so it has become

necessary for manufacturers to develop

technological tools with the CAS facilities

disabled. However, TI-Nspire CAS is a really

powerful pedagogical tool that supports

students’ learning and helps to develop their

mathematics. It is the complete tool giving

access to the full range of mathematical

facilities… so why not use it?

Bibliography

Bohm, J. et al., 2004. The case for CAS,

University of Munster, Austria.

Evans, M., Leigh-Lancaster, D. & Norton,

P., 2005. Mathematical Methods Computer

Algebra System (CAS) 2004 pilot

examinations and links to a broader research

agenda. Building connections: Theory,

research and practice, 223-230

Kutzler, B. & Boykett, T., 1996. Improving

Mathematics Teaching with DERIVE: a guide

for teachers, Chartwell-Bratt.

Lavicza, Z., 2008. The examination

of technology use in university-level

mathematics teaching. In Proceedings of the

Symposium on the Occasion of the 100th

Anniversary of International Commission on

Mathematical Instruction.

�*sight 7

If ICT is made to seem like the specialist’s preserve,

too many teachers will be put off. We need once

again to address the issue of enabling students to

exploit the power of ICT whether it be to develop

understanding or to engage in investigation and

exploration, and to do this we need a robust

and accessible platform. My work with Texas

Instruments technology, fi rst as their Education

Technology Consultant, and now as a freelance

consultant, has led me to believe that TI-Nspire

certainly satisfi es that need for a robust, powerful

and accessible platform.

TI-Nspire is software and not a graphics calculator

(though it does have a calculator application).

Because the software runs both on a computer

and on a handheld device it has great fl exibility

in the classroom. Instead of booking a lesson in

a computer room, there can be access to the

same powerful learning tools sitting on the table.

This is ICT in the hands of the student and software

means menus, fi les, folders, documents – all

familiar territory for teacher and student alike.

With machines such as the Sinclair ZX80, the BBC-B computer, the graphics calculator, the iPhone, the iPad

and with software such as the word processor, the spreadsheet or dynamic geometry, describing exactly what

the technology is provides a bit of a challenge. Once you’ve tried it yourself you know at fi rst hand what it

does, but describing it to someone else inevitably evokes such statements as “it’s like a … but you can also…

but the great thing is…“. In this article Jenny Orton considers whether TI-Nspire offers a similar step change

in technological advance and tries to answer the simple question: what is TI-Nspire?

When I started teaching some 25 years ago, the

curriculum demanded that we write Information and

Communication Technology (ICT) into our schemes of

work for mathematics: if I remember rightly, we didn’t

have sophisticated graphing packages, we didn’t have

dynamic geometry, but I think most maths teachers

at that time recognised the power of ICT to motivate,

engage and illuminate through simple activities. Few

classrooms were set up with data projectors so ICT

was very much in the hands of the students.

Now we hear the recommendation from Ofsted

(Understanding the Score) that secondary schools

should “improve pupils’ use of ICT as a tool for

learning mathematics” – a weakness highlighted

in many Ofsted reports, while the recent Scottish

report into ICT use in schools, also highlighted that

“many staff…do not understand fully enough their

own role in the effective promotion and use of ICT

for learning and teaching”. It seems to me that since

I started teaching the ordinary teacher has been

given less opportunities to offer students simple

hands-on ICT activities, and perhaps has been

seduced by the ready-made teacher presentations

that are so readily available.

So when I was due to begin teaching the equation of

a straight line to a group of year 7 students, I decided

to use the TI-Nspire handheld to help. It really gives

students a chance to feel that they can discover

mathematics for themselves, removing the feeling that

there is a barrier between what is being taught and what

is being learnt.

On the handhelds students were able to manipulate

equations in the form y = mx + c and instantly see

the changes to the straight line. By using TI-Nspire

Navigator’s Screen Capture facility I was able to assess

the understanding of all the members of class and

generate immediate points of discussion. It was easy to:

• fi x the intercept: students had to plot a line with a fi xed

intercept but any gradient and Screen Capture allowed us

to see exactly what the graphs had in common.

• fi x the gradient: students plotted lines with fi xed

gradient but could choose the intercept. Again, Screen

Capture allowed us to compare all the different graphs.

• play Gradient Challenge: I asked students to plot any

line that would be parallel to y = 3x. This really allowed

me to judge their understanding of the equation of a line.

I would encourage anyone to use TI-Nspire and

TI-Nspire Navigator in their teaching. It’s really amazing

how powerful it can be and how much excitement it

can generate in lessons. But more importantly, for me it

promotes greater understanding amongst students and

helps me to teach outstanding lessons.

Matthew DowsonMatt’s magic moment

occurred when a class-

full of handhelds were

connected wirelessly to

TI-Nspire Navigator.

Teaching any topic can be tough. But students often seem to

struggle with using algebra, especially at an early age.

8 *sight

Sometimes a lesson just goes brilliantly with students and teacher both

experiencing a real “wow”! It must be a combination of factors that creates

this: the lesson content, the resources available, the students’ attitude and

inspired teaching sometimes combine to make a magic moment. It is well

worth trying to capture these moments and we asked six teachers to look out

for and record such instances while they were using TI-Nspire technology.

Great Teaching Moments

Matthew ReamesThe Head of Maths at

St Edmund’s Junior

School, Canterbury

describes a Great

Teaching Moment with

younger children.

My experience using TI-Nspire handhelds has primarily

been with children in years 5 to 8.

Having found a tns fi le on the TI website written by

an Australian teacher, I was easily able to modify it

for my own classes.

In this activity, students investigated a variety of

expressions and equations and what happened

when more than one operation is used. For

example, the handhelds allowed students to predict

the answer to an expression such as 2+3x5. It

was interesting to hear the children’s puzzled

remarks when 2+3x5 did not equal 25 as they had

anticipated but the puzzled murmurs were quickly

followed by cries of, ‘Oh, I get it! You have to do it

like THIS if you want to do the adding fi rst!’

Further questions challenged children to determine

where to insert brackets to make an equation

true as well as a section entitled Extra for Experts

–excellent opportunities for them use the concepts

they had investigated!

All this hands-on investigation with the handhelds

led to some excellent discussion about the proper

way to write expressions and which operation

happens fi rst. The children were excited to share

with one another each new bit that they learned

about the order of operations and they were eager

to challenge one another with expressions that

they created. Rather than just memorising a set of

rules, the children were able to develop a far better

knowledge of the order of operations as well as a

much deeper understanding of the concepts behind

the rules.

Fiona MoirFiona teaches at

Grove Academy,

Dundee and her Great

Teaching Moment led

to the publication of

an activity entitled

Introduction to

Trigonometry on the

Nspiring Learning

website.

Previously, I introduced trigonometry by getting students to

measure groups of right-angled triangles.

We would collate the results and deduce that,

e.g. sin 30°= ½. Each of my 8 groups in the class

would have a different angle. The measuring was

sometimes slightly inaccurate (sometimes a bit

more than slightly!) and I had to ask my pupils

to make allowances for this and believe that, in

a perfect world, their measurements would have

shown all the ratios of the comparable sides as

exactly the same value.

When I tried using the TI-Nspire facilities to

introduce trig. in a similar way, I suddenly realised

they could discover this much more quickly and

perfectly accurately… wow! No need to believe that

the slightly different values were meant to be the

same, the values shown were exactly the same.

Since either the angle size or the lengths could be

changed and all the calculations clearly displayed,

pupils very quickly understood the connections

between the sides and angles.

I was really excited about this activity and decided to

show it to my Head of Department, who encourages

the use of TI-Nspire handhelds but had not yet tried

them. After she saw this activity she agreed that it

would be useful for her teaching to install the TI-

Nspire software on her PC too.

*sight 9

Sara BrouwerFor Sara (Southbank

International School),

the Great Teaching

Moment occurred when

she realised the power

of TI-Nspire’s statistical

features.

I tend to teach using the TI-Nspire computer software

projected onto a whiteboard.

During one lesson I was discussing the measures

of central tendency with a class, showing these

dynamically by means of multiple representations.

When we changed a value in the spreadsheet

our related graphs were instantly updated,

for instance changing the value 0.15 to 0.13

elongated the left whisker.

Not only does the box and whisker change but also

the scatter plot. We were able to use this dynamic

shifting of a single point to discuss how a single

value can change the mean but that median and

mode were more robust. For example, data such as

income at a company where the Chief Executive and

everybody else’s salary is recorded might have

a high mean; however the median or mode could

be better indicators of the salary of the company.

However, if the data are symmetric, all measures of

central tendency will be the same and the box plot is

a simple way to introduce skewness and kurtosis.

We were also able to add a movable line and analyse

to show the residual squares allowing the students to

guess the position of the least-squares line.

The students were mesmerized as they watched the

boxes grow and shrink and the digits of the sum of

squares changed like numbers at the petrol pump.

They were bowled over by the dynamic nature and the

speed of the calculations. The technology provided a

most convincing connection between the position of

the movable line and minimum sum of squares.

Jon SkinnerJon’s Great Teaching

Moment occurred with

a Year 8 class at Hele’s

School, Plymouth.

He was using this

pre-made tns fi le,

Triangle Area, which

can be downloaded

from the Nspiring

Learning website

(nspiringlearning.org.uk).

In this activity to explore the formula for the area of a triangle,

students moved between a Geometry and a Lists & Spreadsheet page.

They could drag the vertex point to form

different-looking triangles, capture the data to

the spreadsheet and look for connections in the

calculated values. As the students discovered

what they could do and discovered for themselves

the connections, there were a series of those

unforgettable, magic moments in the classroom.

The TI-Nspire document then offered a series of

other pages. There were multi-choice questions

with feedback on each question readily available by

means of the menu button. It asked students to draw

and fi nd areas of scalene, isosceles and right-angled

triangles. Students were required to draw fi ve triangles

with an area of 18 cm2, checking these on an integer

grid. Finally there were several possible plenary

activities including problems as well as opportunities

to undertake Assessment for Learning.

At the end of the lesson I gave students a feedback

sheet that asked about the use of the TI-Nspire in

aiding their understanding of the concepts involved.

The over-whelming response was that they had

really enjoyed using the handhelds and had really

appreciated the opportunity to work independently.

I realised that my own role during the lesson

had been considerably different from usual,

encouraging them in discussion about the

concepts involved and helping them with using the

handheld. For me this was a change of ethos as

pupils were independently learning for themselves

and not afraid to make conjectures of their own.

10 *sight

Deidre MurrayDeirdre’s great moments

came when she

was using TI-Nspire

Navigator in a

cross-curricular context.

I have made great use of the Nspiring Learning website and, as

I am interested in making links with other subjects, some of the

STEM activities, particularly Hydrocarbons, have proved very useful.

My fi rst lesson was with an S1 maths class where

the focus was investigating the nth term of a

formula. Hydrocarbons provided a real context

and they were engaged and motivated by the

technology. We found TI-Nspire Navigator’s Quick

Poll feature helped focus their thoughts and

the handhelds demonstrated the links between

carbon and hydrocarbons beautifully. Using the

technology helped them see the connections

between a chemical formula, a sequence and nth

term formula, and a straight line.

With our school’s Chemistry teacher I then used

the activity with a Higher Chemistry class to look

at alkenes and alkynes. Some of the class had

used the handhelds before and they helped

those that hadn’t. We used the Hydrocarbons

tns fi le – I went over the formula for alkanes and

then they worked through the problem pages

for alkenes and alkynes. They were quick to

get the connections and then we went through

a couple of Quick Polls to check understanding.

The Chemistry teacher’s “wow moment” came

when she saw Navigator’s ability to capture the

handhelds’ screens, displaying them on the board

and so being able to target those people struggling

or sitting doing nothing!

The maths ability of the class was fairly high and

most had covered the straight-line topic before

but they commented on how useful they found it

to see the links between the concepts. Certainly

we found that TI-Nspire Navigator enhanced

engagement and enjoyment of the lesson – for

students and teachers alike!

*sight 11

What TI technology is available?We offer a range of handheld devices,

software, wireless systems, graphics

calculators, data logging sensors and

probes (to meet the STEM agenda).

Our software integrates with existing

classroom projection systems to enhance

the learning and teaching experience.

• TI-Nspire™ – the award-winning

handheld and software ICT

suite for maths and science

with additional options:

• Teacher Software - includes

an emulator of the TI-Nspire handheld

and enhanced functionality

• TI-Nspire Navigator™ System –

the wireless classroom network

for TI-Nspire

• TI Connect-to-Class™ – document and

fi le sharing for TI-Nspire handhelds

• CBL 2™, CBR 2™, EasyTemp™ and

EasyData™ with support for more than

30 probes and sensors.

• The TI-84 Plus™ and TI-83 Plus™

family of graphics calculators

• TI-SmartView™ – the software emulator

of the TI-84 Plus graphics calculator

• Cabri Junior and a host of other APPS

available on the TI-84 Plus

• TI-Nspire CAS, TI-89 Titanium and

Voyage™ 200, our CAS (Computer

Algebra Software) solutions.

For more information, visit nspiringlearning.org.uk

All handheld devices available in Europe are manufactured under ISO 9000 certifi cation. Cabri Log II is a trademark of Université Joseph Fourier. All trademarks are the property of their respective owners. Texas Instruments reserves the right to make changes to products, specifi cations, services and programs without notice. Whilst Texas Instruments and its agents try to ensure the validity of comments and statements in this publication, no liability will be accepted under any circumstances for inaccuracy of content, or articles or claims made by contributors. The opinions published herein are not necessarily those of Texas Instruments. ©2010 Texas Instruments

TI Technology Loan – to support evaluation of our technology

and your CPD activities.

Using our free loan service, you can fi nd

out more about how TI technology can

enhance your pupils’ learning. It’s an ideal

way for you to get TI products for teacher

workshops and in-service training or to

borrow individual handhelds for class

evaluation. Loans are available for up

to three weeks.

What services do we offer?

T3 (Teachers Teaching with Technology™)Since 1992, T3 practitioners have been

delivering professional development for

mathematics and science teachers.

Their experience and depth of subject

knowledge helps teachers to develop

effective practices through pedagogy

and technical confi dence. The courses

they run place the emphasis on sharing

appropriate uses of ICT in the classroom.

In addition to offering a range of CPD

opportunities, T3 members support research

projects and author supporting materials for

a wide range of activities and topics. T3 is an

international organisation and support from

Texas Instruments enables practitioners to

deliver high quality courses and classroom-

ready materials.

For further details, including dates and

venues, please visit www.tcubed.org.uk or

email t3@ti.com.

Volume Purchase Programme– free TI technology for volume purchases

through our educational suppliers.

With every purchase of a TI-Nspire

handheld device or graphics calculator,

you could obtain free TI technology –

from as little as purchases of 20 devices.

Contact your local Education Technology Consultant etcuk@ti.com

In Central, Eastern

England and Wales,

please contact

Christopher Rath:

T: 01604 663077

M: 07810 152450

In Scotland, Northern

England, Northern Ireland

and the Republic of

Ireland, please contact

Alex MacDonald:

T: 01604 663039

M: 07584 141152

In Southern England

including London,

please contact

Mark Braley:

T: 01604 663060

M: 07584 141146

They are happy to provide more information, help organise loan equipment, share materials

and deliver product demonstrations, as well as support for T3 events in your region.