in this issue: fretboard mathematics using cas… · spring 2011 in this issue: fretboard...
TRANSCRIPT
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, [email protected], 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 [email protected].
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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.
Ch G h ith it bl i d tti
C t t P di l t th i li
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 [email protected].
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 [email protected]
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.