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vce-cas-consids-opts_vid-transcript.htm
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<h1 align=center style='text-align:center'><b><i><span style='font-size:18.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>VCE CAS Calculator
Options and Considerations Video Transcript</span></i></b></h1>
<h2 align=center style='text-align:center'><b><span style='font-size:16.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>On the
Independent Use of Software Calculators by a Year 10 or VCE Student Using a
Screen-reader and / or Braille Display</span></b></h2>
<p class=MsoNormal align=center style='text-align:center'>Produced by Nathaniel
Schmidt on behalf of the EduVis ‘Pat Roberts Accessible Calculator Benefit’.</p>
<span style='font-size:12.0pt;line-height:200%;font-family:"Times New Roman",serif'><br
clear=all style='page-break-before:always'>
</span>
<p class=MsoNormal> </p>
<h2 align=center style='text-align:center'><b><span style='font-size:16.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>Introduction</span></b></h2>
<h3 align=center style='text-align:center'><b><span style='font-size:14.0pt;
line-height:200%;font-family:"Times New Roman",serif'>Aim and General Audience</span></b></h3>
<p class=MsoNormal>Welcome to the Eduvis CAS software calculator considerations
analysis. My name is Nathaniel Schmidt. I completed my secondary Victorian
Certificate of Education (VCE) in 2013 and am currently studying a Bachelor of
Computer Science at Deakin University.</p>
<p class=MsoNormal>In the following videos, it is my intention to give you an
overview of some of the different options available to vision impaired students,
especially when it comes to software calculators, if you want to independently study
maths at an intermediate or advanced level, especially in latter years of high
school, from year ten upwards. If you have never yet thought about studying
maths in late high school, especially if the reason is because you are worried
about not being able to do the work, or if you are worried about not being able
to get a good grade then I hope that the suggestions in this video will help to
alleviate some of your concerns. </p>
<p class=MsoNormal>It is also hoped that more students who are already studying
mathematics may consider transferring there skills over to independently using
their own calculators, rather than completely relying on a human aid such as a
teacher’s aid, a scribe for an exam, or a parent to get their work done.</p>
<p class=MsoNormal>If you have stumbled across this video outside of the Eduvis
website and are still confused as to what this is all about, you can visit <a
href="http://eduvis.com.au">eduvis.com.au</a> for more information.</p>
<p class=MsoNormal> </p>
<h3 align=center style='text-align:center'><b><span style='font-size:14.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>Specific
Audience – Who is This Resource Really Meant For?</span></b></h3>
<p class=MsoNormal>If you are a vision impaired student anywhere in the world,
or if you are a teacher who has a vision impaired student then we think it is
quite likely that you will find these resources helpful. Having said that,
most of what is said here will have very specific relevance to you if you are a
high school student from Victoria, Australia, studying according to the
educational specifications outlined by the Victorian Curriculum and Assessment
Authority (VCAA). If you are a year 10 student and wish to continue mathematics
studies in years 11 and 12, it is hoped that the following information may make
your transition much easier.</p>
<span style='font-size:12.0pt;line-height:200%;font-family:"Times New Roman",serif'><br
clear=all style='page-break-before:always'>
</span>
<p class=MsoNormal> </p>
<h2 align=center style='text-align:center'><b><span style='font-size:16.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>A Note
on Calculators</span></b></h2>
<h3 align=center style='text-align:center'><b><span style='font-size:14.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>CAS
Calculators</span></b></h3>
<p class=MsoNormal>CAS stands for Computer Algebra System. A CAS calculator
allows for manipulation of a computer to use the same mechanical techniques
that a human mathematician would use in order to solve complex equations. It
takes away a lot of the working out process so that you can just type in an
equation to get the answer. You can do this with quadratics (linear
equations), polynomials, combinatorics and a whole range of other things. They
are really helpful and make school and homework a lot faster. CAS calculation
is built into some scientific and graphing calculators; and they are the type
of calculator that VCAA wants students to use when students study VCE. Even if
you use a different type of calculator, such as a graphing or scientific
calculator, you may still find some of this information helpful, since CAS
capabilities are already built into many of these devices, hardware and
software calculators alike.</p>
<p class=MsoNormal> </p>
<h3 align=center style='text-align:center'><b><span style='font-size:14.0pt;
line-height:200%;font-family:"Times New Roman",serif;color:windowtext'>Difference
Between CAS and Scientific Calculators</span></b></h3>
<p class=MsoNormal>Sometimes there is a difference between a CAS calculator and
a scientific calculator but sometimes there isn’t. If you are not sure whether
you are using a scientific or CAS calculator, it is always good to check whether
or not your calculator has CAS functionality built into it as a programmable
extension. If you live in Victoria then In years seven, eight and nine, you
get to use basic scientific calculators which can deal with certain aspects of
geometry and trigonometry, probability and statistics, finance, engineering
measurements and logarithms. But sometimes you will want to use a calculator
to solve, simplify or expand complex algebraic expressions, or to deal with
counting permutations and combinations involving matrices, as well as many
other things. To do this, it can be helpful to use a Computer Algebra system to
replicate the same procedures that you would use yourself when you want to
solve an equation on paper.</p>
<p class=MsoNormal>In Australia, outside of Victoria, different states use
either graphing or scientific calculators, some of which, as already stated,
can come with a certain amount of CAS functionality beyond scientific basics.
But in Victoria, as already stated, it is expected that you use a specialised
scientific calculator that can perform CAS-related operations. In fact, the
student is quite disadvantaged when not using a CAS calculator, since the
subject content uses examples to follow for textbook exercises which rely on
CAS calculator operations.</p>
<p class=MsoNormal> </p>
<h2 align=center style='text-align:center'><b><span style='font-size:16.0pt;
line-height:200%;font-family:"Times New Roman",serif'>Personal Reflection</span></b></h2>
<p class=MsoNormal>When I studied high school maths in years 10, 11 and 12, especially
when I started year 11 VCE, this was at a point where I had just started
transitioning a lot of my work from being written in hardcopy Braille and calculated
on hardware calculators, to using a software calculator and writing my school
work on a computer. It was basically necessary for me to do a lot of my own
homework; although I did get a lot of advice from a friend who was studying
maths at the same time as me and who had already done a lot of research on
calculators and how to write maths on the computer. But there were still a lot
of difficulties. One of the biggest ones was that I did not always know how to
properly read and understand the documentation for the software calculator I
was using. This meant that I could not always figure out for myself how to
translate some of the procedures and functions I had to use into practical
examples. Solving algebra via a calculator was pretty easy. But I had trouble
figuring out how to count combinations and permutations by using matrices,
without consulting someone else beforehand who had already performed the
procedure. I can do this easily enough now but back then it was difficult to
learn on my own. There were probably other issues as well but these are all I
can think of since the 7-8 years or so that it’s been since I specifically worked
on these things in a high school setting.</p>
<p class=MsoNormal>What I did not ever have access to – but wish I did have
access to – was some kind of a guide, specifically tailored to my own
situation, compiling instructions on how to use different software solutions
for performing calculations and writing out maths on a computer. It would have
saved months of research, time that could have been spent on doing actual
school work to get the maths done.</p>
<p class=MsoNormal>This is why we have put together the videos you are now
watching. I hope they are of benefit to you and make life a bit easier. Hopefully
there may also be more vision impaired students who are prepared to take the
plunge and study more advanced levels of mathematics education, such as
mathematical methods or even specialist maths, education and knowledge that is
required if one wishes to pursue a career in any fields of engineering,
computing, physics and other scientific fields.</p>
<b><span style='font-size:16.0pt;line-height:200%;font-family:"Times New Roman",serif'><br
clear=all style='page-break-before:always'>
</span></b>
<p class=MsoNormal><b><span style='font-size:16.0pt;line-height:200%;
color:#2F5496'> </span></b></p>
<h2 align=center style='text-align:center'><b><span style='font-size:16.0pt;
line-height:200%;font-family:"Times New Roman",serif'>Using Software
Calculators</span></b></h2>
<p class=MsoNormal>When you are studying any subject at any level, it is always
good to try your best to work within a standard that is closest to the
technical specifications outlined by the overseeing educational body that your
school is under. In Victoria, the good thing is that VCAA has already approved
around half a dozen software applications that you can use on your computer as
a CAS calculator, so you don’t necessarily have to make too many compromises in
order to work around the requirements for your education. In this examination,
we will be looking at three of these solutions. We will also have a look at a
fourth solution, Maxima, which is the free and open-source software calculator that
a software engineering friend and I used in order to help us do CAS Maths, or what
is officially called Mathematical Methods in years 11 and 12. We will examine
some of the features of these calculators, along with the pros and cons of each
solution when compared with each other. We will not be able to cover
absolutely everything that you can use these calculators for in your studies,
so it will still be very important for you to do your own homework, to figure
out extra features you may need in order to perform calculations from examples
or exercises in a textbook or workbook. Hopefully these insights get you off
to a good start.</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Available and approved CAS software calculators:</p>
<p class=MsoNormal>Maple</p>
<p class=MsoNormal>At the end of every command line, you need to input the ';'
for Maple to know the line is finished.</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Basics</p>
<p class=MsoNormal>Add </p>
<p class=MsoNormal>+</p>
<p class=MsoNormal>subtract</p>
<p class=MsoNormal>-</p>
<p class=MsoNormal>mulitply</p>
<p class=MsoNormal>*</p>
<p class=MsoNormal>divide</p>
<p class=MsoNormal>/</p>
<p class=MsoNormal>to the power</p>
<p class=MsoNormal>^</p>
<p class=MsoNormal>Numbers</p>
<p class=MsoNormal>Rational or irration number expansion:</p>
<p class=MsoNormal>evalf(6/9);</p>
<p class=MsoNormal> 0.6666666667</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>square root:</p>
<p class=MsoNormal>sqrt(8);</p>
<p class=MsoNormal> (1/2)</p>
<p class=MsoNormal> 2 2 </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>cube root:</p>
<p class=MsoNormal>root(8, 3);</p>
<p class=MsoNormal> 2</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Solve Equations</p>
<p class=MsoNormal>solve(n/6 = 5);</p>
<p class=MsoNormal> 30</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>solve(2*b - 4*b = -b + 3);</p>
<p class=MsoNormal> -3</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Inequalities</p>
<p class=MsoNormal>One step linear inequalities</p>
<p class=MsoNormal>solve(`>=`(z + 4, 1));</p>
<p class=MsoNormal> RealRange(-3, infinity)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Advanced inequalities</p>
<p class=MsoNormal>solve(`>=`(-k - 2, 14));</p>
<p class=MsoNormal> RealRange(-infinity, -4)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Logarithms</p>
<p class=MsoNormal>log(2);</p>
<p class=MsoNormal> ln(2)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>log10(2);</p>
<p class=MsoNormal> ln(2) </p>
<p class=MsoNormal> ------</p>
<p class=MsoNormal> ln(10)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>log10(100);</p>
<p class=MsoNormal> 2</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>log[5](5) = log[5](5);</p>
<p class=MsoNormal> 1 = 1</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Exponential and Logarithmic Functions</p>
<p class=MsoNormal>solve(8^x = 9);</p>
<p class=MsoNormal> 2 ln(3)</p>
<p class=MsoNormal> -------</p>
<p class=MsoNormal> 3 ln(2)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>solve(log[6](y) = 1);</p>
<p class=MsoNormal> 6</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>solve(log(2*t) = log(8));</p>
<p class=MsoNormal> 4</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Monomials</p>
<p class=MsoNormal>4*u^5 + u^5;</p>
<p class=MsoNormal> 5</p>
<p class=MsoNormal> 5 u </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>(9*u^5)*(3*u^6);</p>
<p class=MsoNormal> 11</p>
<p class=MsoNormal> 27 u </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>need to put asterix here or else will result with:</p>
<p class=MsoNormal>(9*u^5)(3*u^6);</p>
<p class=MsoNormal> 5</p>
<p class=MsoNormal> / 6\ </p>
<p class=MsoNormal> 9 u\3 u / </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>(4*g^2)/(4*g^9);</p>
<p class=MsoNormal> 1 </p>
<p class=MsoNormal> --</p>
<p class=MsoNormal> 7</p>
<p class=MsoNormal> g </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Polynomials</p>
<p class=MsoNormal>add and subtract polynomials</p>
<p class=MsoNormal>(5*x^2 + 2*x - 4) + (-2*x^2 + 4*x - 5);</p>
<p class=MsoNormal> 2 </p>
<p class=MsoNormal> 3 x + 6 x - 9</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Multiplying polynomials (exapnding)</p>
<p class=MsoNormal>expand((q - 3)*(q + 3));</p>
<p class=MsoNormal> 2 </p>
<p class=MsoNormal> q - 9</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Factorising</p>
<p class=MsoNormal>factor(g^2 + 14*g + 13);</p>
<p class=MsoNormal> (g + 13) (g + 1)</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>factor(m^2 - 10*m + 25);</p>
<p class=MsoNormal> 2</p>
<p class=MsoNormal> (m - 5) </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Quadratic Equations</p>
<p class=MsoNormal>solve(2*(y + 4) = 0);</p>
<p class=MsoNormal> -4</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> "(->)"</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>still need to find out how to group and solve quad equations</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Mathematica</p>
<p class=MsoNormal>Initialisation for usage:</p>
<p class=MsoListParagraphCxSpFirst style='text-indent:-18.0pt'>1.<span
style='font:7.0pt "Times New Roman"'> </span>Create
a system and / or user (preferably system) environment variable for the Wolfram
engine / Mathematica directory</p>
<p class=MsoListParagraphCxSpMiddle style='text-indent:-18.0pt'>2.<span
style='font:7.0pt "Times New Roman"'> </span>Press
Windows+R and then type “cmd” to open a command prompt.</p>
<p class=MsoListParagraphCxSpLast style='text-indent:-18.0pt'>3.<span
style='font:7.0pt "Times New Roman"'> </span>Type
either “wolfram” for the command-line client, or “mathematica” for the
graphical interface.</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>Usage:</p>
<p class=MsoNormal style='margin-left:18.0pt'>% stands for previous result
e.g. %+6</p>
<p class=MsoNormal style='margin-left:18.0pt'>Use a space or * for
multiplication, not the “x” character e.g. </p>
<p class=MsoNormal style='margin-left:18.0pt'>Use parentheses (not braces or
brackets) to show levels of grouping e.g </p>
<p class=MsoNormal style='margin-left:18.0pt'>Arguments to built-in functions
are separated by commas and enclosed in square brackets:</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>If you don’t know what function
to use, type = at the beginning of a line for natural-language input: e.g. =
Plot a sine curve</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>Lists represent collections of
items and are indicated by { ... } e.g. { 1,2,3} +2</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>construct lists with functions
like Range[10]</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>(Use CTRL+ / to enter fractions</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>Put fractions over their lowest
common denominator with Together: </p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>Scientific form e.g. </p>
<p class=MsoNormal style='margin-left:18.0pt'>Variables start with letters and
can also contain numbers:</p>
<p class=MsoNormal style='margin-left:18.0pt'>(It’s best to start with
lowercase letters, reserving capitals for built-in objects</p>
<p class=MsoNormal style='margin-left:18.0pt'>use /. and  to make
substitutions in an expression: e.g. 1+2x/.x→2</p>
<p class=MsoNormal style='margin-left:18.0pt'> </p>
<p class=MsoNormal style='margin-left:18.0pt'>Define your own functions with
the construction e.g f[x_]:=2x+1</p>
<p class=MsoNormal style='margin-left:18.0pt'>:= means that any argument passed
to f is substituted into the right-hand side upon evaluation: e.g. f[2] = 5</p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Matlab</p>
<p class=MsoNormal> </p>
<p class=MsoNormal> </p>
<p class=MsoNormal>Modes of usage:</p>
<p class=MsoNormal>GUI: None or possibly Maple.</p>
<p class=MsoNormal>CLI: Maple and Mathematica.</p>
<p class=MsoNormal>Web app frontend: Matlab.</p>
<p class=MsoNormal>Compatibility across common devices and platforms.</p>
<p class=MsoNormal>Installation files / process.</p>
<p class=MsoNormal>Maxima.</p>
<p class=MsoNormal>Compatibility with common screen-readers.</p>
<p class=MsoNormal>Ease of locating and learning commands for operation.</p>
<p class=MsoNormal>Flexibility and intuitivism.</p>
<p class=MsoNormal>Support for teachers on using CAS in CLI.</p>
<p class=MsoNormal>Demonstrate mathematical examples.</p>
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