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Nemeth
Subjects:
- Questions about Nemeth Braille
- Sighted Reading of Nemeth
- Performing calculations as blind students, tips, tricks and advice for the NFB Youth Slam
- Learning Nemeth
Related Topics:
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1.Subject: Question about Nemeth Braille
Michael Whapples
mikster4@msn.com
Sun Jan 14 2007
Hello,
For a few reasons, I have looked a little at Nemeth braille, and the code seems understandable to me, but there is one bit that I am puzzling at. From what I have seen of it (when some of my notes have been produced in Nemeth rather than BAUK, and when looking at how Alastair Irving's LaTex access scripts are coming on) I noticed that it seems like = and kappa are the same. Is this right, or how are you meant to know what is meant?
Also, one of the reasons why I was looking at Nemeth is that I will be giving a talk about maths accessibility for the blind, and I felt as mathspeak (I think) is based on Nemeth rules and Nemeth has such a following, it could not go unmentioned as a system used. Would anyone be interested in a recording of the talk (if I can get permission for a recording)? The talk will head in the direction of what technology has done for accessibility in maths, what needs to be done to make maths accessible with technology (e.g. mathml rather than html with image equations), and what still needs to be tackled, while covering some of the basics of how maths can be done by the blind. It is going to be aimed at staff (not necessarily any previous experience with the blind) for how they can support students, and where the difficulties may lie.
Responses:
Louis Maher ljmaher@swbell.net
Sun Jan 14 2007
Equals is dots 4-6 1-3.
The letter kappa is 1-3, and the Greek letter indicator is 4-6; therefore, equals and kappa would look the same. The National Braille Press sells a $15 Braille reference booklet on the Nemeth code
(http://www.nbp.org/ic/nbp/NEMETH.html).
Michael Whapples
mikster4@msn.com
Sun Jan 14 2007
Thanks for confirming that. It now leaves the question, how should one know the difference between equals and kappa? This seems a bit of a stupid thing for a braille code which has been suggested to me over BAUK (due to its better design?).
Alastair Irving alastairirving19@hotmail.com
Sun Jan 14 2007
The = sign always has a space before and after it, whereas Greek letters are generally unspaced.
Louis Maher ljmaher@swbell.net
Mon Jan 15, 2007
Hi Michael,
Keep in mind that there are only 6 dots in a Braille cell, and that leaves 2 to the sixth power -1 = 63 combinations. The minus one comes from not brailing any dots--a blank cell. Nemeth code is the most efficient mathematics code, for the blind, of which I am aware. You have to read some equations using context to figure them out.
Michael Whapples mikster4@msn.com
Tue Jan 16 2007
I realize the limitation of the braille cell, but something as simple as kappa and equals is much more well defined in BAUK. May be it is due to BAUK using more prefixes, which I realize makes it slightly more bulky, but which is preferable, clear braille or compact braille where great thought is needed to know what might be meant? As far as I can think it is very rare that a space is actually required in BAUK (usually they are used to help separate terms for ease of reading). I don't know if it is just simply that I have grown up learning BAUK, so have this view, but could it be equally that people who learn Nemeth find the change hard?
Robin Williams robster3@hotmail.com
Tue Jan 16 2007
I can only comment from having used both and Nemeth for a couple of years now, that if you read enough material in certain Braille code you will adjust sooner than you might think. When you read at speed the interpretation of the Braille cells is almost subconscious, in my opinion, and you will be aware of the context of what you are reading. Taking your kappa example, you would expect more equations to read Kappa equals ... Rather than Equals kappa...
Obviously there will be exceptions where you may have to put some thought in but I think that the amount of proficiency that Nemeth has over BAUK far outweighs any potential confusion, which as I say will be few and far between.
Having grown up on BAUK, if I was now asked how somebody starting out with Braille mathematics should proceed, I would probably advise Nemeth, partly due to its less bulky nature but also due to the wider range of materials available and projects that are focused on producing Nemeth output.
Michael Whapples mikster4@msn.com
Tue Jan 16, 2007
I would most certainly think the number of projects working towards Nemeth output and the number of texts is one reason for using Nemeth, but is mass use necessarily an indication of what is best (Linux user in me coming through again). The fact of number of users was why I am now working on making BrlTex modular, so that all users of Nemeth parts of it would be testing input modules (the hard part of translation hopefully) which would also be used by BAUK (or any other output format), so Nemeth users would also be testing parts of the BAUK translator.
Just out of interest what do you feel are the advantages (for reading, regardless of availability of materials) of Nemeth over BAUK, as initially there seems to be very few to me.
Robin Williams robster3@hotmail.com
Wed Jan 17, 2007
Probably the feature I like most about Nemeth over BAUK is that it seems, in my opinion, to follow more logically the concepts that a print user would be familiar with when reading/writing mathematics. For example, in BAUK there is often a need to put brackets around expressions that would not be bracketed in print, whereas this is not the case in Nemeth. I therefore think that becoming familiar with Nemeth has probably enabled me to produce mathematics in LaTeX that appears to be as a sighted reader would write it, rather than having extra unnecessary brackets etc.
2.Subject: Sighted Reading of Nemeth Math
Susan Jolly easjolly@ix.netcom.com
Fri Mar 13 2009
I disagree with the claim about Nemeth math printed out from a BrailleNote making "no sense to the naked eye."
If you print out Nemeth math from a BrailleNote in the original computer braille (not back translated) it will show up as ASCII characters. It shouldn't take a math-knowledgeable sighted person more than a few minutes to learn to read it. (The reason is much of computer braille was based on Nemeth math. For example, the digits and common symbols such as the plus sign are identical.) Here's an article I wrote several years ago on this topic that you might want to pass along to your teachers. http://www.dotlessbraille.org/readnem.htm
I'm glad to correspond with any sighted persons who need more help than is in my article.
3.Subject: Performing calculations as blind students, tips, tricks and advice for the NFB Youth Slam
Birkir R. Gunnarsson birkir.gunnarsson@gmail.com
Tue Jul 12, 2011
Hey yea wise people.
I am giving a presentation to the NFB Youth Slam students next week on math accessibility and issues to deal with in college. There has been a lot of talk and a lot of resources on reading math, and not insignificantly, to writing math as well. However one thing I feel often gets lost in the mix are techniques for actually performing calculations and working one's way through equations in order to find a solution i.e. the calculation part itself. I have some experience of course, but I'd be curious to hear what works for people around here, especially VI or blind folks who have completed STEM degrees in college.
Did you use LaTeX, Nemeth or some other code to write your way through each step in the process of solving your calculations? If not, how did you do it? Is some software particularly useful for those (anyone remember Derive? It was a dos software and it saved my behind quite a lot in high school and college, but I am not even sure it is available anymore, and it was too powerful for some things). I want to devote a few minutes to this in my presentation, but I am having trouble finding material that is not just based on my own experience.
Any input is more than welcome.
Responses:
John Gardner john.gardner@orst.edu
Tue Jul 12, 2011
Hello Birker, it is certainly possible to solve algebraic equations using Latex notation, but that is pretty verbose and clumsy. As is just about every other standard notation. Most blind people who have to do this sort of thing seem to invent their own shorthand. Even people who work in Braille often use shortcuts instead of official Nemeth.
For years after losing my sight, I used an abbreviated form of Latex for working out algebraic equations. It worked but was pretty clumsy. My group developed WinTriangle with the purpose of reducing notation to a minimum, and I used that for a while too. It was really nice, having single keystrokes for many common symbols such as Greek letters, integral sign, raised symbols for superscripts, dropped symbols for subscripts, etc. It was the most compact way I have ever seen for writing math on a computer. Unfortunately, Triangle also had disadvantages, and they have meant that it is no longer a viable thing with modern OS. ChattyInfty is not quite as compact as WinTriangle, but it is pretty close. I would recommend it as the best alternative that I know for writing and developing math equations on a computer. Among other benefits, you can cut, copy, and paste parts of equations. And copy them into separate files for pasting in a number of times. That's a great advantage when working with complicated equations.
Steve Jacobson steve.jacobson@visi.com
Wed Jul 13, 2011
I won't say too much about my experience as it predates the use of personal computers as they are used today. However, there are a couple of things that I think are worth considering.
Students need to have some idea of how much math they are going to take. Nowadays, if one plans on majoring in math, for example, it is going to be worth their time to become familiar with some sort of math system such as Latex to do their math, and students need to keep up with other developments. I am less certain, though, that this investment is worth it for students trying to simply fulfill a math requirement for a major in another area. I have known students to get bogged down in trying to come up with an independent way of dealing with accessibility issues at the expense of their coursework.
Particularly if a student is using braille, knowing Nemeth Code, writing it on paper and using a reader is still not an option to be ignored. John's point that when writing one may well use a relaxed form of Nemeth with their own shorthand is a good one. Becoming stuck on writing something the right way when you are the only one reading it doesn't make sense. The point needs to be made that the most independent way of approaching a situation may not always be the most efficient. Also, when I was in school, the role of math in other sciences such as physics required a completely different level of rigor than did my math classes. I gather this is still the case, and the role of calculating and stastical software is going to play a more important role for someone studying other sciences than will mathematical notation.
I would also tell your students that if one is serious about taking a lot of math, some of the investigation and learning of notation systems needs to take place outside of ones classes and should best be done beforehand. It doesn't wash to say that one couldn't complete an assignment because one was still slow at using Latex or other notation system. Yes, it is an additional level of knowledge that we may have to deal with, but it is one that should and can be anticipated.
Students have to think carefully about the role of a computer. I still see high school kids who are sighted using paper a lot to solve equations. This doesn't mean there isn't a role for the computer, but thought has to be given to what that role should be. I have no doubt that the use of paper is going to die out, especially with the flexibility of pad style computers, and in time that may help us as well, but blind students have to realize that there isn't just one answer, and part of their responsibility as students is to figure out the approach that will work best for them. While no approach is perfect, at least there are some options, and that is exciting.
Birkir R. Gunnarsson birkir.gunnarsson@gmail.com
Wed Jul 13, 2011
Thanks to everyone who has contributed so far. I agree with Steve that we mustn't get too focused on computers when solving math problem. In fact, the natural way to solving math has-been pen and paper for all the people I have worked with and I have had better success with certain problems by diggin up my Perkins and using it to simplify equations. Also braille support for math is sadly still inefficient, especially in the refreshable braille department. But that's a whole separate issue I don't want to take over this discussion. Please keep the ideas coming, if you have new ones. I will post my write up/presentation notes on www.access2science.com (if desired)after I have given the presentation in Baltimore.
Pranav Lal pranav.lal@gmail.com
Wed Jul 13 2011
Hi all,
I used a talor frame for basic math operations. This was before the personal computer. I recently had to relearn converting decimal to binary and vice versa. A spreadsheet came in handy since I was able to enter the problem and do the process manually.
Ken Perry kperry@blinksoft.com
Wed Jul 13 2011
I agree with this 100%. I majored in Software Engineering and had to take Matrixes, Trig, and three levels of Calculus. I lost my site in the military and was not a skilled Braille user. So I did everything in a scrolling calculator and a text editor. Assisted by a reader when I had assignments I would do them my computer based method and have the reader write them out. Yes this was not an optimal solution but it got me through math. I was skilled in math since my field in the military was Electronics and found that by the time I took Trig I was already able to do quite large problems in my head. The instructor used to call on me to tell him what steps came next because he knew I kept up that well. That or he just wanted to see if he could stump me. That continued through Calculus. I tried to make sure to pick instructors that gave homework but did not require it as a grade. This way I could do the amount of problems I needed to, to understand each problem type without going nuts on repetitive work. I would only call the reader in if I had to either take a quiz, test or turn in some homework which I found was pretty rare.
You might think I didn't learn much this way but I did turn around and help my sons, daughters, and my brother all through math courses and in some cases equivalent courses. I couldn't do a 3rd Integral today but I know what one could be used for and I know where to find functions in math libraries for my job if I need them. I use math in coding almost every day but I haven't had to have a reader for some time because in a coding job its more if you use the fastest possible method and get the most accurate answer not if you can write it out on a piece of paper.
When I was in college I also tutored for another blind student who had no idea what a graph looked like. This amazed me since we were in a college setting I would have thought someone would have taught him earlier. I actually went to home depo cut up some peg board and created a large graphing board we could work on. That I think helped him more than anything as he was getting going in Algebra it's amazing what you can do with some peg board, rubber bands, and golf pins.
I am only now learning Nemeth Braille 20 years after I lost my site and I am doing that for a project I am working on. I am probably to slow at it to make it very useful but I will give it a shot.
I will say though if you're going to use readers writers for your math make sure they have a math background. I had a reader in my trig class that was an English major. When I told her X^2+x-22=5 she wrote X to the power of two plus x minus twenty two equals five
If you don't see what is wrong with what she wrote read character by character and you will. My trig teacher gave me a 96 on the test but he said it took him 2 hours to grade the thing. I doubt it took that long but from that point on I always asked for someone who at least knew what I was talking about.
Sharon Clark sharonjackson03@comcast.net
Wed Jul 13 2011
Ken
I agree with your statement that when using a reader/scribe for math one needs a person with a math background. When taking stats., I ran into the same issue. Now that I am a teacher of the visually impaired, I have my students ask for a list of symbols and the equivalent name so that they always have a reference on hand for the high school level.
The students must have as many tools in their toolbox (low and high tech.)to accomplish the task. I always show a student the concrete method first then they can use what method works for them. For example, I have students demonstrate their knowledge of graphs using a rubberized board with pushpins and rubber bands. Once they understand the concepts, I show them how to use the Audio Graphing Calculator. The same goes for using an Abacus before using the calculator. On some assessments, the students are asked to use mental math and are not able to use a calculator. The Abacus is their pencil and paper.
Richard Baldwin baldwin@dickbaldwin.com
Wed Jul 13 2011
I'm not blind, and it has been almost 50 years since I received my engineering degrees, but I have been mentoring a blind STEM student for couple of years and I have some unconventional suggestions.
The first suggestion is the use of the Google calculator for performing calculations. My student does well with it using a screen reader and a USB Braille display. If I were a physics or engineering student, blind or sighted, I would consider it to be a major asset. One of its main strengths is its ability to accept and use units such as meters, newtons, Joules, etc.
My biggest complaint is that when it displays an exponent, it uses a superscript character instead of "^x" and I don't know how that character plays in screen readers and Braille displays. Here is an example of what I mean by that.
Input:
6 m/sec^2/3
Output
*(6 (m / (sec^2))) / 3 = 2 m / s2*
In case you can't read it, the final two characters in the output are a lower-case "s" followed by the exponent "2". Perhaps someone should lobby. Google to make the output from the calculator totally accessible to blind students.
My other suggestion has to do with the use of JavaScript. With a rudimentary knowledge of JavaScript programming, a blind student can write scripts to solve algebra, trigonometry, physics, and engineering problems. In addition to providing an accessible way to perform the calculations, this approach also gives students the opportunity to organize their thoughts and organize the solution to the problem in a beneficial way.
My blind physics student does very well with this approach also.
By using these two tools, my blind physics student doesn't have any difficulty performing the calculations necessary to solve physics problems. Her main difficulty is understanding the requirements of the problem as a result of an inaccessible physics textbook.
If you are interested in more information on this, see http://cnx.org/content/col11294/latest/
Susan Jolly easjolly@ix.netcom.com
Wed Jul 13 2011
I noticed that no one mentioned using a slate and stylus. Wouldn't that be most like using pencil and paper? I'm far from being a high school student but, like the students Steve mentioned, I still find that sketching out a rough solution on pencil and paper is often the best way for me to start making progress on solving a problem.
I'm also a big fan of working things out with Fortran pseudo-code or something similar so I can use as many intermediate variables as desired in order to not have to rewrite complex expressions. This strategy also makes it possible to minimize the amount of change going from one step to the next which has the advantage of reducing the amount of information I have to keep track of mentally.
David Andrews dandrews@visi.com
Wed Jul 13 2011
While I am a big proponent of the slate and stylus, and not a big Math person, I will say that generally it doesn't work well for Math. This is because you write down, and turn over to read. The advantage of pencil and paper, and the Braille Writer is that you immediately see/feel what you put down, and spacing allows you to establish and examine relationships. This is much more cumbersome, if not impossible with the slate.
However, I am not a Mathematician, so may be missing something.
Sharon Clark sharonjackson03@comcast.net
Wed Jul 13 2011
Dave,
I agree. My students are able to look at their progress as they solve a problem without needing to flip over the page each time they want to review a step.
James McCarthy jmccart@lbph.lib.md.us
Thu Jul 14 2011
Susan,
Let me preface this by saying I am one of those who took only as much math as I was required to... "math for historians." Also, many teachers of the blind discouraged use of a slate and stylus for math equations. One way a slate and stylus is not like pencil and paper is that the writing is not easily visible. To read what has been written, one must turn over the paper, which would lead one in many cases to keep the material in the head or prove something of a distraction. I am not aware of blind people who used a slate and stylus for math, though perhaps there are some. A Braille Writer gives the most direct view of what has been written and I think use of an abacus probably is also a really good way for blind people to learn. I had minimal instruction using one, though if I were working with a blind elementary school student, I would introduce it early in the process.
Pranav Lal pranav.lal@gmail.com
Wed Jul 13 2011
Hi all,
I used to do math years ago in high school and had it for college too. At that time, I used turbo Pascal’s functions for solving problems. So, my math would be Sin(x)+cos(x)=something. Computer programming really helped me solve math problems for instance, my concept of the use of brackets became very strong after I used them in computer programs. Many times, I would write my own program to solve a class of problem to solidify my understanding.
Littlefield, Tyler tyler@tysdomain.com
Wed Jul 13 2011
At least I’m not the only one that does that. I learn something new, then I write a program to solve the equations. IT's kind of fun and it makes me think about it, and/or do research.
Steve Jacobson steve.jacobson@visi.com
Thu Jul 14 2011
I used to use the BASIC interpreter to perform calculations in the days of DOS. I suspect that our approaches are probably seen as old-fashioned now, though. Still, as someone said, there is a lot of flexibility in Excel which is sort of between programming and using a calculator. I know that others here have mentioned the statistical package R. This is what I was getting at in my note, though, that there are really two different problems to solve. How does one write down and communicate complex equation solutions and math proofs, and how does one actually perform calculations. The two are different and the tools one might use are different. I advocated that sometimes using a braille writer and paper is not a bad alternative for solving equations and that various math notation systems need to be investigated if one is going to take a lot of math. However, to perform statistical or other kinds of calculations, there are definitely other alternatives, including the calculators on some note-takers. This point of there being two separate problems to solve, solving equations and performing calculations, might be a good one and not one that will occur to all students. I also realize that one can perform calculations using some math notation systems as well, but learning a notation system to perform calculations only is probably not worth it given that there are other alternatives.
Ken Perry kperry@blinksoft.com
Wed Jul 13 2011
That's why I loved the Xplore calculator being a coder it used Pascal as its functional language. Then I got into simply with python and love it even more. For example the Calculator on the Braille+ and Icon are written in python and you can write your own functions. There is nothing like doing math in code.
Amanda Lacy lacy925@gmail.com
Wed Jul 13, 2011
Pranav,
In physics, I write programs to work out the math and will likely do so in other STEM courses. During high school (my pre-programming days), I simply could not comprehend certain math because most humans have a tendency to say what they don't mean and skip the small "unimportant" steps. Programming allows me to work in small increments
4.Subject: Learning Nemeth
Susan Jolly easjolly@ix.netcom.com
Sun Jul 18 2010
The gh-mathspeak site has a lot of good information about Nemeth and most of the code book is online in accessible form. http://www.gh-mathspeak.com
Response:
Jose Tamayo jtblas@hotmail.com
Sun Jul 18 2 2010
The entire code book for Nemeth has been placed in the BANA web site. You may download BRF files that you can read on a refreshable Braille display