Future Reflections Fall 2006
A panel presentation from the 2006 NOPBC Annual Seminar, ďThe Equation for Success,Ē Dallas, Texas, Saturday, July 1. Panel Presenters: Lindsay Yazzalino, high school student, Washington State; Larry Jacobsen, executive director, MATHCOUNTS® Foundation, Virginia; and Denise Mackenstadt, educator of blind children and orientation and mobility specialist, Washington State.
Editorís Note: Can blind kids do math? With the right skills, tools, motivation, positive expectations, and supports from parents and teachers, the answer to this question is a resounding ďYes!Ē However, the disturbing fact is that hundreds of blind students are routinely steered away from math and math-related courses. In our technological world, where math skills are increasingly vital to most jobs and even daily living, this is simply unacceptable. Although the following material, which is a transcription of three speeches given at the 2006 convention, would normally be published in our convention issue, the topic is too important and too timely to wait. So we have included it in this, our back-to-school issue. Here is a transcription of the panel discussion. We have edited for clarity and to eliminate repetition; otherwise we have preserved the original presentations.
The first speech is from Lindsay Yazzalino, a 2004 Rocket On! Academy participant and a high school student from Washington State:
My name is Lindsay Yazzalino, and the reason why Iím speaking today is to give you the perspective of a blind math student. Iím seventeen years old. I live in Washington State and attend public high school, where Iím going to be a senior. Currently Iím in the process of completing an independent study--an AP statistics course.
Some of you guys may be wondering if blind people are capable of doing math. Well several different factors have helped me develop skills and succeed in math classes. One of them is having the right tools to work with. What I mainly use to complete my math assignments is the Perkins Brailler. I think many of you guys are familiar with it. Itís like a typewriter. You feed the paper in and, as you type, the paper comes out, and you get to see exactly what you typed. But since it embosses only in Braille, I often ask my vision specialists to transcribe the print equivalent underneath the Braille; that way my math teacher knows exactly what I have done. Also I have several different tools to make graphs. I use tactile graphing paper, tacky dots for points (people use these dots to stick vases on tables or stuff on walls), and to make graph lines I use Wikki Stiks. These are strings covered in wax. When you press them down on paper, they stick. Basically this is how I do most of my math assignments.
One of the most important factors that have enabled me to succeed is the attitude that people have. Iíve always been in an environment where people--parents, teachers, especially math teachers--have encouraged me to succeed in math. Iíve never been given the message, ďNo, you canít do it.Ē Thatís important because I have a math brain and I want to use it and I want to succeed. Iíve always been interested in math, and I have determination and the attitude that Iím not going to let the fact that my eyeballs donít work get in the way.
Also, as I said, using the Perkins Brailler has helped me succeed because itís important to be able to see the whole problem together. If you use a Notetaker with a refreshable display you only get one line and sometimes that line isnít very big. Also important is being able to use the Nemeth code. Thatís very important. Iím totally blind and I use Braille, and Nemeth is the Braille math code. If you are a blind Braille reader and if you want to succeed in a math class, Nemeth is the Braille standard, and itís important to know it.
One other vital factor that has helped me in math is having good communication with my teachers. Math teachers will develop different systems, so it is important that you--the student--develop a system of turning in assignments, knowing what to do, and how to adapt materials for each class. Often math teachers rely heavily on the overhead. Being able to have the overhead materials printed up (in Braille) ahead of time, before class, is a help. But sometimes I need someone in the class (like a vision specialist or another sighted person) to help me take notes, especially if the math teacher has a lot of material on the overhead.
Although Iíve mainly encountered positives, there have definitely been some roadblocks that Iím working to overcome. One of them is the lack of nonvisual, accessible graphing calculators for the blind. Teachers rely heavily on graphing calculators, especially in advanced math classes. The challenge for me is to get my technical skills up in certain areas so I can use mathematical technology to learn more advanced math subjects. Also getting math books on time has been a tough one. This year, as I said before, Iím taking an independent studies class, and my biggest problems have been the graphing calculator issue and the fact that math books havenít always come in on time. And when the math book isnít on time, keeping up is very difficult. Oftentimes I canít keep up because itís not just the Braille text I need, but itís the graphics, and graphics consume a great deal of time for my vision specialists to make. Also the capability to translate math Braille into print by computer is not perfected, which means that you have to use the Perkins Brailler and rely on a sighted person to help translate, and that can be inconvenient.
After I graduate from high school, I plan to go into a field of math or science. One thing I want to emphasize again is the importance of attitudes. If you have children who are math students, donít allow blindness to hinder them. Encourage them; thatís one of the best things you can do. Blindness doesnít have to be an obstacle. It hasnít been for me, and it doesnít have to be for anyone else.
Larry Jacobson, the second member of the panel, is the executive director of MATHCOUNTS, which is the math equivalent of the National Spelling Bee. A private non-profit foundation, MATHCOUNTS conducts an annual nationwide math competition for middle school students. Last fall they contacted the national NFB office seeking help in getting an accurate estimate of the cost in making the MATHCOUNTS program accessible in Braille to potential blind competitors. And the rest, as they say, is history. From that meeting Barbara Cheadle invited MATHCOUNTS to speak at the NOPBC seminar at the NFB convention in Dallas and to help NOPBC put together a mock math counts competition to demonstrate the techniques used by blind people to do math and as an educational, but also entertaining, way to encourage blind kids and their parents to think beyond the classroom when considering math. But we will talk more about the mock competition in a later issue. Here is what Jacobson had to say:
Good morning, everyone. I represent MATHCOUNTS, and MATHCOUNTS is a twenty-three-year-old organization that was formed by CNA Insurance, the National Society of Professional Engineers, and math teachers. These three groups put together materials with the aim of helping middle school students become passionate about mathematics. Now they all had ulterior motives for this: CNA needed actuaries; the professional engineers needed more professional engineers; and the teachers kind of liked teaching math. So that was the beginning of it.
Since then itís developed into a much more serious business. On the one end, mathematics is the key to social and economic empowerment--no matter who you are. At the other end of the scale is a national security issue. That one runs this way: right now we are retiring more smart mathematicians than we are able to hire young, smart mathematicians. To give you one statistic, Lockheed Martin--who builds all kinds of airplanes and neat stuff--will retire 138,000 engineers within the next few years. There arenít 138,000 engineers coming out of all of our engineering schools put together. So this has become something of a looming national crisis that is understood very well right to the top. In fact, three or four weeks ago I presented the [MATHCOUNTS] national winners to the President in the Oval Office and got into a discussion with Mr. Bush about it. He is very much aware about the national security [implications]. You know, the National Security Agency--NSA, the spy agency--consumes more mathematicians than any other group in the world. The Pentagon is number two, in general.
Everything in a digital world is math, and thatís both good and bad as it applies to blind people, deaf people, and what I will immoderately call any group of people that has traditionally been along the fringes. The bad part is that if you donít have a very good understanding of mathematics, you are that much more divorced from employment, because everything has to do with a digital world. On the other hand the digital world opens huge doors for so many people who may have been on the fringes before.
I deal with brilliant, brilliant, kids all day long. These kids are so smart that they glow in the dark. But Iíll tell you, it doesnít make any difference to the kids at that level whether you are deaf, blind, have any sort of certifiable handicap, or disadvantage or advantage. Because in the digital world Iím not so sure there are disadvantages. There are compensations, but Iím not so sure there are disadvantages. Thatís because the level of sophistication is so high that those who are involved at the level we are talking about with the kids at the very top end will compensate for anything. They are all compensating for something, regardless of what it is. I would throw that out to you as an idea that may not have been embraced by many. The fact is that every kid out there at this level is compensating for something.
Over our twenty-three years of doing math competitions, [we have grown]. We start out now with half a million kids going into the system. We send materials to 40,000 middle schools. There is a state competition, there is local competition, and by the time you get to the nationals, itís down to 280 kids. These 280 kids and the kids that are in the state competitions--these are your corporate leaders. These are your military leaders. This is the leadership group.
One of the interesting things that we are seeing is that kids who knew each other in MATHCOUNTS in the middle schools clump together; they find each other on college campuses. A few weeks ago I got a call from some kids at Yale. They said, ďDo you mind if we use your trademark?Ē
I said, ďWhat are we talking about here?Ē
They said, ďWell, weíve got a bunch of kids who are old mathletes, and weíd like to get together on campus and we would like to teach underserved kids in the black and Latino communities of New Haven.Ē
Now thatís kind of interesting.
So I went to see them. I said, ďWhy do you want to do this?Ē
They said, ďFrankly, if it hadnít been for MATHCOUNTS, we donít feel any of us would have gotten into Yale. We couldnít have done as well as we did on the SAT exams, and we want to give back.Ē
When you look at that set of kids, it was quite a crew. Theyíre not kids that you would have picked out anyplace. I can tell you right now, it wouldnít have made any difference at all if one of those kids had been blind. It wouldnít have made any difference. These kids would have embraced that kid just like everybody else, because everybody else had something that might have marginalized them.
A week later I got a call from some kids at Princeton. I said, ďI understand what your thing is; youíve got friends at Yale.Ē
They said, ďYes, we have friends at Yale.Ē
So we go up and meet the kids there. Weíll do the same thing at Penn, and Johns Hopkins, and Columbia, and Brown, and Harvard. Weíre talking with them all right now.
For years we served the kids that Iíll call diamonds. It was a matter of finding the diamonds, which were easiest to find in the white suburbs around rich cities. You didnít have to find them, because their mothers would bring them forward and say, look at how brilliant my kid is. [But] in the world now of national security issues, we canít overlook anybody. My board of directors has said to me, ďYou have to go find ways to find the kids that are harder to find.Ē
Let me tell you a little story. We just put a person on our board of directors, a Dr. Dwight Williams. Dr. Williams is the chief nuclear scientist for the Pentagon. Dr. Williams is a black man from southeast Washington. I said, ďTell me about yourself.Ē
He said, ďHereís the story. Iím from Southeast Washington. My mom was a schoolteacher in the D.C. school system. My mom realized two things: one, that the D.C. school system was a crappy school district, and two, that she had a smart kid. So she moved me to Fairfax, Virginia, arguably the best school system in the country. I ended up getting my Ph.D., and now I am a professional engineer.Ē
I said, ďThatís kind of neat. Now tell me, whatís your interest in MATHCOUNTS?Ē
He said, ďLook, Iím smart, but Iím not unique. There are thousands of kids in D.C. who will never be discovered. Theyíll be overlooked. Theyíre smart; they just have to be found. How do we do it?Ē
I said, ďYou tell me, because
if you can tell me how to find these kids, weíll work with them.Ē
The story is pretty much the same with blind kids. Theyíre smart. We have not to this point known how to find them. Through this organization we hope we can do that. So, when we got to talk with Barbara, we said, ďWe need to find a way to discover these kids, and we need to find a way to get them involved in MATHCOUNTS.Ē
On the one hand we donít want to dilute the rigor of the mathematics program. On the other hand there has to be some sort of reasonable accommodation. I donít know what that is. I know that it would be relatively easy to run a MATHCOUNTS program with all blind kids. Iím not so sure we know how to do it with blind and sighted kids for the same reason that I know how to do it with all English-speaking kids, [but] Iím not so sure how I would do it with half English-speaking and half who speak Lithuanian, because I would be speaking different languages. So weíre dealing with different languages, and we are just going to have to learn how to do that.
So one of the things we are going to do while we are here is, tomorrow, weíre going to do a little MATHCOUNTS competition. By definition we will say that it is going to be a failure because we are going to mess up along the way because we really donít know what weíre doing on this translation. On the other hand, weíre going to learn a heck of a lot, and on that part it is going to be successful. So I ask you to bear with us as we kind of fumble around, not knowing what weíre doing, but we will do our best.
I guess my message today is that the digital world has leveled the playing field. As has been said before, Braille is very, very important, so your kids have to learn Braille. They have to learn the mathematics version of Braille. Once they have those tools in place, they can operate with the best of them. Iím talking doctors, lawyers, engineers, on and on and on because mathematics is logic. Itís not numbers necessarily; itís logic. And when we think of mathematics that way, it doesnít matter if youíre blind, if youíre deaf, if youíre sighted; you just have to have some logic. As Lindsey was talking today, with the way she spoke, thereís no way that I would know that sheís blind. I talk with smart kids all day long, and Lindsey is smart. She happens to be blind, but she will be absorbed in the college curriculum just like everybody else with the whole math crew, because these are people who think.
Today I have tried to explain what we do, how we do it, how weíre changing, and hopefully bring to you a new perspective on the way blind people will be operating in a digital world. Thank you very much.
The final speech is from longtime Federationist, Denise Mackenstadt, of Washington State. Mackenstadt is a blindness educator with expertise, experience, and certification in Braille transcription and orientation and mobility. Here is what she had to say:
Well I have to say it: I am a math-a-phobic, big time. However, I have served as a Braille transcriber and a para-educator for students from grades two through eleven, and I think that means that I can safely say that Iíve passed tenth grade math; so Iím in good shape.
Math is really an international language. For example, did you know that the Japanese use Arabic numerals? Math is a language that scientists and engineers from all over the world use to communicate with each other. We donít want to deny this to our [blind] kids. There is a myth that math is too visual for blind kids to learn. Not true. It is all in the presentation of the material. Obviously a blind student is not going to learn math visually (thatís a given), so we teach math nonvisually.
Be careful about the needs of your low-vision students too. Most of the time learning media assessments (which is the term for the assessment which helps teachers decide whether the student is going to read print or Braille) are given using text, but no math symbols or math diagrams. How a student sees these things (the numeral and math diagrams), with whatever the visual impairment is, can be different from how the student sees words. So, if a learning media assessment is being done on your child, make sure that whoever is doing the assessment understands that you want it to include math symbols as well. Because, again, the student may be able to read text well but may confuse numbers. Keep that in mind.
Most importantly, the professionals working with the student need to have prerequisite skills; and I say this for both the teacher of the blind and whatever Braille transcriber or para-educator is working with the student. These professionals have to be Braille competent, and I donít mean that they took a class in Braille. I mean, are they competent in reading and writing Braille? [And that includes Nemeth, the special Braille code for mathematic numbers and symbols.] Nemeth should be taught to students from kindergarten on. A lot of discussion has occurred on a listserv to which I belong about when a teacher should teach Nemeth. [My answer:] Nemeth symbols should be started from day one, as soon as the blind student gets his/her first math assignment. You teach Nemeth when you teach everything else.
The [Braille] transcriber in particular should be very confident in putting together tactile graphics. There are certain kinds of criteria (you can find them on the Internet) for good tactile graphics. Many transcribers and teachers will do a tactile graphic that looks terrific visually, but it makes no sense tactilely. I never used a tactile graphic with a student until I was certain that the student could actually read what I was doing. Your blind student really needs to be involved in the tactile graphics. As a transcriber you need to learn what works for a student and what doesnít work for a student.
[Next, you need to know about equipment that produces tactile graphics.] There are a couple of different products. You need to learn what a Puffer is; that is, a machine that puffs paper. You need to learn what a Tiger Embosser is. Most school districts canít afford a Tiger, but you need to know what it is and what it can do. And you need to know how to do graphics by hand--the quick and dirty way. Please excuse me, but school transcribers are not going to do the NLS-required transcription process, because we donít usually have time to edit what we do. And because we donít, we actually have to be more knowledgeable. Very often we will get a test--with graphics--maybe twenty-four hours before the exam is going to be given, and we may be just a four-hour employee. So, we need to be able to transcribe and do graphics quickly, confidently, and in a way that the student can really read them.
We need to be familiar with certain kinds of software that are particular to producing Braille math. One of these is Scientific Notebook. This is off-the-shelf software that is compatible with Duxbury. It produces pretty good Nemeth code. It actually produces better Braille math than the Duxbury math does; for example, Duxbury math is very hard to use with mixed fractions, like one and three-quarters. Also you have to put in certain symbols by hand using a six-key keyboard. So you need to know what these are. However, you canít buy Scientific Notebook and expect someone who does not know Braille to produce Nemeth Braille with it immediately. You canít do it that way. No math software is perfect and produces reasonable Nemeth Braille. The software just makes it easier.
Some old-line transcribers think it is absolute heresy to do math on the computer. But Iíll tell you itís nice when you have to come up with pages and pages of stuff. Besides, we all have kids, and we all know that kids lose things or drip milk on the one copy of the math homework you have just Brailed for them on the Braillewriter. Thatís why the computer is really cool; you can save the files and make new copies fast.
Mostly you canít do that with tactile graphics. However, there is an old-fashioned machine called a Thermoform machine. Every district ought to have at least one. They are still manufactured, and they are still useful. With a Thermoform machine you can make multiple copies on special plastic paper. Basically, the machine melts the plastic paper around your hard copy of whatever tactile graphic you have made by hand. Most Braille exams and textbooks that need multiple copies of graphics use thermoform.
Teachers of blind students need to have the proper materials on hand and readily available to the student in the classroom. As Lindsey was saying, the tools are necessary. What are the tools? Manipulatives. Get to know your kindergarten, first, and second grade teachers. The same manipulatives that are used in lower grades are really important for blind high schoolers. I know, they donít like to use them from sixth grade on; they think they donít need them. Well, I have news for you. If we continued to use manipulatives with all kids, they would all be a lot better off. Other tools: tactile measuring devices, Wikki Stiks (bendable, sticky waxed strips of cord), and stickpins on corkboards. The student can use a number of tools in the classroom to do quick-and-dirty tactile illustrations. They may require that the student explain to the teacher what he or she is doing, but again, part of math curriculum in schools today is demonstrating what you know. Thatís the name of the game: you have to demonstrate it.
Second, math as taught today is not computation. When we were kids, we all had sheets and sheets of computations. Today math is really higher thinking. It doesnít mean itís harder; it means that the students are using a different part of the brain. It is just as important to talk about the process as it is to get the answer. And the process is probably multi-stepped. The thing is, I have known vision teachers who let children be opted out of a schoolís math curriculum because they said it was too visual. Thatís a myth; math is not too visual. Donít let it happen to your child. Opting out puts those students at a real disadvantage as they go through the school system. The student needs to be assertive in the classroom, needs to communicate with the classroom teacher. The transcriber and blindness teacher need to communicate with the classroom teacher.
What about using another student as a note-taker in the classroom? As Lindsey was saying, using overheads and board work is really an integral part of what math teachers do. Thatís how theyíre taught to teach. Only a remarkable teacher can articulate everything put on the board. A human note-taker is helpful, sometimes essential. You need to take it case by case, class by class. The note-taker may be the blindness teacher, a para-educator, or another student, depending upon the circumstances.
If you can get what the teacher is going to put on the board ahead of time so that the student can peruse it while itís being used, thatís great, but the vast majority of the time youíre not going to have that opportunity. My daily schedule as a para-educator went something like this. I would get to the high school by 7:30 a.m. Classes started at 8:10 a.m. I would go to each classroom to find out what the teacher was teaching that day. Nine times out of ten the teachers had just figured it out that morning. Theyíre looking at me and thinking, ďShe wants something.Ē So you would have to figure out how to talk to the teacher with respect. The teacherís classroom is her or his domain, a personal kingdom. As a para-educator I need to respect this and let the teacher know I am not looking over her or his shoulder. Itís the same with the elementary school teacher. These teachers have planning books. Very cool, but those books are private. You really have to work with a teacher to allow you to observe those planning books but not disturb the teacher before classes start so that you have some idea what volume of the math book the class is going to be using.
The vast majority of math teachers do not use math books cover-to-cover. Most math materials today are disposable; most are not even in a book. You are at a real disadvantage if youíre thinking that all you have to do is come up with a page in a book, and itís going to be sequential. Well, it doesnít work that way.
In Washington State, as in many states, we have a high-stakes test. We call it the WASL (Washington Assessment of Student Learning), and currently students have to take and pass the tenth-grade WASL in order to get a high-school diploma. This is very high stakes. It has been said that blind kids cannot pass the math WASL. Yes and no. As written, yes, itís difficult to pass; but do not allow your blind child to opt out of these high-stakes tests because that could change how theyíre admitted into college. Donít let your state tell you that blind kids donít have to take high-stakes tests. Thatís not good enough.
In conclusion, I would say math is for all of us--blind kids, too. Iíve heard about the MATHCOUNTS competition, and I am excited to see them represented here. I think MATHCOUNTS is used in the Northshore School District in Washington State a lot.
I would say that, for blind kids to do math, you need the right materials, the right skills, and the right media. And donít ever let others sell your kids short because math can be--and is--successfully taught to blind kids. I know Lindsayís teacher of the blind. Sheís wonderful. Unfortunately she has retired, but I talked to her before this seminar, and she gave me wonderful tips.
Last, itís all about attitude, attitude, attitude. You need to be positive. You need to believe in blind people and talk to blind people about how math is done. Many wonderful blind engineers and mathematicians are here at this convention. Also there are some great blind teachers who teach math--from kindergarten through high school. Talk to them. Go for it; enjoy it. Even I made it through tenth grade math!