## Textbooks for improving braille readers'math skills

OLIV: Picture yourself entering a classroom and suppose there are 20 first graders in this room. One of them is blind. The pupils are working on math using their individual textbooks.

TOVE: Then the pupil, who reads braille, should have a textbook in braille.

OLIV: If a specific textbook from a publisher is an integral part of classroom life..

TOVE: Then the braille reader should have access to the same version in braille. Hi, my name is Tove Riseth. I work with mathematics, braille transcribing, and I produce textbooks in braille.

OLIV: My name is Oliv Klingenberg. My doctoral research focused on mathematics, education and braille-reading pupils in primary school. Tove and I are now members of a project team working to develop learning resources in mathematics for braille-reading pupils in first grade. We are both employed by Statped, the National Service for Special Needs Education in Norway.

TOVE: Statped produce educational materials for braille readers in paperback and eBooks. However, for a few years now, we have not been able to offer textbooks in mathematics to first-grade pupils.

OLIV: In Norway, pupils with visual impairment attend regular school, often with a two-teacher model, also known as co-teaching, which, of course, may be slightly different in each classroom. The teachers choose the math textbooks from different publishers, so one of the main goals of our project is to find a way to provide braille readers with the same textbook as their classmates. The learning resources that this project will make available consist of textbooks in braille, A-books or materials for math assignments that cannot be transcribed into braille, and teacher guides. Today, we'd like to share our solutions for turning print textbooks into braille.

TOVE: And how we have developed guidelines for production so that I can transcribe and produce these books as quickly as possible.

OLIV: The presentation core is five didactical elements which we believe are essential to math education for our pupils at this age level. The didactical elements ordinate from literature and empirical practise in the field of visual impairment. We have decided to talk about reading and writing numbers, and we'll be showing examples of how the elements are included in the textbooks. The first didactical element is preparing the fingers for reading. Learning to read with your fingers is different than learning to read with your eyes. Partly because hands and fingers have countless missions in the reading process. One essential mission or reading skill, is to practise horizontal hand movements. Other skills are the ability to coordinate the movements of both hands while reading, using as many fingers as possible against the line, and using the fingers in smooth, fine movements from left to right. Some teachers compare this way of positioning the fingers to shaping a train with numerous train cars.

TOVE: This is a typical page in the braille binder. The page have eight lines with an open line between every line. The top line has no text characters. The entire line contains only one character, dots, two and five without spaces in between.

OLIV: Those familiar with Sally Mangold's developmental programme of Tactile Perception and Braille Letter Recognition will understand that the exercises are inspired by what we have learned from her. The Norwegian term for such a line is “ledelinje”, which can be translated into running line or leading line, leading the fingers along the line. There are no mathematical symbols to reading this first line. The pupil practises lightly touching the dots to get a good flow in the reading moment. So the first line is a kind of warm-up exercise for both the reading movements and reading fingers. For a five or six-year old girl or boy, it is hard to be able to maintain physical contact along a long line and every time the fingers lift away from the paper, and thus lose contact with the line, it becomes difficult to find the next line. At this skill level, we therefore recommend that the pupils reverse all the course back along the line that has been read, and then find the next reading line using the horizontal helpline in the left margin. In this way, the pupils fingers stay in contact with the paper at all times.

TOVE: The horizontal helpline is written using dots one, two, three, and one, two, three, five.

OLIV: The second, the didactical element is number reading exercises because most first-grade curricula teach a variation or addition and subtraction strategies for numbers from zero to 20. In general, pupils are expected to perform task like recognising and writing numbers. Focus on the sighted pupils in the classroom you have just entered, how many times do you think in learning to read and write numbers they have now come across the number five? Maybe a thousand times? We know that tactile reading develops gradually, but at the start of first grade, we cannot expect all peoples to have enough reading with the fingers experiences to be able to perceive how numeric symbols differ from each other in the presence or absence of a dot in one of the six or eight possible locations. The teacher must make sure that the braille reader has the ability to recognise the numeric symbols a thousand times. Let's now take a closer look at how exactly we include reading exercises in the textbook.

TOVE: This is a page where a new number is presented. The page shows the model for how we have decided to present a new number and how reading with fingers exercises are integrated into these pages. The new number of this page is five. Line number two on these pages consist of six dots braille cells here, five cells and a leading line at the start and end of the line. The new number presented is located on the six next lines.

OLIV: The pupil should know what is to be read. The task is to articulate every time the number five is under the fingers. The fingers run across the leading line until they encounter a blank space which is a signal that the finger will now encounter something that is different. In a way, the blank space helps the pupil to pay closer attention. On the next page, the reading exercise is to identify the numerals and ignore the other characters. The task here is to recognise, to read all the fives and ignore the other characters.

TOVE: We have chosen characters, braille structures that differ as much as possible from both the number sign and the numerals. So we have chosen two cells, that's two, four, six, one, three, five and two, four, five, six, one, two, three, five. The third page in the presentation of a number is a page with all the numbers that have been introduced so far.

OLIV: The pupil has to read these three pages several times or receive reading assignments from the teacher in order to become familiar with all numbers. Helping children to read and write single digit numerals is similar to teaching them to read and write the letters of the alphabet. Neither has anything to do with numerical concepts but it is an impossible task to add or subtract if the numbers in the arithmetic problem are unfamiliar. The pupil must practise until familiar with the numbers as if they have seen them, have read them a thousand times because familiarity with the numbers is incredibly important for learning algebra later on. My experience has been that some pupils, in their early reading development prefer to articulate every character the fingers touches, so that they read number sign five. Gradually, they skip the word number sign and just read five. The number sign has then become a mental numerical indicator for the next characters. Reading a merged digit number is another example of how reading visually and tactilely are different because tactile reading is more sequential. Take 15, for example. We adults perceive the double digit number one and five as the number 15. That is because we perceive the two digits as a cluster. However, young reading fingers decode one character at a time, so that the articulated reading becomes number sign one, five which is later perceived as 15. Experienced braille readers will be able to read 15 without decoding character by character but it takes time to learn. We will now like to move on to the third didactical element labelled as repeated layout or text structure.

TOVE: The numbers and other mathematical symbols are introduced in the same order as in the printed textbook. But as you have seen, the braille binders have supplementary reading exercises.

OLIV: It is the same type of exercises and the same layout for each number presented because a familiar text structure can help the pupil prepare for what to do when he or she turns a new page. It's a bit like when sighted pupils take a look at a new page and understand what to do because they have done something similar before. Once the layout is well known, it increases the pupil's possibility for personal control which again can gradually reduce the need to be close to the teacher or one-on-one education. Of course, there is a need for variation in the training, so the project group will outline activities and materials that the teacher can use in the classroom. - Braille binders have two types of page numbers, both or which are located at the bottom of the page. The number that is centred here, 51 is page 51 in this braille binder The number on the right here, 64, refers to braille to page number 64 in the ink print textbook. I then follow the guideline and transcribe this page 64 into three braille pages. Braille page 51 has the same mathematical counting as page 64 in the print textbook, which is an introduction of the number 10. So the ink print page 64 refers to braille pages, 51, 52 and 53.

TOVE: A repeated layout or structure offers predictability which can lead to more appropriate social interaction with other pupils and less dependence on adults. A talented teacher is close by when the braille reader is to learn something new and maintains a distance once the pupil masters the task without help. The fourth didactical element concerned writing.

OLIV: In the braille textbook, a model for writing exercises is placed on the fourth page or an introduction of a new number. There are no leading lines on this page but the model shows two long lines with a new number and one line consisting of all the numbers that have been introduced so far here, one, two, three, four and five.

TOVE: We know that the pupil needs a lot of practise before he or she can align with numbers but the right balance needs to be found between practising to master and drill and kill which can be tricky. Sighted people cope it, the written symbol as they can alternate between looking at the number five in the textbook and checking their own writing. The braille reader must remember which dots make up the number and transfer the dots into correct fingers and correct keys on the writer. However, there are a multitude of activities that encourage a child to develop the skills and the teacher must be creative so that writing becomes a skill that the pupil masters better and better until it becomes completely automatic. And as writing has acquired its own rhythm, number sign five space, number sign five space, number sign five space and once the written is mastered, it requires less concentration and the pupil can focus on the arithmetic problem. Listen to these xylophone tones. (xylophone plays) Do you hear them as separate tones or as a short melody? Here is an analogy, does the pupil perceive each number and arithmetic sign as separate characters or as an entire mathematical expression? The teacher's knowledge of what a sequential processing means in math education is the fifth didactical element. This element is not mirrored in the textbooks but it is an extremely important element that the teacher must understand and take into account when teaching. Braille readers must decode characters in an expression while at the same time, gaining an overview of the expression. This is a very challenging and another example how visual and tactile reading and writing are different at least at this age level. The pupil needs to practise all of the sequences repeatedly until the entire mathematical expression is fully mastered. Experiences have taught me that it is worthwhile to practise writing and reading arithmetic in a child without the necessity to calculate.

OLIV: In this presentation, we talked how numbers are introduced in braille textbooks but we have not talked about the guidelines for eye transcribed tasks, such as count and match, how many all together, write the missing numerals, extend the sequence, et cetera. The guidelines helped me in transcribing to print textbooks so that each braille reader can have access to the same version in braille, as the classmates' print textbook. - The same version, but different because to read visually and to read tactilely are different at this age level. The fingers need to be prepared for reading, the braille reader needs extra exercising in both reading and writing numbers. A well-known layout in the textbook increases the pupil's possibility for personal control, which can lead to more social interaction in the lessons. The teacher must understand how to support the braille reader to build an overview of the sequences in an arithmetic expression. We have argued that these elements are essential to math education for pupils at this age and wish all the pupils and their teachers the very best. Thank you for your attention.

TOVE: Thank you for your attention