NUMBERS & COUNTING ADAPTATIONS
By: Carmen Willings
teachingvisuallyimpaired.com Number sense refers to a students fluidity and flexibility with numbers as well as the concept that numbers mean and an ability to perform mental math and make comparisons to math in the environment. This page describes adaptations for students who are blind or visually impaired. Developing the concept of number sense for math success and understanding is comparable to phonemic awareness for reading. It is important for older students to continue to work on this skill as well if they have not yet mastered it. To do this, it is important to provide many opportunities for students to explore groups of concrete & real objects and to compare the relative size of groups of things.
Math instruction in the primary grades should be as concrete as possible." ~ Bishop, Virginia. Teaching Visually Impaired Children. Charles C. Thomas. 1996. p.67. Students should have many opportunities throughout the day to count both small and large groups of objects; match the number of objects to braille or print numbers; and to talk about numbers discussing how many, how much more or less, and how many more are needed. Word problems can be a particular challenge for students. Keeping word problems as concrete as possible will help students who have a difficult time with problems completing mental imagery.
As students explore materials related to the unit, talk about similarities and differences in materials. In addition to providing many opportunities to count, encourage students to explore numbers within the environment. Personalized and interactive books can also be created with the student's name, age, birthday, phone numbers, and address to practice number skills specific to the student. Although hands on experiences with real objects is essential, it is also essential for students who are blind or visually impaired to memorize their math facts as it is for their sighted peers.
The Nemeth Braille Code is a math code for encoding mathematical and scientific notation linearly using standard six-dot braille cells for tactile reading. The most significant difference between Nemeth braille and standard literary braille, besides the new symbols, is the use of context-dependent rules that require shifting back and forth between the Nemeth code and the literary code. The most obvious change is the use of the dropped or lower-cell numerals rather than upper-cell ones in depicting numbers.Students who will be braille learners, will need to be exposed to and formally instructed in the Nemeth Code at an early age similar to when their sighted peers learn numbers.
MATERIAL SUGGESTIONS...
The EZeeCOUNT Abacus consists of a 10x10 grid of flat beads. The beads can be flipped and distinguished by color and/or texture. The red beads are wavy/rough and the yellow beads are smooth. Each row of beads slides along an elastic band from left to right. The reverse side is a dry-erase board. EZeeCOUNT abacus can be used for: addition, subtraction, multiplication, patterns, place value, addition, number combinations, fractions, graphs, and games.
The expanded Beginner's Abacus kit introduces visually impaired students to early math concepts and number operations, as well as abacus terminology. According to their product description, it "supports concepts and skills such as one-to-one correspondence, number meaning, addition, and subtraction. It also prepares students for the Cranmer Abacus."
The abacus is a calculation tool but it should not be confused with a calculator. A better comparison is that it is used like paper and pencil for students with vision. The Cranmer Abacus was designed specifically for individuals who are blind. What makes it unique is the piece of soft fabric or rubber that is placed behind the beads so that they will not inadvertently move while the person performs calculations.
Braille magnets are available from Playskool in both numbers and letters. These magnets can be a fun learning tool for students with low vision as well as dual print/braille learners. Care should be taken if using them with students who are braille only learners as the print letters/numbers will need to be properly oriented in order to read the braille.
Base ten blocks are a mathematical manipulative used by teachers to instruct students on basic mathematical concepts including addition, subtraction, number sense, place value and counting. The student can manipulate the blocks in different ways to express numbers and patterns. This hands-on tool is ideal for students who are visually impaired and blind.
Bold line paper is a tool that can be used in mathematics for students with low vision. The paper can be turned sideways to form columns that can assist students in performing paper/pencil activities that require keeping numbers lined up.
Math Flash Software from APH helps elementary students sharpen math skills with talking electronic flash cards. It's a self-voicing program that uses the computer's sound card to communicate instructions, drills, practice sessions, and games.
Tactile Dice, like these dice available from APH, can make games and other math activities accessible to students with low vision or who are blind.
APH Catalog Number: 61-131-027 
$1.99 Talking Calculator app speaks button names, numbers, and answers aloud through a customizable built-in directory that lets users record their own voice. The company also offers a Talking Scientific Calculator for $4.99
Counting books are a wonderful way to practice counting with students. Commercially available counting books can be adapted, or homemade books can be created. Jellybean Jungle is one of several Twin Vision books available through APH that introduce students to counting.
Braille number and alphabet blocks provide children an early play and interaction with braille. The numbers on the block are in Nemeth braille.
Digi-Blocks are small rectangular-shaped blocks and empty holders. These materials help children discover the important relationship between ones and tens – a concept crucial to understanding how arithmetic operations work.
Graph Paper. Some students will have significant difficulty lining up math problems. Provide students with strategies such as using graph paper or turn lined paper sideways to create columns.
The APH hundreds board and manipulatives includes manipulatives that can be used to help teach basic math concepts. It includes two 10x10 boards made of heavy duty plastic.
MathBuilders Unit 7: Fractions, Mixed Numbers, and Decimals from APH is a supplementary math program that consists of materials that are accessible to students who are blind or who have low vision.
The Number Line Device from APH is a basic tool for teaching number concepts, number sequence, counting, addition, subtraction, multiplication, division, rounding, estimating whole numbers, common fractions, and decimals. The number line teach mathematical concepts including representing whole number sums at the elementary level, to representing fractions at the intermediate level, to locating irrational numbers at the middle school level.
This Number Line to 10,000,000, available from Slide-A-Round Math Manipulatives, was developed by Jim Franklin who is a special education teacher. This number line is accessible to students with low vision as well as those who are blind.
These Numbered peg boards can be easily adapted with a braille label to make them accessible for a possible braille learner. They are excellent for students with low vision as well as they are in high contrast.
Quick Pick Math is a math game from APH.It consists of a plastic packet with large print/braille cards. The front and back of each card contains a math question and four possible answers. To play, the student inserts the included tool in one of four holes in the front of the plastic packet.
The Nemeth Tactile System from TackTiles is ideal for students who may not be able to read braille tactually from loss of finger sensitivity. It provides these students with the opportunity to access math.
The Twist and Shout game by Leapfrog provides an fun way to practice and learn math facts. Different Twist and Shout games are available including addition, subtraction, multiplication, and division.
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To develop mathematical concepts, students must have numerous and varied interactions with their environment - exploring, comparing, and arranging real sets of concrete objects - before they move to symbolic representations." 
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