Developing Early Number Sense for Students with Disabilities
By: Bradley S. Witzel, Christine J. Ferguson, and Dale S. Brown
Elementary school and kindergarten students with learning disabilities often struggle to learn math. They have trouble counting, naming numbers, remembering numbers, and writing them down. This basic problem is called "number sense." "Number sense" is to math what "reading comprehension" is to reading.1 Students with learning disabilities, particularly dyscalculia, have less "number sense" than their non-disabled peers.
Students with trouble in "number sense" have a great deal of difficulty conceptualizing mathematics. So, even though some children might memorize that 6 X 8 equals 48, they might not understand that six packages of hot dog buns (8 per pack) is the same as having forty-eight buns.
- Give students concrete experience with numbers along with the more abstract lessons.
- Teach the skills until they master them.
- Teach them to talk about math, write about math, and understand words relating to math. Have conversations with them about mathematics, using the new terms.
Concrete experience for students
- Have them count various objects such as plastic bears, counting chips, Popsicle sticks, base ten blocks, chairs in the classroom and other items of interest. 3
- Have them use their fingers to count. Count your fingers from the left and work to the right as shown below. This helps them associate counting with their fingers with going from left to right on a page.
- Have them count objects outside the classroom. Make counting part of their daily life. You could ask them to count cars, trees, bugs, and the number of feet in the room. When possible, associate counting with tasks that they actually want to achieve such as cutting a cake so that everyone in the class has an equal piece.
- Exercises in counting actual objects should be mastered before students do textbook exercises where there are pictures using specific numbers of objects.
Teach skills to mastery
- Avoid the tendency to praise the child for effort without clarifying the correct response. Be encouraging while modeling the right answer. Here are some examples;
- "Good counting John. You had all the numbers in order but you skipped one of the numbers. Let's count together. 1, 2, 3, 4, 5, 6..."
- "I'm so glad you are continuing to work on this with us even though you are behind. Those 7 times tables are tough! I call them the tough times tables! Okay, why don't you say them with me? Let's start right where you began to have difficulty. 7 times 6 is 42 so 7 times 7 is … 49."
- Give the students plenty of opportunities to solve problems with the number skills you are teaching.4 Here are some examples:
- "I need to give you, John and Mary, two pieces of paper each for this assignment. How many pages of paper should we get from the supply closet?"
- "On the way home tonight, please count the number of traffic lights. Also, count the number of green versus red lights you see. When you see me next, tell me how many of each you saw."
Teach children the language of mathematics. In some ways, it is another language! Be sure they thoroughly understand the meaning of each mathematical term and symbol. For example, using place value language can help children develop a sense that numbers have a meaning and pattern. Explicitly interpret numbers such as 12 as one ten and two ones, 18 as one ten and eight ones, and 25 as two tens and five ones. Using concrete objects that can be grouped by ten, such as base ten blocks, can help develop this connection.
Connect each mathematical term or symbol to many examples of how it is used. Use fiction and non-fiction books, maps, calendars, architectural sketches, newspaper graphs and statistics.5 Try to connect the concepts to the student's lives and interests. For example, you could introduce money through Barbara Adams' The Go-Around Dollar, classify geometric shapes with Marilyn Burns' The Greedy Triangle, organize time sequences with David Weisner's Flotsam, and estimate measurement through Loreen Leedy's Measuring Penny.
Teach mathematical key words. For example, teach them that "and" means addition. (Here are four books and here are five books. How many books do we have?) Teach them that "3 groups of 5" means 3 X 5. Give them a lot of examples in their daily life, from breakfast to grocery store trips to bedtime routines.
The United States needs a major improvement in the mathematical literacy of its citizens. Our weaknesses in international comparisons have given rise to programs such as Singapore Math and newly called upon mathematics reform. Students who do not learn math often have trouble later with managing their money. A citizenry that is innumerate will have trouble understanding important concepts such as the difference between the national debt and the national deficit. Some people do not realize that a billion is one thousand times bigger than a million. The inability to conceptualize numbers threatens our democracy, as citizens can not participate intelligently in national debates about our budget.
Give your students concrete experiences in math. Teach them their skills until they master them. And talk to them in mathematical language and be sure they understand it. This will make a major difference in their lives.
Research on mathematics with students with disabilities is starting to increase in number and quality. Keep abreast with the new findings. Help students succeed beyond what were once considered reasonable expectations.
Click the "Endnotes" link above to hide these endnotes.
- Gersten, R., & Chard, D. (1999). Number sense: rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33 (1), 18-28.
- Smith, S. S. (2006). Early childhood mathematics (3 rd ed.). Boston:Allyn & Bacon.
- Kamii, C. (2000). Young children reinvent arithmetic (2 nd ed.). New York: Teachers College Press.
- National Council of Teachers of Mathematics, (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
- Ferguson, C. (2001). Discovering, supporting, and promoting young children's passions and interests: One teacher's reflections. Young Children, 56, 6-11.
Bradley S. Witzel, Christine J. Ferguson, and Dale S. Brown (2007)