Addition and subtraction, the operations, are often lumped together into “rithmetic,” the ability to “cipher” which took precedence in the old days over true mathematics, which is more than sums. Unfortunately some of the methods used by our grandmothers are still used today, and often only confuses children, especially children with disabilities. They include using fingers, terms like “take away,” rather than subtract or “carry and borrow,” rather than “regroup.”
Still, mathematical operations are foundational to other math skills, number theory and understanding algebra. In order to build this foundation, here are some key strategies:
No More Baby Talk
Start using the correct mathematical terms when teaching math. These words belong on your word wall, so they are rehearsed often. Your children will hear “answer” for “sum” or “difference” at home: they should hear and use the correct terms at school.
- Addition:addends, sum, plus.
- Subtraction: Minuend (top), subtrahend, difference, minus
No More Fingers
Fingers are incredibly handy counters, but if the goal is to “fade manipulatives, it’s kind of hard to get rid of those fingers (mittens, maybe?) So, start with counters, or my favorite, the number line.
Find a Method that Works
No single method is going to work with every child. The goal is to find a method of instruction that will eventually lead to automaticity, when students can quickly and automatically answer math facts.
Perhaps some children will need to move eventually to a calculator, but if a child has no sense of how big 400 plus 700 should be, when they get 24,000 as an answer, they will have no idea they did something wrong. To those people who will say “But, really, how often do you do the math?” I would have to say “every day.”
Manipulatives: For many kindergarten and first grade children with disabilities, repeated use of manipulatives, or counters, will help them generalize and visualize the addition or subtraction of addends or subtrahends less than ten. This may go hand in hand with understanding one to one correspondence.
Numberlines: This is my preferred method of teaching addition and subtraction. A numberline is a strip of paper (or adhesive backed vinyl) numbered from zero to 20, which can be used for addition or subtraction. For addition, start with one addend and count jumps the the right for the other addend. For 4 + 3, start at the four and make three jumps, to land at 7. For subtraction, begin at the minuend and jump back (to the left,) counting back for the subtrahend. For 7 – 3, start at the seven and jump back three spaces to land on the 4.
The reason I like the numberline is that I remember visualizing the operation in my head in the same way, as I learned to count to 100 and began doing math. I know it sounds weird to remember something that happened more than 50 years ago, but on the same hand it reflects how strongly that early intellectual activity shaped the way I still understand numbers.
Understanding numbers using a numberline will help students understand negative integers when they are introduced in the 6th grade ( Common Core Standards, later than Everyday Math.)
Touch Math
Touch Math can be a useful tool for children who are strong counting skills but have memory deficits that make it difficult for them to gain automaticity with addition and subtraction skills. A copyrighted method of teaching addition, subtraction and counting coins, Touch Math involves teaching students touch points, and then counting all of the touch points in an addition problem, or counting backwards by touch points for a subtraction problem.
When adding and counting manipulatives and using the numberline fail to help students consistently and accurately add numbers, I like to introduce Touch Math.
I believe it too easily becomes a crutch for students who may be able to gain automaticity, or, on the other hand students who don’t count the touch points consistently will never become accurate.
Algebraic Thinking
Success later in a child’s academic career may hinge on familiarity with important math ideas. This can be introduced in the primary grades through missing number problems and operation tables.
Missing number problems state a problem with a blank or a shape in the primary grades. It may look as simple as 6 + ____ = 9. When introducing the idea, use nine manipulatives and have the student place six counters on top of the six. The three left over solve the problem: confirm by using the manipulatives to find the sum.
Operation tables are sometimes called “math machines” or “What’s My Rule?” (Everyday Math) tables, but children will be expected to know how to solve them in high stakes tests. Using either two columns or two rows of squares on the left or top column or row is the in box, and the other is the out or output box. If the rule is N – 3, then an input (N) of 7 will have an output of 4.