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Teaching Math One Step At A Time  

By Diane Ryckman   To contact Diane Ryckman:


    Because math skills are in use all around us, we can give our children many opportunities every day to see and hear math in action. Whether they hear you count out plates for the dinner table or help you sort laundry according to color, as you purposefully surround your child with math words and concepts you lay a rich groundwork for future formal math instruction.

But what about formal math instruction? Where do I start? How can I help my child learn what he needs to know? These are questions I’ve asked for the sake of Andrew, our son with Down syndrome. The following are some of the things I’ve gleaned about teaching math, one step at a time. Where do I start?

    When we think of math, the first thing we think of is numbers, since the manipulation and use of numbers is what math is all about. However, there are some concepts a child needs to know before numbers are learnt. The following is a list of some pre-number skills that can be taught formally as “school”, informally throughout the day, or both! The way I like to teach is to zero in on one concept, and create or look for opportunities to teach that concept as often as possible in our daily activities.

    Pre-number skills:

- locating an object in relation to another object (the ball under the table; the cup on the table)

- identifying color, size and shape

- sorting things according to color, kind, size, shape (find all the pink buttons; put all the forks in this slot; determine which one doesn’t belong in a group of objects)

- problem solving (wooden insert puzzles; 5-10 piece jigsaw puzzles)

- ordering objects from smallest to largest (buttons, shoes, vegetables)

- comparing objects (the longest pencil; the thickest carrot)

- identifying which is the right hand

    (We greet people by shaking right hands. Help avoid confusing left with right by giving your child many opportunities to “shake hands” before ever mentioning that the other hand is the left hand.)

- matching objects or pictures that are the same (“Here’s a butterfly. Can you find another butterfly?”)

- making two-color patterns (“red, blue, red, blue, what comes next? Use beads, blocks, fruit on a plate)

- identifying first, next and last (the first to the table; the last to wake up)

Many of these pre-number skills involve teaching your child math words and their meanings. Learning math vocabulary is a very important part of learning math.


    Number Skills

As a child is becoming familiar with the pre-number concepts, begin to teach number skills. Teach only a few numbers at first, then as these are learnt introduce more numbers a few at a time.

Andrew learnt to rote count by counting stairs. As we walked down the stairs with Andrew, we would count, “1-2-3, 1-2-3, 1-2-3” to the bottom. Once Andrew was counting these numbers, we would count to 4, later to 5, until we were counting all the steps together.

As Andrew was learning to count, I was thrilled with how easily he seemed to catch on…until I realized that, though he could say the numbers from 1 to 10 in order, he had no idea that “3” meant three things. It was then that I realized teaching math skills to Andrew might have its challenges!

Beginning number skills:

- rote counting (from memory)

- identifying the numerals that match the number words ( 5 says “five”)

- understanding number quantity (that “three” or “3” means three objects)

- putting the numbers in order (1 – 10)

- counting objects (family members, raisins, everything!!)

Math-type Life Skills

Once beginning number concepts are understood, you may want to teach your child math life skills. Others may prefer to continue learning number skills. Marilyn, mom of Priscilla (15 with DS), has this to suggest:

“Now as for teaching math, I believe you really have to look at where the child is at developmentally. Can he count to 100, recognize all the numbers to 100, can he tell time, can he identify money, can he look at the calendar and tell you the month, day, and current date? All of these are 'math' concepts. For money - recognizing the coins - penny, nickel, dime, quarter. After recognizing these, can he relate that 5 pennies make 1 nickel, and 2 nickels make 1 dime, and so on. This is a math function that is practical for everyday living, as are numbers 1 to 31 - the days in a given month. I personally think starting with the above for math is very important. After learning the above I would then expand to more practical math - adding for example.”

More Complex Number Skills: again, teach these skills using a few numbers at first, then build up as your child is able.

- comparing sets – which has more? less? (Master "more” before talking about "less”. Don't teach two related concepts together if possible.)

- understanding the idea of adding two groups to find the total ( 2 crackers and 3 crackers are 5 crackers in all)

- learning the math words to describe two groups and their total ( 2 crackers plus 3 crackers equal 5 crackers)

- learning the math symbols to write a math equation ( 2 + 3 = 5 ). If writing is a challenge for your child, make up number and symbol cards for your child to select and make equations with.

Once the idea of adding using symbols is understood, you may want to introduce your child to the use of a calculator. For some children, learning math facts by memory is very difficult. Teaching the use of a calculator could be a practical alternative for your child.

Maximum Math, by Kathryn Stout is a helpful resource in planning where to go from here. It lists math skills according to grade level, and gives ideas how to teach the skills.

See also the NATHHAN product review for Teaching Math to People with Down Syndrome and Other Hands-On Learners – Basic Survival Skills by DeAnna Horstmeier, page 63.


When teaching your child math concepts, it is important that he learn a concept properly right from the start, as it can be difficult to unlearn and relearn what has been learnt incorrectly. Guide your child step by step through whatever exercise he may be doing, and don’t allow him to fail. As he becomes more familiar with the concept, your help can be diminished until he is able to do the exercise successfully all by himself. This method of teaching is known as

Errorless Learning. The following are some “errorless learning” techniques you can use to adapt math materials to suite your child.

Hand over hand – place your child’s hand on yours or your hand on hers as you do the exercise with her. Here’s an example from Amy and Reagan: “We rote count only with a number line, which gives Reagan visual and verbal input. She usually rides piggyback (her hand on top of mine) as we slide or jump along the number line.”

Model – you do it first, then have

your child do it with you, then have your child do it on his own. Don’t expect that this will happen all in one day! Once your child is doing an exercise with you, slowly reduce your help. For example, as you teach your child to use math symbols, model what he is to do using objects, and write an equation below (4+1=5). Once you are sure he understands the concept and is not just memorizing the equation, reduce your help by leaving out one number of the equation, having your child fill in the missing blank (4 + 1 = ). Continue to reduce your help until your child is able to write the whole equation describing the objects before him on his own. When modeling a concept, it is important to teach it the same way every time: follow the same steps, in the same order, use the same words.

Visual clues – provide your child

with something she can see in order to help her do an exercise correctly (number lines; color-coding; fingers).

Thinking out loud – say each

step out loud as you show your child what to do, then as your child does his work. Again, follow the same steps, in the same order, using the same words. Have your child think out loud with you.

Match, select, then name – could

use for teaching shapes, colors, numbers and math symbols. Begin by making up a double set of flashcards of the items you want your child to learn – for example, the shapes – circle, square and triangle. Match: Lay one set of cards in front of your child, naming them as you do. Show your child one of the second set of cards, saying, “This is a circle. Match the circle.” Continue with the square and triangle cards. When you feel your child knows these, go on to, Select: Ask your child to pick up the circle card, the triangle card, the square card. When your child can do this without your help, go on to, Name: Have your child name the shape as you show her the card.


Some Final Do’s and Don’ts

Do give your child all the time he needs to learn a new concept.

Do provide many opportunities to practice the same skill in a variety of situations with a variety of materials.

Do use manipulatives first when teaching a concept. Then introduce work sheets along with real objects.

Don’t give more than five problems of the same type on a work sheet.

Do demonstrate each step of an activity, including the completion, so your child understands all he is to do.
Do review basic math skills often to make sure there are no gaps in your child’s understanding.

Don’t push your child if he’s not getting it. Put it aside, work on another concept, then come back to it later.
Do practice, practice, practice, then practice again!

As you surround your child with opportunities to “do math” daily, you will see progress – one step at a time.