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Teaching Math One Step at a Time
Because math skills are in use all around us every day, we can give our children many opportunities to see and hear math in action. Whether it's hearing you count out plates for the dinner table, helping you sort laundry into piles of light and dark clothes, or hearing number names as he watches you press the buttons on a microwave oven, as you purposefully surround your child with math words and concepts you can lay a rich groundwork for future formal math instruction.
But what about formal math instruction? Where do I start? What do I do? How can I help my child learn what he needs to know? These are questions I've asked for the sake of my son with Down syndrome, Andrew. 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 - and rightly so, since the use and manipulation of numbers is what math is all about. But there are some concepts children need to know before number skills are learnt. The following is a list of some pre-number skills that can be taught formally, can be taught informally throughout the day, or both! The way I like to teach them 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; use a flannel board and flannel figures, placing them as directed "put the boy by the dog")
· identifying color, size and shape (point them out and name them as you read through picture books together)
· sorting things according to color, kind, size, shape (find all the pink buttons; point to all the round things in the picture; put all the forks in this slot; determine which one doesn't belong in a group of objects)
· doing wooden insert puzzles, then simple interlocking puzzles (5-10 pieces)
· ordering objects from smallest to largest (buttons, shoes, books on a shelf, garden produce)
· comparing objects (the biggest apple; the longest pencil; the thickest carrot)
· identifying which is the right hand (we greet people by shaking our right hands - giving your child lots of opportunity to practice this a long time before ever mentioning that the other hand is called the left hand can help avoid confusion of left and right)
· matching objects that are the same, or pictures that are the same (as you look at picture books together - "Here's a butterfly. Can you find another butterfly?")
· making two-color patterns (beading; block towers; slices of apples and oranges on a plate)
· identifying first, next, last (the first to the table; the last to receive a snack; the next in line)
Many of these pre-number concepts involve teaching your child math words and their meanings. Learning math vocabulary is a very important part of learning math. Amy, mother of Reagan (7 with Down syndrome), has this to share about teaching math words:
"I try to target these words naturally while we are working/playing around the house, along with defining them during formal school work. I have found that Reagan just does not pick things up without structured teaching and defining of the language of math."
Number Skills:
As a child is becoming familiar with the pre-number concepts, begin to introduce number skills. Teach the concepts using only a few small numbers at first, then as these are mastered introduce larger numbers a few at a time. My husband, John, taught Andrew to count by counting stairs at church (we don't have any at home). As they walked down the stairs together, John would count, "1-2-3, 1-2-3, 1-2-3" until they got to the bottom. Once Andrew was counting these numbers with John, he would then count to 4, later to 5, until they were counting all the steps together.
Beginning number skills:
· counting from memory (rote counting)
· identifying the numerals that match the number words (that 5 says "five")
· understanding number quantity (that "three" or "3" means three objects)
· putting the numbers in correct order (1 to 10)
· counting objects (family members, raisins, everything!!)
When Andrew was learning to count, I was thrilled with how easily he seemed to catch on to counting…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. This was a concept that our older children had figured out on their own, as far as I could remember. I began to realize then that teaching math skills to Andrew might have its challenges! Here are some game ideas to help you teach number concepts to your child.
Number Games
Make a "game board" out of a piece of construction paper with 3 recipe card size squares glued onto it. On the squares, write the numbers 1 to 3 as well as the corresponding number of dots. Use a different color for each number. As numbers are learnt, expand the game board by adding another piece of construction paper with three more numbers on it.
Make a set of number cards, with numbers on one side and corresponding dot patterns on the other. Color-code the dot patterns to match with the colors on the game board, but make the numbers on the cards black.
The games for this board are simple matching ones - match the numbers, match the dot patterns, name the numbers as you match them, call the number that you want your child to match, place the number cards in order. The purpose is to help your child to become familiar with numbers, to recognize number names, to be able to count in order.
Make a second "game board" similar to the first, but with just the dot number patterns on it - still color-coded to match the game cards (I made it on the back of the first boards).
The game for this board is to match the number cards to the dot patterns. Peeking at the colored dot pattern on the back of the card is allowed and encouraged until it is no longer necessary. Another use for the game board is to place counters (buttons, coins, lego, whatever might be fun and interesting for your child) on the dots, counting them as you do. From here you could match counters to the number cards without the dot patterns to guide, though allowing peeking on the back as necessary. The purpose of these games is to help your child recognize that numbers represent specific amounts.
Math-type Life Skills
Once number concepts are understood, your child may be ready to go on to more complex number skills. Or perhaps you would prefer to concentrate on teaching your child math-type life skills. Marilyn, mother of Priscilla (15 with DS) has this to suggest:
"Now as far teaching math (or reading). 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 calender 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 this 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. These are all things a child would learn in kindergarten to grade 2 - and very practical things they can use when they are adults. After learning the above I would then expand to more practical math - adding for example."
More Complex Number Skills:
Again, teach these concepts using small numbers at first, then build up as your child is able.
· comparing sets - which has more? less? Carol, mother of Naomi, has this to share:
"Here is something I am doing with Naomi (7 1/2) to help her understand the concepts of more and less. I have a blue gingham tablecloth on my kitchen table which happens to be where we "do school." We play a little game using a pair of dice, some marbles that are flat on one side, and the tablecloth. We each roll one of the dice and then place the corresponding number of tokens in a row left to right, one on each square. We make sure to place the die at the beginning of the line of tokens, and my row of tokens is exactly beneath hers. This way we can see how my amount compares to hers, and determine which row has more. We can also visualize 1 to 1 correspondence this way. When we master "more", we can begin talking about "less". I don't
like to throw two related concepts together if I don't have to."
· understanding the idea of adding two groups to find the total ( 2 crackers and 3 more crackers is 5 crackers all together)
· learning the math words to describe the two groups and their total ( 2 crackers plus 3 crackers equals 5 crackers)
· learning the math symbols to write the math sentence ( 2 + 3 = 5 )
The book "Maximum Math", by Kathryn Stout is a helpful resource in planning where to go from here. It lists math skills according to grade level (these I pay no attention to, other than to know what usually gets taught first) as well as gives ideas how to teach the skills. The following are some suggestions for adapting whatever math curriculum you use, so you can help your child learn math skills no matter what level she is at.
Errorless Learning
When teaching your child math concepts, it is important that he learn a concept properly right from the beginning, as it can be difficult to unlearn and relearn something that has been learnt incorrectly. By guiding your child step by step through whatever exercise he may be doing, not allowing him to fail, your child experiences success right from the start. 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" teaching techniques.
1. 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 with a number line, which gives her visual and verbal input. She usually rides piggyback (her hand on top of mine) as we slide or jump along the number line."
2. 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. You can do this by waiting a bit before going on to the next step to see if your child will do it without your prompt. Just be careful not to wait so long that your child makes a guess - and guesses incorrectly! When modeling a concept, it is important to teach it the same way every time: following the same steps, in the same order, using the same words.
3. Visual clues - provide your child with something she can see in order to help her do an exercise correctly. Number lines to count on; a container with a sample of what to sort (a pink button glued on the bottom), and color coding as in the math game described above are all examples of visual clues.
4. "Thinking out loud" - say each step out loud as you show your child what to do, then as your child does his work. Always follow the same steps in the same order using the same words. Encourage your child to "think out loud" with you.
5. Match, select, then name - this technique is used in teaching sight reading, and works well with many math concepts as well, including shapes, colors, numerals, 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 well, 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 at each step of learning a new concept.
· Do provide many opportunities to practice the same skill in a variety of situations with a variety of materials.
· Do use real objects first when teaching a concept. Once your child is showing understanding, introduce work sheets along with the manipulatives.
· Don't assign more than five problems of the same type on a work sheet.
· Do lots of real life math.
· Don't forget that learning math vocabulary is essential to learning math skills.
· Do demonstrate each step of an activity, including showing the completion so your child understands all that is required of him.
· Do review basic math skills periodically 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 this one another time.