A child must learn to count before he can learn anything else in math. Most children learn to recite the numbers from 1 to 10 first, then later learn what the numbers actually mean. Once a child can recite the first 10 numbers from memory, it is time to start learning to use the numbers to count.
To make it more enjoyable, ask a child to count items that she likes. For example, ask a child who loves stuffed animals to count teddy bears. A child who enjoys toy cars can count his collection. Offer the child a different number of toys to count each time.
When the child becomes proficient at numbers up to 10, begin teaching her to recite higher numbers. You do not need 50 teddy bears to count to 50; at this point, the child should understand the concept that a number represents an amount. At a minimum, a 3-year-old preschooler should be able to count to 25 and a 4-year-old preschooler should be able to count to 100.
Most children learn to count before learning to recognize written numbers. Once a child can easily count to 15 or 20, begin introducing what the numbers look like. Counting books are a great way to learn to recognize these numbers.
Make flash cards from 3-by-5 cards that each have a number written on it in large print. Spread them out on the floor in a random order. Show the child actual objects such as three books or one pillow and ask her to find the card with the correct number on it. This gives the child practice counting as well as helping her to recognize the numbers themselves.
Once a child can recognize the numbers 1 through 10, it is time to start practicing writing them. A chalkboard or dry-erase board makes a good tablet for writing numbers. Show the child how to write number 1 and have her copy you. Practice one number each day so that the child does not become overwhelmed.
Once a preschooler can count to 25, recognize numbers and write them himself, he is ready to begin learning basic addition and subtraction. Start with addition in increments of one. "When you have one apple and you add one more, then you have two apples. When you have two apples and you add one more, then you have three apples" and so on. Whenever possible, have physical objects the child can view when learning addition.
Once the child is comfortable with adding from one plus one up to nine plus one, begin subtraction. Start subtraction by learning to count backwards from 10 to 1. When the child is good at that, begin showing the child easy subtraction problems. Again, use physical objects as a visual to help the child understand the concepts.