Teaching a child to count and do simple math is much more challenge then many would believe. Below is a simple process that I accidentally developed from working with kindergarten home-school student for two years. Keep in mind that often these steps overlapped.

1. Number recognition
2. Counting
3. Counting with manipulatives
4. Flashcards with larger numbers
5. Writing numbers
6. Adding with manipulatives
7. Subtraction with manipulatives
8. Visual math

1.  Number Recognition

Number recognition simple involved the use of flashcards with the child. I would hold up a number and tell the child what the number was. Memorizing is perhaps one of the easiest things the young mind can do as critical thinking comes much later. This initial process probably took about 6 months with a four-year-old to learn number 1-20.

2. Counting

With the numbers memorized, the next step was to actually learn to count. I did this by holding up the same flashcards. After the child identify what number it was I would then flip the flashcard over and have them count the number of objects on the card. My goal was to have them make a connection between the abstract number and the actual amount that could be seen and counted.

Again it took about six months for the four and half-year-old student to master this from numbers 1-20. It was a really stressful six months.

3. Counting with Manipulatives

The next few steps happen concurrently for the most part. I started to have the student count with manipulatives. I would show or say a number and expect the student to count the correct number using the manipulatives. This was done with numbers 1-20 only.

4. Flashcards with Larger Numbers 

At the same time, I worked with the student to learn numbers beyond 20. This was strictly for memorization purposes. This continued from 4.5 to 6 years of age. Eventually, the child could identify numbers 1-999. However, the never discovered the pattern of counting. By pattern, I mean how the 0-9 cycle repeats in the tens, how the 1-9 cycle repeats for the tens when moving to 100s, etc. The child only knew the numbers through brute memorization.

5. Writing Numbers

Writing numbers was used as preparation for doing addition. It was as simple as giving the student some numbers to trace on paper. It took about 8 months for the student to write numbers with any kind of consistency.

6. Adding with Manipulatives

This involved me writing a math problem and having the student solve the problem use manipulatives. For example, 2 + 2 would be solved by having the student count two manipulatives and then count two more and then count the total.

My biggest concern was having the child understand the + and = sign. The plus sign was easy but the equal sign was mysterious for a long time. However, the learning rate was picking up and the kid learn this in about 3 months

7. Subtraction with Manipulatives

Same as above but only took one month to learn

8. Visual Math

At this stage,  the child was doing worksheets on their own. Manipulatives were allowed as a crutch to get through the problems. However, the child was now being encouraged to use their fingers for counting purposes. This was a disaster for several weeks as the lack the coordination to open and close the fingers independent of each other.

Conclusion

This entire process took two years to complete from ages 4-6 working with the child one-on-one. By the age of six, the child could add and subtract anything from 1-30 and was ready for 1st grade.

I would recommend waiting longer to start math with a child. Being 4 was probably too young for this particular child. Better to wait untili 5 or 6 to learn numbers and counting. There more danger in starting early then there is in starting late.