Doman’s Method

The Doman math program is divided into five main subject areas:

• Quantity recognition
• Equations using quantity
• Problem solving
• Numeral recognition
• Equations using numerals

This is the order in which the subjects are taught. However, it is not necessary to finish one subject before moving on to the next. Rather, they overlap.

Quantity recognition

Doman points out that quantities are the reality of numbers, while the numerals we use to represent them are arbitrary symbols. The program begins by teaching the numbers 0 to 100 as quantities. The IAHP sells flash cards for this purpose, with the quantities represented by red dots arranged in random formation.

On the first day, you show one set of five cards (numbers 1-5), three times a day. On the second day, you add a second set (numbers 6-10), which you also show three times a day. This means that you will be doing six math sessions a day. Starting from the third day, shuffle cards between the two sets (but keep five to a set). Except for the first time you show the numbers 1-5 and 6-10, remember to shuffle the cards before every lesson.

Starting from the sixth day, retire and add two (or more) cards per day. Begin by retiring and adding two, but be prepared to retire and add more, if you sense that your child would like to move faster.

Teach 1 to 100, and finish with 0.

Equations using quantity

Once you have taught the quantities 1 to 20, it is time to start teaching equations using quantity. You can use any of the quantities your child has so far learned. Do three equations per session, and three sessions per day. Since you are already doing six quantity sessions a day, this means that you will now be doing nine math sessions a day.

In the beginning, keep to two steps (e.g. 1 + 2 = 3). Spend two weeks on each operation, covering addition, subtraction, multiplication, and finally division. Now, it is time to move on to the next stage.

Problem solving

Your child has come far enough for you to be able to present her with two or three possible solutions to an equation from which she can choose the answer. (You should not ask the child for the solution outright, since that would be “testing” – which is frowned on by Doman).

Give your child one problem-solving opportunity per session, tagged on to the end of his equations. So in each session, you will be giving him the answer to three equations, and asking him to choose the answer to a fourth.

You can now move on to three-step equations (e.g. 2 x 2 x 3 = 12) – for both the regular equations and problem-solving one. Do this for a few weeks.

Now, it is time to start making mixed equations. You can mix addition with subtraction, and multiplication with division. However, no mixing of addition/subtraction with multiplication/division is allowed. This is because, writes Doman, “Serious errors can result, errors which can be avoided only after learning both the rule about the Order of Operations AND the reasons behind it.”

After a few weeks of mixed equations, add another term to your equations. This means that you will now be doing four-step mixed equations.

Problem solving does not just have to be about equations however. Doman mentions the following additional subject areas for consideration:

• Sequences
• Greater than and less than
• Equalities and inequalities
• Number personality
• Fractions
• Simple algebra

More on what these areas of study would entail can be found in How To Teach Your Baby Math.

Numeral recognition

This extremely easy stage involves presenting the numerals from 1 to 100 and 0 in much the same way as you presented their quantities. In order to maintain your child’s interest, you should move much faster than you did when teaching quantity. This means retiring three or four cards a day.

Once you have taught the numerals up to 100, show a variety of higher numerals – up to 1,000 and beyond. Choose any and show at random; there is no need to teach every numeral.

Equations using numerals

Now, just as you taught progressively longer equations involving quantity, do the same with equations involving numerals. Remember not to mix addition or subtraction with multiplication or division.

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Shichida’s method…