Division:

Everyday Mathematics doesn't like division. It becomes apparent quickly that division is too dull and difficult. Dividion should be done with a calculator.

Fact triangles are used to show how division is the inverse of multiplication. No problem there.

     

Unfortunately, the times table is made available in the workbook and even on fourth grade homework sheets. This crutch ensures that the basic facts are never mastered. Ask your 4th grader, 'What is 72 divided by 6?" Potential trouble. The EM times table stops at 10.

Division is 'discovered' by 'sharing' items among friends.

When dividing moves beyond the times table, EM introduces their own version of the standard long division method.

Here is the same problem solved using the standard method and the EM version.

  

The EM method asks for an estimate of how many times 7 goes into 1850 as the first step. That guess is recorded on the right. Subtraction is the same as for the standard long division method. None of the examples in the books show partial differences or any other method for this subtraction. It appears that the standard method is what is used.

Once the division is complete, all the estimates are added. Once again, the examples appear to use the standard addition method.

I showed the example above using the same estimates as the standard method just to show how it works. In the EM method, any guess is good enough. Students are encouraged to use guesses they are comfortable with. Using the same example problem, if a student is not comfortable guessing 7 x 200 = 1400, he could just as easily use 7 x 100 = 700. Here is how that would look.

     

So what is wrong? The answers are the same.

Look at the opportunities for errors. The EM method has many more opportunities to go astray. But then, EM emphasizes calculators for correct answers.

Also take a look at what happens when you try to find out about that remainder.

     

The standard method just keeps on going, easily showing how the digits repeat. The repeating pattern, 428571, would not be apparent on a calculator (MS Excel does show enough digits if needed). This is an important concept developed later when studying irrational numbers.

The EM 'can' function the same way as shown here. I gave up on finishing it, since it is such a pain.

     

Now let's take a look at two digit divisors.

     

Once again, the EM method is much more prone to simple math errors. Estimation is much more difficult.

I wanted to include dividing by a decimal in the comparison (1850 / 1.2), but couldn't find any EM way to do it. They must consider it beyond 6th grade material or exclusively calculator territory.

The Everyday Mathematics method for long division appears to have been developed with the assumption that students don't (or can't) know their basic multiplication facts.

This method will not be useful as a basis for Algebra. Division will have to be re-taught in middle school. The EM method should not be taught in our schools.