Division
One reason why long division is difficult
Long division is an algorithm that repeats the basic steps of
1) Divide; 2) Multiply; 3) Subtract; 4) Drop down the next digit.
Of these steps, #2 and #3 can become difficult and confusing to students because they don't seemingly have to do with division—they have to do with finding the remainder. In fact, to point that out, I like to combine them into a single "multiply & subtract" step.
To avoid the confusion, I advocate teaching long division in such a fashion that children are NOT exposed to all of those steps at first. Instead, you can teach it in several "steps":
Step 1: Division is even in all the digits. Here, students practice just the dividing part.
Step 2: A remainder in the ones. Now, students practice the "multiply & subtract" part and connect that with finding the remainder.
Step 3: A remainder in the tens. Students now use the whole algorithm, including "dropping down the next digit", using 2-digit dividends.
Step 4: A remainder in any of the place values. Students practice the whole algorithm using longer dividends.
