There are so many great math curricula out there. Some are very heavy on drills: and who can deny that drills are extremely important? Others are wonderful at demonstrating concepts....the thought processes behind working out problems. Drills can easily bore a student to death and make them feel like math is a punishment, rather than an interesting investigation. However, they seem to have some mastery of math when, in reality, they don't understand the language of math. Some children pick up on concepts so quickly that a teacher or parent begins to think the student is a prodigy and is past the drills. So the teacher tends to "zoom" through lessons, allowing the student to lose important ground that has already been gained. Eventually, this leads to a halt in the student's progress.
Obviously, this means that both concepts and drills are equally important, and a tutor should never sacrifice one for the other. A student MUST know their tables by heart, and I mean instantly! Since this can become a drudgery, the tutor needs to find many roads to lead the student down the path of mastering the multiplication/division and addition/subtraction tables. There are different methods for different ages.
For example, a primary student delights in making a colorful lapbook. Examples are abundant over the internet. Children love opening a book that they made on their own and reading it over and over.
For elementary students, taking a timed quiz over and over increases their confidence and lets them see their progression. They take pleasure in beating their own score each day until they reach "perfection".
Middle school students need to begin recognizing patterns. For instance, the pattern in the 8's times tables look like this:
08, 16, 24, 32, 40, 48, 56, 64, 72, 80
Notice that the left side of the number (the ten's place) increases by one, except that 4 repeats itself twice (0, 1, 2, 3, 4, 4, 5, 6, 7, 8). The right hand side of the number (the one's place) repeats the pattern: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0...... etc. When written vertically, this pattern is much more obvious.
Teaching concepts, for me, always begins with learning the "language" of mathematics. For example, one can substitute the word "of" for the multiplication sign. 1/4 of 40 is the same as saying 1/4 times 40. Fractions can always be read as a division problem. 2/4 is the same as saying two divided by four. If a tutor doesn't explain concepts, math will become drudgery and uninteresting.
Therefore, please include drill and concepts in your lessons on a consistent basis to ensure success and the pleasure of learning mathematics!
Have Fun Teaching!