Recently, my fourth grader succeeded in cutting in half the time he takes to complete a multiplication speed drill, while my seventh grader managed to come close to beating his father's time in the same drill. Both were justly happy about their accomplishment. By being able to compute multiplication facts quickly and easily, both will find it easier to move further in math without getting bogged down in basic computations.
This kind of fluency is an important building block in mastery. Imaging studies have shown what common sense tells us -- that when information or procedures are automatic, they take less work in the brain. This means that a person who can instantly decode written words, knows his math facts well or can drive easily will be able to devote more mental energy to more advanced skills like reading for meaning, solving complex math problems or maneuvering a vehicle on a busy city street.
So it is well worth spending some time on memorizing in the homeschool. Memorization does not replace reasoning and imagination, but it does provide a solid base for these things. In addition, studies have shown that using memory actually builds its strength. So a child who has made the effort to memorize one time will be able to memorize more easily next time. He builds memory strategies that aid further learning, and also gains confidence in his ability to learn.
Memorizing does take effort. The first effort is attention -- the power of focusing on a learning task. I notice that my younger children have some difficulty applying their minds to something, particularly if it is not something of immediate interest to them. Good food, sufficient sleep, and some kind of routine lay a good groundwork for children. If your kids get discouraged easily, it’s helpful to start off slowly and try to build a pleasant emotional environment; I’ve found that out the hard way.
I've also found it helpful to do some sort of introduction or overview of the material to be memorized, and to help the children figure out strategies for memorization. Setting concrete goals and making time for a celebratory break after the goal is mastered can also work well.
Take the multiplication facts as an example. Most math books carefully transition from addition to multiplication, demonstrating that multiplying is simply repeated addition. This helps the students understand the process, and it is very helpful in placing the new material in the framework that already exists in the child's mind. The child can double-check the multiplication facts against what he already knows -- the "repeated addition" -- which is a barrier against wild guesswork. One very important component of successful memorization, then, is building upon existing knowledge and teaching for "meaning" not just for rote learning.
Another strategy important in memorization is finding patterns, or categorizing. Again, a typical math book will introduce multiplication facts in an orderly sequence -- 1's and 2's first and then on from there. This helps the child find order in the material, which cuts down on the effort in acquiring the knowledge.
Once the child understands what he is doing and has some strategies for helping himself remember, it is important to practice in order to gain fluency. However, our minds get accustomed to sameness and that does not reinforce learning. So it's a good plan to approach the repetition with some variety. With the multiplication facts, we have used computer drills, flashcard matching games, math "bees" where kids call out the answers as fast as they can, and "moving math" where the kids jump on the trampoline or take steps while answering the questions. Another strategy is to build a "mental map" of the facts to be memorized. Some kids find charts and manipulatives helpful to reinforce what they are learning.
Finally, there is the jump to real fluency. I've noticed that sometimes a child will transition into fluency automatically. My 7th grader never really had to drill his multiplication facts very much when he was younger; he seemed to already have a mental framework for them in his mind. My present 4th grader knew the multiplication tables well, but he was not yet fluent. He took a few seconds to solve each one, which slowed him down as we started on more complicated math operations. So we spent a couple of days focusing on speed and automatic answers, and it paid off well. Learners always do slightly worse in applying skills or information to new tasks -- it's harder to remember multiplication facts when you are trying to learn long division -- so it is important to "overlearn" the basic skills so they are second nature and can be counted on even in challenging new tasks.
Memory projects approached this way take some time and energy. So I set aside a bit of time daily for memory work, and once in a while, I cut back on everything else to really work at progressing in one area. The kids find it motivating to be "done" with a project like mastering a speed drill or memorizing a poem. A younger child enjoys seeing his progress, sometimes with charts or pages on display, and older children often enjoy some element of emulation or competition, like taking part in a contest or being part of a group effort.
All children are naturally good at memorization. Think of what they learn effortlessly simply by living in your family. In some ways, memorizing in academic subjects is simply a more artificial way to do what we all do effectively in everyday life. The trick is to use and build on these natural abilities.