By Pam Woodbury

While it is most important for children to understand the how's and why's behind mathematics, it is equally important for them to be able to reproduce what they know in a timely way.  Being perfectly acceptable and even desirable for a youngster to use blocks to learn that three added to four results in seven, it would be undesirable for that same child, a while later, to still be using his fingers to "count up" three plus four.  This is where drill comes into play.  Once a child has begun to master the concepts, he needs to begin to master their recall.  It is much easier for a child who knows that five plus five equals ten to learn that five times two, being equivalent to five plus five, also equals ten. 

Math efficiency doesn't just mean memorizing the addition and the times tables.  Once concepts have been learned at any level, the student should work on improving their speed and accuracy with that concept.  Since mathematics builds on itself, each new concept will be easier to learn if the previous one was thoroughly mastered, both conceptually and through drill.  Often, the drill itself helps cement the concept into the learner's mind.  In the words of my daughter, "In my high-school math books, concepts that I do not thoroughly understand when reading the lesson are made clear by their application in problems and really learned by my experience in repeatedly using the concept to obtain the solution."

Calculadders is an excellent program designed to improve the students' speed in mathematics.  Starting with basic addition facts and proceeding up through fractions, decimals and percents, this program gives the child a set time in which to finish a group of problems on a page.  Over the years, depending on the child, we have used these pages in a variety of ways.  One method is to stop the child when the given time is up and see how far he has gotten.  The next day he does the same set again for the same amount of time and then you see if he got any farther.  In this way, he can see progress made each day by watching how far down the page he gets.  Another method is to let the child work the entire page recording his total time when done.  Each day he proceeds in this manner until he can finally do the entire page in the allotted time.  This second method is my favorite because it actually has the student working all of the problems each day.  However, when my son came along we had to stop and think again.  For the first few years he couldn't complete the pages in time solely because he couldn't write the numbers fast enough.  So, after having him work all problems on paper for four or five days, we would sit together on the sofa and he would tell me the answers as I pointed to the problems.  If he could say them all in time, then he would pass that level and move on to the next.  At the time, this really helped and now that he is older he can proceed on his own, no longer needing my assistance.

I recommend starting children at a level slightly lower than their current math level so that they can adjust to the timing and gain mastery from the beginning.