Photo by jetheriot.
One of the most common math questions on homeschooling discussion forums is, “How can I help my child master the math facts?” Unfortunately, when it comes to drilling facts, many children think math is spelled “B-O-R-I-N-G.” Worksheets are tedious, flash cards make them groan, and even the latest computer game is a yawner.
Mastering the Math Facts
School supply stores and catalogs feature a wide variety of educational products designed to make the process easier, from rods and blocks to math fact Bingo. I’d hate to have to account for all the money I have spent on products designed to help my children learn the math facts. Maybe a multiplication coloring book with silly stories will help this year, or perhaps we should try an audio tape of skip-counting songs, or…
Children who understand arithmetic well may yet struggle to master the math facts, and my college calculus student with a straight-A average still makes occasional, maddening math fact errors on her tests. Even mathematicians sometimes have difficulty with arithmetic. Check out this frequently-quoted anecdote about Ernst Eduard Kummer.
[You can find this story and many other delightful anecdotes in the books Mathematical Apocrypha and Mathematical Apocrypha Redux.]
Learning to understand math is a conceptual task, but learning the math facts is more like rote memory work. Yet rote memory is not enough. A student can recite the times tables perfectly and still be reduced to counting on her fingers in the middle of a long division problem.
An Analogy: “Math Is to Typing As…”
Training one’s mind to recall math facts when needed is a lot like learning to type. It comes in stages:
- Hunt and peck
In typing, we understand that we have to push down the proper key to get the letter we want, but it may take us a few minutes to find that key. In math, this is the manipulative or counting-on-fingers stage. - Slow but steady
Now we have learned that each finger controls certain keys, but we have to think about whether “c” is up or down from the home row. In math, the student understands the concepts behind each math fact, but he still has to count by fives to calculate 5×7. - Automatic response
The professional typist looks at a word on the paper she is copying, and her fingers automatically hit the proper sequence of keys. Typing has become a reflex. A math student who has reached this stage can see 2×5 on a worksheet and instantly think “10.”
Of course, we do not progress evenly from one stage to the next. As a typist, I work primarily in stage 2, but simple words (the or and) come automatically, while I still hunt and peck the numbers and unusual forms of punctuation.
For our students, progress in learning the math facts will come the same, slow way. They may know instantly that 3×5 is the same as 15, while they still count on their fingers to solve 8×6.
What Is It Worth to You?
Also, notice that not all typists reach the automatic stage — and that is okay. I have a friend who can type over 100 words per minute, almost as fast as she can think. I can type around 30wpm, which is about as fast as I can think, too. My daughter is still at the hunt-and-peck stage, but she gets by.
Does my daughter need to work at typing faster? Yes, and she plays around with Mavis Beacon every once in awhile, but it is not super-high on her priority list. It is not nearly as important to her as writing her novels. Fortunately, the work on her novels will help gradually to increase her speed.
Would I like to type faster? Sure I would, but not enough to work at it. I will never be a medical transcriptionist, but I can type well enough for e-mail.
In the same way, not every student will reach the automatic stage with all the math facts. Most of us still struggle with remembering a few of them as adults, particularly the times-7 or times-8 facts. As long as we know how to calculate the ones we cannot recall, we will survive.
The Game that Is Worth 1,000 Worksheets
Finally, as with typing, there is only one way to reach the automatic stage: practice, practice, practice. The student must calculate the math facts over and over, so many times that the correct response becomes a reflex.
Thankfully, with the right math drill game, practicing the facts can be fun.
This is the first post in my Times Table Series. To be continued…
Denise Gaskins' Let's Play Math 
I stressed over math facts (multiplication tables) so much with my now fourth-grader last year. According to her curriculum, she should know her math facts cold by the end of third grade and be able to respond with the correct answer within three seconds. I was positive she would be able to go no further in math until she had them all memorized and could respond within the alotted time. We used flashcards, dice, Times Tales and a computer game called Timez Attack (the free version), and a very helpful website – http://www.mathisfun.com.
Then I read on a homeschooling blog that you should review math facts until they graduate high school. They recommended not getting stressed out about it, since theoretically they have 12 years to master them instead of 1.
At any rate, she does know her math facts well, but is still having trouble with the 11’s and 12’s. She has successfully moved on to harder math in spite of this flaw, though. 😉
From a former transcriptionist who types 100+ wpm, but only thinks about 30 wpm! 😉
Ok. I get that you are using this as an analogy, so I will try to just try to tell you how I see the value of both typing and knowing math facts.
I cannot tell you how grateful I am that typing was required when I was in high school. I took an actual class in public school. It taught me everything I needed to know to type. Even though I correct typos faster than I can think, I look at the keys some of the time, and I really thought it was the most boring classes I ever had to take, I still learned indispensable life skills from it.
So, when you compare typing to learning math facts, I have to say, I realized how miserable it was in “hunt and peck” stage and it’s good to learn to type and know the math facts, after some work. It’s okay to not like learning the multiplication tables, but I don’t think it’s okay to not try to learn them. If a teacher expects you to learn them, you can do it- or at least I did. My high school math teacher had us memorize the squares of the numbers from 2 to 21, to help us in algebra. I still know them now that i have a teen learning algebra. Knowing those squares is fun and helps with mental calculations.
So, make math facts fun to learn and expect them to learn them before they get to algebra. You won’t regret it!
The memory you use to find the keys is either motor memory or muscle memory- it’s something that is your mind and muscles remembering together. So, perhaps you have a suggestion of a fun game that would connect motor memory with remembering the math facts.
Do you know how to play Baseball Math? I heard it is a good game.
Mia–
I wonder why your comment got kicked into the spam folder. I don’t usually check there anymore (who wants to read through hundreds of ads for intimate pharmaceuticals and off-color websites?), but I’m glad I checked today!
Thanks for the link to the Math is Fun website. I have put it into my ever-expanding “to add to the resource page someday” folder.
Nice anology. Thanks for the post – a reminder to take it easy as i watch my son learn how to type & do basic addition at the same time 😉
Schoolhouse Rock is what got me by, even though I only saw it on Saturdays between cartoons. Thankfully, we have it on DVD and the 2 kids are learning the same helpful songs that I did. Because we all know that “3 is a magic number”! To this day, I have to sing the Preamble to get it correct.
I’m actually really enjoying trying to teach Giselle about math and the shortcuts and fact families and how all numbers are related and that it’s all just really about 0 through 9. I hope that she comes to love numbers some day.
R’acquel, Natalie — I’m glad you dropped by!
Schoolhouse Rock is fun, isn’t it? We have a great computer game from them, called Math Rock. I haven’t seen the kids pull it out for quite awhile, but now that you’ve made me think of it, I will have to remind Princess Kitten.
This is something that some of my 4th graders struggle with. I try to use various ways to practice them, but it does come down to them having to memorize them. The trick is to get them to realize this is something they will need on a regular basis throughout their lifetime. I wish there were more ways to reinforce this skill. I have tried all of the things that are on your blog and am still looking for more useful and fun ways to practice.
I love your analogy of math and learning to type. I agree that one must master each stage of learning math before moving on to the next stage. Some of the stages you discuss are similar to stages that cognitive scientists have termed “declarative” (hunt and peck) and “procedural” (slow but steady). The next step in these stages the cognitive scientists have defined would be “conceptual”. However, I think your first stage has to do with grasping the concept as well. The last stage that you mention (automatic response) I believe is VERY important and I wish that cognitive scientists would give it more attention in regard to learning math. Total recall and memorization of the multiplication facts is a prerequisite to computing fractions and more complex math. Why is memorization being treated as if it were TABOO in the world of learning math? Give the children all of the strategies and manipulatives in the universe, but computing fractions and math work beyond that
will be very difficult for learners if they don’t have their multiplication facts memorized. Any comments, anyone?
One more thought…. for some of you that posted that your children are having some trouble with the multiplication facts. Have you tried the color-coded multiplication method? It’s been tested and really does work. They say that color is the “secret weapon” and it is used in a very nontraditional way. If you’re interseted, post a message and I’ll get back to you. MaMaMath
Hi, Margo,
Thank you for your comment! I think you are right that automatic recall is very helpful for future math work, though the story of number theorist Ernst Kummer shows that it isn’t essential.
But more important than automatic recall is for us as parents/teachers to give our children LOTS of practice in using mental math thinking skills, so that when their memory goes blank (as often happens during the stress of a test), they will have something to fall back on. Memory is not nearly as reliable as strategic thinking skills, like the ones I teach in my Times Table Series blog posts.
A great way to build math fact memory (and to practice those thinking strategies) is to play a math game like Contig or Times Tac Toe.
I agree that math facts are so vitally important for our children, but I don’t think total rote memorization is the answer. I feel that students should have strategies to solve their math facts. Their number sense will grow as they can use the same strategies of double double with 8’s in 3rd grade that they use with 80 or 80,000 in 5th grade.
I agree, Patty!
(Though I think you mean “double-double-double” for the times-8 facts.) Rote memorization is unreliable, and it doesn’t give students a tool for figuring out a fact they can’t remember. That’s why I encourage parents to spend more time working on mental math strategies than on any sort of rote drill. And if you read the rest of my Times Table Series, you’ll find it’s full of number sense tips.