The study of numbers is a polarizing subject. Kids (and adults) love it or hate it. Very few students shrug their shoulders with a neutral opinion when asked how they feel about math.
In urban elementary schools like the one where I teach, test scores follow a predictable pattern. Many students speak English as a second language and score poorly on reading tests but fare better in math. There’s no mystery here. Numbers are a universal language, and computation and multiplication tables are more accessible to limited English speakers than Ernest Hemingway is.
Yet many students are proficient with arithmetic in their elementary years and then begin to fail when they enter the world of advanced mathematics. Algebra, geometry, and other areas become a mystery to kids who once called math their favorite subject. It is rare for students to sigh and say, “I used to be good at history.” But it is all too common to hear students cry in frustration, “I was a really good math student, once!” Why does this happen?
Students today are so busy preparing for exams that they often do not have an actual understanding of numbers. As schools become more and more beholden to standardized testing, students are drilled to death with multiplication tables and math problems based solely on computation. Kids are taught “tricks” to help them compute. They have no idea what they are doing but can get the right answer. Their test scores are decent, and everyone is happy.
But this should not be our ultimate goal in teaching numbers. We want our children to understand the power of numbers, to appreciate that mathematics is both relevant to their lives and fun. Simply training kids to pass a test, like Pavlovian dogs, will only lead to the familiar story of students hating math when they reach high school.
Sadly, I have seen far too many elementary school math classes in which the teacher says the following:
Boys and girls, open your math books to page 142. There you will see five hundred multiplication problems. Please do the five hundred problems. When you have finished the problems, please turn to the back of your book, where on page 543A you will find five hundred more multiplication problems. Let’s keep the room silent and do our math.
If a child can do ten multiplication problems, why make her do five hundred? And if she can’t do ten multiplication problems, why in the world make her do five hundred? The only real purpose of this drill-and-kill strategy is to make life easier for the teacher. I have discovered more effective ways to spend a math period. Here are some activities that can be applied in any classroom, at any dinner table, or during any car ride.
The kids and I love to play a game called Buzz. It’s a ten-minute math exercise with numerous variations that we usually play several times a week. All of the students stand, and I randomly choose a number—3, let’s say—which I tell them may not be spoken aloud. Whenever the number 3 comes up in the course of the game, the word buzz must be said in its place. Then we go around the room counting to 100, with individual students announcing the next number. For example, if the buzz number is 3, the first student would say “One,” the second “Two,” the third “Buzz,” and the next child “Four.” I point to the child who is next to speak, and do not point to the kids in order. This way they all have to concentrate on the upcoming numbers. In the current example, numbers such as 23 or 73 would have to be buzzed because they contain the forbidden number 3. Students who get an answer wrong simply sit down, and we see who survives the game when we reach 100. The game in question would get particularly exciting when we arrived at the number 30 because it would be the start of ten buzzed numbers in a row. The kids have to pay close attention; at the end of the series one of them would need to say the number 40 at the right time.
As kids grow, you can challenge them by adding new elements, such as multiples and fractions. For example, if the taboo number is 6, the kids might count in this manner:
1 2 3 4 5
Buzz (You cannot say the number 6.)
7 8 9 10 11
Buzz (You cannot say 12 because it is a multiple of 6.)
Buzz (You cannot say 15 because 1 + 5 = 6. Ouch!)
Buzz (You cannot say 16 because it contains 6.)
Buzz (18 is a multiple of 6.)
In still another version, students are not allowed to say prime numbers. It’s fantastic to watch the wheels spin in a child’s mind when her turn comes up. You can see her mentally running the rules of divisibility before she either says the number or buzzes it. Meanwhile, thirty-plus students wait silently. They respect the fact that she is concentrating. They’ve been there. When she finally announces “Ninety-one,” I ask the class why she didn’t buzz the number. Hearing all the children say that 13 x 7 = 91 is music to my ears. There is communal laughter and excitement and all kinds of learning that does not take place when doing a worksheet.
A Mental Math Warm-up
Many teachers admire the fact that in Room 56 we flow from subject to subject without wasted time. We always begin our math lessons with a mental exercise, and the transition to math from another subject is made infinitely smoother by using “number tiles.” Each number tile is a one-by-one-inch soft tile on which a digit from 1 to 9 is printed.
As our grammar lesson winds down, I ask the students to put away their work and, in the same sentence, begin announcing a mental math problem. This captures the children’s attention. While they listen to the problem, they quietly put away their grammar work and bring out their number tiles. The tiles are placed on their desks. The beauty of these mental warm-ups is that all the kids participate. When a problem is finished, they all hold up the tile they believe to be right. Since they are not called upon, no one is put in the spotlight and the fear of embarrassment disappears. By having all the kids hold up their answers, I can see immediately who understands the concepts and who needs help. This game can be played by kindergartners learning to count and trigonometry students searching for cosines.
Rafe: Okay, kids, everyone think of the number 7. (They do.)
Multiply by 4. (The kids silently are thinking of 28.)
Double that number (56).
Subtract 50 (6).
Show me your answers.
Immediately the students hold up their tile with the 6.
I love to weave other subjects into our mental math game. There are so many numbers we want our kids to know.
Rafe: Start with the number of states in the United States of America (50).
Add a dozen. (Now they are thinking 62.)
Subtract the number of Supreme Court justices. (The kids subtract 9 to get 53.)
Add the number of weeks in a fortnight. (There are 2—now the kids have 55.)
Divide by 11 and show me your answer.
All the students will hold up a 5. It is amazing how well the kids retain an astonishing amount of information.
Rafe: Start with the number of pints in a gallon (8).
Add the number of innings in a baseball game (17).
Multiply by the number of millimeters in a centimeter (170).
Subtract the total number of U.S. senators (70).
Subtract a half dozen (64).
Show me the square root.
Like lightning, the 8s appear.
By the end of the year, my students know their metrics, fractions, and all sorts of numbers that help us remember facts from science, history, and literature. This simple little game gets the kids warmed up, happy, and energized. By the time we are ready to focus on the skill of the day, all of them are ready to do good work.
This game is simple to do, it takes practically no time, and the kids have a ball. Many students, in fact, like to run the game and make up their own problems for the class.
Obviously, math problems and games are only a beginning. But first things first: If kids are going to succeed in mathematics for many years, they have to develop a true love of numbers. As with reading, exceptional children find joy in numerology at all hours of the day. Math is not just something that happens at 9:30 in the morning from Monday to Friday but at any time and in any place.