The day started like most other school days when I was in the first grade; Mrs. Schwartz instructed us to take out our Big Chief Tablet and, using our rulers, draw ten columns and then write the numbers from 0-100 with 10 numbers in each column. Now I am fairly certain that most of you probably don’t know what a Big Chief tablet is, and you probably never did this exercise daily for weeks on end. But, that doesn’t matter; the most important thing is that after weeks of writing the numbers I was about to make an amazing discovery that I was sure my teacher didn’t know. Much to my amazement, every number in the second column was just like the first column, but each of the numbers in the second column had a “1” in front of it, and the third column had a “2” in front of each number and so on. That was an amazing discovery for a six-year-old. I kept this secret to myself for a few days and played with a wide variety of ways to write all one hundred numbers, without going in order. But I thought I might be cheating, so I decided to tell Mrs. Schwartz about this mind-bending discovery. She seemed just as surprised as I was, and she responded with, “That’s interesting. I wonder what else numbers can do? I wonder what numbers after 100 might do.” That was all I needed to challenge my thinking in the first grade. This response prompted many questions and a curiosity about numbers that lasted for many years. Through the early years I found that numbers were always logical and orderly, but my questions and curiosity were sometimes illogical and random, yet amazingly I learned through those experiences as well.
Mrs. Schwartz could have crushed my curiosity by blowing me off, but she didn’t and I didn’t become one of those people who say, “I’m just not a math person,” which is such a sad thing to hear because numbers can really be fascinating. Many times a dislike for math comes from
the teacher or parent, who unwittingly makes a comment or cuts short a student’s natural curiosity for numbers. Students, particularly young students, need a “Mrs. Schwartz.”
Dr. Samuel Johnson (1709-1784) once said, “Curiosity is one of the permanent and certain characteristics of a vigorous mind.” And if there was ever a need for “vigorous minds”, it is now, and if there was ever a subject that could offer so much about which to be curious, it is the subject of numbers. Here are four things you can do to develop vigorous minds in students for numbers.
Create an environment of curiosity.
To create an environment of curiosity, you must first be curious yourself. Spend some time dwelling on the character of the Creator of numbers. God must like numbers because He used them often and we see great patterns in His creation. Recently, I asked my Sunday morning Bible study group, “What is God’s favorite number?” That launched a lot of discussion and a list of questions that took the study beyond Sunday morning. There is no Scripture that says, “God’s favorite number is —,” but it has made all of us pay closer attention as we read and studied the Word together.
Look around you and see all the places you find numbers and what you need to know about those numbers. Can you estimate your total grocery bill before you get to the check-out? Is “tax-free” weekend really a good deal? Telephone numbers, ID numbers, speedometer, temperatures around the nation, speed limits, prices for new cars, or new clothes – numbers are everywhere and every day you have to calculate something. If you don’t believe it, keep a number diary for a week and see how often you do something with numbers.
Try to discover some of the characteristics of numbers and draw your own conclusions without depending on a book to tell you the answers. After you stimulate your own curiosity, you will probably have some questions and develop some ideas for letting students make some grand discoveries of their own. Think about the things related to numbers that might be problems for students.
Heighten curiosity in the classroom by showing the importance of numbers. I taught third grade for several years and noticed fairly early that third graders do not like to “guess” or “estimate”. They want a definite answer and will either not guess at all or be outlandishly silly in guessing. Knowing this and knowing that my class had just voted earlier that year to add blue to the M&M color mix, I took a very large glass jar and filled it with M&M candies (not peanut of course), but as I filled the jar, I counted the number of each color of the M&Ms. Day one, I placed the jar on a shelf all the students could see and asked them to answer this question on a sticky note, “How many blue M&M s are in this jar?” and as predicted the guesses verged on ridiculous, but when the person who was closest to the correct number received a baggie with the correct number of blue M&Ms in it, the class saw this was more than a silly guessing game and they got serious. Every day I removed the previous day’s color of candy from the jar and then asked the same question using a different color. The last day, when there were only brown candies left in the jar, I had to delay the presentation of the winner’s bag of M&Ms because three students had guessed 12 more or less than the total. But the amazing thing was not their increased ability to estimate, it was the question that followed, “Why are there always more brown M&Ms in a bag?” followed by my question, “Are there always more brown candies in the bag?” You can imagine where we went from there. Today our conclusions are no longer true, but I do wonder which color is the most prominent? I bet it is blue.
Teach older elementary students about averaging their grades. Highly competitive classes will go crazy with this and some of the more curious will figure out what grade they need on the next test to raise or maintain their averages. Use the skill of averaging to answer questions like, “What is the average size family in our class?” and then deal with the hilarity of half a person. During a study of the American Civil War, a student found a source that said the average height of a soldier was 5 feet and 8 inches and the average weight was 145 pounds. A quick-thinking teacher followed that with, “I wonder what the average height of our class might be?” You see numbers aren’t just in math.
Older elementary students are interested in spending money. The week before Christmas break is not a great time to teach new concepts so an enterprising fourth- grade teacher told students that they had a pretend $200 to spend on Christmas presents for family and friends. She gave them a stack of catalogs and a worksheet with the instructions that they didn’t have to worry about shipping, but did have to figure the tax. The students loved the project and also found that the money didn’t go as far as they had expected. While studying Colonial America, a student stated that the colonists should have paid the tea tax since it wasn’t very much. The ever-planning teacher had a box of receipts she had saved from a wide variety of stores. She cut off the tax and total and then had the students figure the total and then figure the tax at their area’s tax rate. The result was an eye-opening exercise for both students and teacher.
A second grade teacher asked the students in his class to name as many pairs of things as they could in the world around them. Of course, he had two eyes, two ears, etc., and his list was about 10 things, but the students couldn’t quit with ten and after several minutes there was a very interesting question: “Why do we have a pair of pants when it is really just one piece of clothing?” Ponder that one for a while. All of these were great activities, some of which were planned but generated unexpected questions.
Sometimes curiosity can be planned and sometimes it is spontaneous; keep your ears open and your mind engaged. Think about all of the subjects you teach each week; where are the numbers in those subjects? What can you do to enhance your student’s curiosity about the numbers in that lesson?
First grade for me was one of two of the most wonderful times of my elementary education years; the other, by the way, was fifth grade. I had lots of questions about a lot of things, and looking back on that first year, I think I may have driven Mrs. Schwartz crazy, but she never let on.
She always promised to answer my questions under the condition that I would complete my work. I am sad to say that this attitude did not carry over to my second-grade teacher, who one day in her frustration, angrily said to me, “Stop asking so many stupid questions.” I obeyed; I never asked another question in class until I was in graduate school. Even when I was older, I still believed my questions were stupid. That is the power of any teacher especially over the mind and emotions of young children.
Children need to know that no question is stupid; it is just sometimes ill-timed, or rude and self-centered when others are being neglected, both of which are social skills to be taught. Questions can be deferred, but don’t forget to get back to the student who asked. A third grader was barraging his teacher with many questions and it was driving her crazy. I gave her a note pad and told her to have this curious young man write his questions that weren’t related to the topic on the pad and then set a time to talk about them later in the day and don’t conveniently forget. Much to the teacher’s delight this young scholar learned appropriate interaction and his daily list of questions became shorter and more insightful. Not surprisingly, he later became a National Merit Scholar. Be careful and don’t kill their enthusiasm.
“But,” you say, “my students don’t ask questions.” That is not surprising; several studies have shown that in our age of “I-phones, I-pads, I-pods, and I-everything else” students are becoming less socially interactive, except through on-line social media. It is time to reverse the trend and uncover their curiosity and let the sun shine on astounding discoveries. If students aren’t asking questions, then ask questions you might have. Draw their attention to fascinating details. Take a cue from Albert Einstein, who said, “I have no special talent. I am only passionately curious.”
Learn together. One of the joys of learning is making discoveries with others. One child can spark an interest in another for the wonder of numbers. Students love to hear a teacher’s personal stories about discoveries. Share your own discoveries about numbers and where those discoveries led you. Allow students to share their discoveries with the class; oh my, you may even teach some rhetoric skills.
Teach a number trick and then say, “Let’s see if it works all the time.” Here is a trick for multiplying 2-digit numbers by 11. Add together the two digits of the number you are multiplying by 11. Separate the two digits and put the added number between them. If the added number is ten or more, add the first digit of the added number to the left- hand number and you have your answer.
31 X 11
3 (3+1) 1 341 Answer 341
76 X 11
7 (7+6) 6 7(13)6 7+136 Answer 836
Remember this is for multiplying 2-digit numbers by 11; does it work every time?
What would you have to do if you were multiplying a 3-digit number by 11?
Do you notice a pattern? Using a chart similar to the one I drew every day in first grade, ask students to find various patterns that they can see. Where are all the numbers divisible by 5?
Do you notice a pattern of odd and even numbers? There are so many things you can find with young children by helping them notice details.
What am I missing? Sometimes feigning ignorance or intentionally making mistakes can show students that they really do know how to work with numbers and may even keep them watching so they can find your next mistake. One of my favorite math lessons was the day that I taught some third graders the steps in long division using the “Family” mnemonic: “Daddy, Mommy, Sister, Brother” = Divide, Multiply, Subtract, Bring down. We did several problems together and then I started doing them on my own and purposely adding instead of subtracting, until one young man, who really didn’t like math, frustratingly said, “But Mrs. Howell, you’re leaving out the sister and bringing in the Aunt.” That was a moment worth celebrating.
Celebrating discoveries is an important step toward motivating the students to be more curious. The teacher’s attitude that kept me motivated was an attitude of celebration. Even though I know now that Mrs. Schwartz already knew the discoveries I was making, she always made those experiences full of wonder and celebration. I made the discoveries myself and she encouraged more. Celebrating the discovery of one student can be motivating to another to make his own discoveries that should be celebrated with as much joy as the discoveries of the first student. Pay attention to the little things they learn and then wonder out loud about the next step. Don’t leave out the quiet child, the shy child, the defiant child; find the celebrations for all of them. It is these celebrations that will motivate not only the students, but you will find much joy in teaching every day.
Teachers of students between the ages of 5 and 12 are critical in the development of student attitudes about a wide variety of subjects. Maybe math is not your favorite subject, but you too can be a “Mrs. Schwartz” for someone. Make them curious.